diff options
Diffstat (limited to 'references/math/Gallager__CircSymGauss.pdf')
-rw-r--r-- | references/math/Gallager__CircSymGauss.pdf | 9784 |
1 files changed, 9784 insertions, 0 deletions
diff --git a/references/math/Gallager__CircSymGauss.pdf b/references/math/Gallager__CircSymGauss.pdf new file mode 100644 index 0000000..2aac24c --- /dev/null +++ b/references/math/Gallager__CircSymGauss.pdf @@ -0,0 +1,9784 @@ +%PDF-1.3 +%
+2 0 obj +<< +/Length 9750 +>> +stream
+BT +/F2 1 Tf +20.6625 0 0 20.6625 109.7096 659.726 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(Circularly-Symmetric)-302.3(Gaussian)-302.1(random)-302(v)26.2(ectors)]TJ +/F1 1 Tf +14.3462 0 0 14.3462 246.6929 620.2491 Tm +[(Rob)-27.2(ert)-326.4(G.)-326.4(Gallager)]TJ +0.7275 -2.2215 TD +[(Jan)27.3(uary)-326.4(1,)-326.4(2008)]TJ +/F4 1 Tf +10.9091 0 0 10.9091 281.9995 548.6476 Tm +(Abstract)Tj +/F3 1 Tf +-15.0035 -1.781 TD +[(A)-294.5(n)27.8(um)27.8(b)-27.8(e)0(r)-294.4(o)0(f)-294.5(basic)-294.4(prop)-27.7(erties)-294.4(ab)-27.7(out)-294.4(circularly-symmetric)-294.3(Gaussian)-294.3(random)-294.4(v)27.8(ectors)]TJ +-1.5 -1.242 TD +[(are)-381.8(stated)-381.7(and)-381.7(pro)27.8(v)27.8(e)0(d)-381.8(here.)-589.6(These)-381.7(prop)-27.7(erties)-381.7(are)-381.8(eac)27.8(h)-381.8(probably)-381.7(w)27.8(ell)-381.7(kno)27.8(wn)-381.7(to)-381.8(most)]TJ +T* +[(researc)27.8(hers)-317.4(who)-317.5(w)27.8(ork)-317.4(with)-317.5(Gaussian)-317.4(noise,)-320.6(but)-317.4(I)-317.5(h)0(a)27.8(v)27.8(e)-317.5(not)-317.5(found)-317.4(them)-317.5(stated)-317.5(together)]TJ +T* +[(with)-358.3(simple)-358.1(pro)-27.8(ofs)-358.1(in)-358.3(the)-358.3(literature.)-519.1(They)-358.2(are)-358.2(usually)-358.2(view)27.8(ed)-358.3(as)-358.2(to)-27.8(o)-358.2(adv)55.5(anced)-358.1(or)-358.3(to)-27.8(o)]TJ +T* +[(detailed)-290(for)-290(elemen)27.8(tary)-290(texts)-290(but)-290(are)-290(used)-290(\(correctly)-289.9(or)-290.1(incorrectly\))-289.9(without)-289.9(discussion)]TJ +T* +[(in)-410.1(more)-410(adv)55.6(anced)-410.1(w)27.8(ork.)-674.7(These)-410.1(results)-410(should)-410.1(ha)27.8(v)27.8(e)-410.1(app)-27.8(eared)-410(in)-410.1(Section)-410(7.8.1)-410.1(of)-410.1(m)27.8(y)]TJ +T* +[(b)-27.8(o)-27.8(ok,)-333.8(R.)-333.8(G.)-333.6(Gallager,)-333.8(Principles)-333.6(of)-333.8(Digital)-333.6(Comm)27.9(unication,)-333.6(Cam)27.7(bridge)-333.7(Press,)-333.8(2008)]TJ +T* +[(\(PDC08\),)-272.5(but)-257.2(I)-257.2(came)-257.3(to)-257.3(understand)-257.1(them)-257.3(only)-257.3(while)-257.1(preparing)-257.3(a)-257.3(solution)-257.2(man)27.8(ual)-257.2(when)]TJ +T* +[(the)-333.4(b)-27.7(o)-27.8(ok)-333.4(w)27.8(a)0(s)-333.3(i)0(n)-333.3(the)-333.3(nal)-333.3(pro)-27.7(duction)-333.3(stage.)]TJ +/F5 1 Tf +17.2154 0 0 17.2154 79.2 377.4655 Tm +[(1)-1125(Pseudo-co)31.3(v)62.5(ariance)-375(and)-375(an)-375(example)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 347.195 Tm +(Let)Tj +/F11 1 Tf +1.7537 0 TD +(Z)Tj +/F1 1 Tf +1.1288 0 TD +0.2778 Tc +(=\()Tj +/F7 1 Tf +1.4202 0 TD +0 Tc +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 138.6511 345.4018 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 143.3833 347.195 Tm +0.1667 Tc +(,Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 156.6396 345.4018 Tm +0 Tc +(2)Tj +/F7 1 Tf +11.9552 0 0 11.9552 161.3719 347.195 Tm +0.1667 Tc +[(,...)-166.6(,Z)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 197.597 345.4018 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 203.2339 347.195 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 207.7858 351.5338 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 216.5191 347.195 Tm +[(b)-27.2(e)-326(a)-326(complex)-326(join)27.2(tly-Gaussian)-326.1(random)-326(v)27.2(ector.)-435.1(That)-326(is,)]TJ +/F9 1 Tf +23.8734 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 523.1283 345.4018 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 528.2481 347.195 Tm +(\))Tj +-37.561 -1.2083 TD +(and)Tj +/F9 1 Tf +1.9471 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 123.6762 330.956 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 128.796 332.7492 Tm +[(\))-369.6(for)-369.5(1)]TJ +/F9 1 Tf +3.1301 0 TD +()Tj +/F7 1 Tf +1.1289 0 TD +(k)Tj +/F9 1 Tf +0.894 0 TD +()Tj +/F7 1 Tf +1.1289 0 TD +(n)Tj +/F1 1 Tf +0.954 0 TD +[(comprise)-369.6(a)-369.5(set)-369.5(of)-369.5(2)]TJ +/F7 1 Tf +8.207 0 TD +(n)Tj +/F1 1 Tf +0.954 0 TD +[(join)27.2(tly-Gaussian)-369.6(\(real\))-369.5(random)-369.6(v)54.4(ariables)]TJ +-20.5454 -1.2084 TD +[(\(rvs\).)-407.1(F)81.6(o)0(r)-241.9(a)-241.8(large)-241.9(p)-27.2(ortion)-241.9(of)-241.8(the)-241.9(situations)-241.9(in)-241.9(whic)27.2(h)-241.9(i)0(t)-241.9(i)0(s)-241.9(useful)-241.9(to)-241.8(view)-241.9(2)]TJ +/F7 1 Tf +30.1622 0 TD +(n)Tj +/F1 1 Tf +0.8263 0 TD +[(join)27.1(tly-Gaussian)]TJ +-30.9885 -1.2083 TD +[(rvs)-482.2(as)-482(a)-482.1(v)27.2(ector)-482.1(of)]TJ +/F7 1 Tf +8.7314 0 TD +(n)Tj +/F1 1 Tf +1.0666 0 TD +[(complex)-482.1(join)27.2(tly-Gaussian)-482.2(rvs,)-521(these)-482.1(v)27.2(ectors)-482.2(ha)27.2(v)27.2(e)-482.1(an)-482.1(additional)]TJ +-9.798 -1.2083 TD +[(prop)-27.3(ert)27.2(y)-373(called)]TJ +/F14 1 Tf +6.8657 0 TD +[(cir)50(cular)-392.9(symmetry)]TJ +/F1 1 Tf +7.7804 0 TD +[(.)-574.9(B)0(y)-373(d)0(enition,)]TJ +/F11 1 Tf +7.1121 0 TD +(Z)Tj +/F1 1 Tf +1.2239 0 TD +[(is)-373(circularly)-373(symmetric)-373.1(if)]TJ +/F7 1 Tf +11.1583 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 492.7791 293.7504 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 501.1945 289.4117 Tm +(Z)Tj +/F1 1 Tf +1.2239 0 TD +(has)Tj +-36.522 -1.2083 TD +[(the)-289.3(same)-289.3(probabilit)27.2(y)-289.3(distribution)-289.3(as)]TJ +/F11 1 Tf +15.4972 0 TD +(Z)Tj +/F1 1 Tf +1.1403 0 TD +[(for)-289.3(all)-289.3(real)]TJ +/F7 1 Tf +4.6484 0 TD +()Tj +/F1 1 Tf +0.5795 0 TD +0.4228 Tc +[(.F)504.4(o)422.8(r)]TJ +/F7 1 Tf +2.4118 0 TD +0 Tc +(n)Tj +/F1 1 Tf +0.8623 0 TD +0.2779 Tc +[(=1)278(,)]TJ +/F14 1 Tf +2.0977 0 TD +0 Tc +(i.e.)Tj +/F1 1 Tf +1.35 0 TD +[(,)-296.7(for)-289.3(the)-289.2(case)-289.3(where)]TJ +/F11 1 Tf +8.5037 0 TD +(Z)Tj +/F1 1 Tf +-37.0908 -1.2083 TD +[(is)-248.5(a)-248.5(complex)-248.6(Gaussian)-248.5(random)-248.6(v)54.4(ariable)]TJ +/F7 1 Tf +16.6366 0 TD +(Z)Tj +/F1 1 Tf +0.742 0 TD +[(,)-264.1(circular)-248.5(symmetry)-248.6(holds)-248.5(if)-248.6(and)-248.5(only)-248.5(if)]TJ +/F9 1 Tf +16.5114 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.742 0 TD +[(\))-248.5(and)]TJ +/F9 1 Tf +-35.735 -1.2083 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.742 0 TD +[(\))-355.1(are)-355.2(statistically)-355.2(indep)-27.3(enden)27.2(t)-355.2(and)-355.2(iden)27.2(tically)-355.3(distributed)-355.2(\(iid\))-355.3(with)-355.2(zero)-355.2(mean,)]TJ +/F14 1 Tf +34.4748 0 TD +(i.e.)Tj +/F1 1 Tf +1.35 0 TD +(,)Tj +-37.6698 -1.2083 TD +[(if)-313.4(and)-313.4(only)-313.5(if)]TJ +/F9 1 Tf +5.7957 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(Z)Tj +/F1 1 Tf +0.742 0 TD +[(\))-313.4(and)]TJ +/F9 1 Tf +2.5851 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.742 0 TD +[(\))-313.4(are)-313.4(join)27.2(tly)-313.4(Gaussian)-313.5(with)-313.4(equi-probabilit)27(y-densit)27.1(y)-313.4(con)27.1(tours)]TJ +-12.0709 -1.2083 TD +[(around)-326.4(0.)]TJ +0 -1.5417 TD +(Since)Tj +/F12 1 Tf +2.6887 0 TD +(E)Tj +/F1 1 Tf +0.5832 0 TD +([)Tj +/F7 1 Tf +0.272 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 126.9948 203.0904 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 135.4102 198.7516 Tm +(Z)Tj +/F1 1 Tf +0.851 0 TD +0.5024 Tc +(]=)Tj +/F7 1 Tf +2.0384 0 TD +0 Tc +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 175.3793 203.0904 Tm +(i)Tj +/F12 1 Tf +11.9552 0 0 11.9552 183.7938 198.7516 Tm +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +[(],)-491.3(an)27.2(y)-458.4(circularly-symmetric)-458.6(complex)-458.4(random)-458.4(v)27.2(ector)-458.5(m)27.2(ust)-458.4(ha)27.1(v)27.3(e)]TJ +/F12 1 Tf +-10.4552 -1.2083 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +0.2778 Tc +[(]=0)277.8(,)]TJ +/F14 1 Tf +2.6268 0 TD +0 Tc +(i.e.)Tj +/F1 1 Tf +1.3501 0 TD +[(,)-276.1(m)27.2(ust)-263.6(ha)27.2(v)27.2(e)-263.7(zero)-263.6(mean.)-414.3(In)-263.6(a)-263.6(momen)27.2(t,)-276.2(w)27.2(e)-263.6(will)-263.6(see)-263.6(that)-263.6(a)-263.6(circularly-symmetric)]TJ +-5.6832 -1.2083 TD +[(join)27.1(tly-Gaussian)-345.4(complex)-345.3(random)-345.4(v)27.2(ector)-345.3(is)-345.2(completely)-345.3(determined)-345.4(b)27.2(y)-345.2(its)-345.3(co)27.2(v)54.4(ariance)-345.4(ma-)]TJ +T* +(trix,)Tj +/F12 1 Tf +2.3231 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 115.0326 153.6209 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 128.4722 155.4142 Tm +(=)Tj +/F12 1 Tf +1.2767 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +0.142 Tc +(ZZ)Tj +/F10 1 Tf +7.9701 0 0 7.9701 174.3073 159.7529 Tm +0 Tc +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 178.5694 155.4142 Tm +[(],)-500.7(where)]TJ +/F11 1 Tf +4.0128 0 TD +(Z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 236.7163 159.7529 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 247.1372 155.4142 Tm +(=)Tj +/F11 1 Tf +1.2768 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 272.5739 159.7529 Tm +(T)Tj +/F10 1 Tf +7.9701 0 0 7.9701 277.4097 160.7491 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 287.7121 155.4142 Tm +[(is)-465.8(the)-465.9(complex)-465.9(conjugate)-465.9(of)-465.8(the)-465.9(transp)-27.2(ose.)-853.6(A)]TJ +-17.4412 -1.2083 TD +[(circularly-symmetric)-343.7(join)27.1(tly-Gaussian)-343.5(complex)-343.5(random)-343.5(v)27.2(ector)]TJ +/F11 1 Tf +26.8176 0 TD +(Z)Tj +/F1 1 Tf +1.1944 0 TD +[(is)-343.5(denoted)-343.5(and)-343.5(referred)]TJ +-28.012 -1.2083 TD +[(to)-446.8(as)]TJ +/F11 1 Tf +2.6397 0 TD +(Z)Tj +/F9 1 Tf +1.3336 0 TD +0.4826 Tc +[(C)424.3(N)]TJ +/F1 1 Tf +2.8131 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F12 1 Tf +0.4386 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 184.0418 124.7293 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 191.3215 126.5225 Tm +[(\),)-476.8(where)-446.8(the)]TJ +/F9 1 Tf +5.8853 0 TD +(C)Tj +/F1 1 Tf +1.0316 0 TD +[(denotes)-446.8(that)]TJ +/F11 1 Tf +5.9034 0 TD +(Z)Tj +/F1 1 Tf +1.2977 0 TD +[(is)-446.7(b)-27.2(oth)-446.8(circularly)-446.8(symmetric)-446.8(and)]TJ +-23.4966 -1.2083 TD +(complex.)Tj +0 -1.5417 TD +[(Most)-404.1(comm)27.1(unication)-404.1(engineers)-404.1(b)-27.2(eliev)27.2(e)-404(that)-404.1(v)27.2(ectors)-404.1(of)-404.1(Gaussian)-404.1(random)-404(v)54.4(ariables)-404.1(\(real)]TJ +0 -1.2083 TD +[(or)-411.6(complex\))-411.6(are)-411.6(determined)-411.7(b)27.2(y)-411.6(their)-411.7(co)27.3(v)54.4(ariance)-411.6(matrix.)-690.7(F)81.6(o)0(r)-411.6(the)-411.6(real)-411.6(case,)-432.9(this)-411.6(is)-411.5(only)]TJ +18.7262 -2.5 TD +(1)Tj +ET +endstream +endobj +3 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F2 5 0 R +/F3 6 0 R +/F4 7 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +21 0 obj +<< +/Length 19745 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(true)-342.4(when)-342.4(the)-342.4(v)54.4(ariables)-342.4(are)]TJ +/F14 1 Tf +12.08 0 TD +(jointly)Tj +/F1 1 Tf +3.1302 0 TD +[(Gaussian)-342.4(\(see)-342.4(Section)-342.4(7.8,)-346.4(PDC08\).)-483.2(F)81.6(o)0(r)-342.3(the)-342.4(complex)]TJ +-15.2102 -1.2083 TD +[(case,)-289.1(as)-279.8(emphasized)-279.9(and)-279.8(explained)-279.9(here,)-289.1(it)-279.8(is)-279.8(only)-279.8(true)-279.8(when)-279.8(the)-279.7(v)54.4(ariables)-279.8(are)-279.8(b)-27.2(oth)-279.9(join)27.2(tly)]TJ +T* +[(Gaussian)-326.5(and)-326.4(circularly)-326.4(symmetric.)]TJ +/F5 1 Tf +0 -1.5417 TD +[(Example)-388.4(1:)]TJ +/F1 1 Tf +5.989 0 TD +[(Consider)-338(a)-338(v)27.2(ector)]TJ +/F11 1 Tf +7.8734 0 TD +(Z)Tj +/F1 1 Tf +1.1485 0 TD +0.2974 Tc +(=\()Tj +/F7 1 Tf +1.4398 0 TD +0 Tc +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 283.8834 658.9291 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 288.6157 660.7223 Tm +0.1667 Tc +(,Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 301.872 658.9291 Tm +0 Tc +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 306.6042 660.7223 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 311.1562 665.061 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 320.0329 660.7223 Tm +(where)Tj +/F7 1 Tf +2.8403 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 362.0005 658.9291 Tm +(1)Tj +/F9 1 Tf +11.9552 0 0 11.9552 370.2894 660.7223 Tm +0.2975 Tc +[(C)239.1(N)]TJ +/F1 1 Tf +2.628 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +(,)Tj +/F1 1 Tf +0.4387 0 TD +[(1\))-338(and)]TJ +/F7 1 Tf +3.1238 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 462.7148 658.9291 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 471.0038 660.7223 Tm +(=)Tj +/F7 1 Tf +1.059 0 TD +(Z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 492.535 665.061 Tm +()Tj +/F6 1 Tf +-0.1077 -0.9153 TD +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 497.2673 660.7223 Tm +[(.)-469.9(Then)]TJ +/F7 1 Tf +-34.9696 -1.2083 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 87.213 644.4832 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 96.2441 646.2765 Tm +[(has)-359.7(iid)-359.6(real)-359.7(and)-359.7(imaginary)-359.7(parts,)-368(eac)27.2(h)]TJ +/F9 1 Tf +16.7888 0 TD +(N)Tj +/F1 1 Tf +0.9678 0 TD +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +(,)Tj +/F1 1 Tf +0.4387 0 TD +(1)Tj +/F7 1 Tf +0.4896 0 TD +(/)Tj +/F1 1 Tf +0.4896 0 TD +(2\).)Tj +/F7 1 Tf +1.6772 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 363.9462 644.4832 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 372.9783 646.2765 Tm +[(also)-359.7(has)-359.7(iid)-359.6(real)-359.7(and)-359.7(imaginary)]TJ +-24.5733 -1.2083 TD +[(parts,)-421.1(b)-27.2(oth)-402.1(Gaussian,)-421.1(so)-402.1(it)-402.1(is)-402.1(also)-402.1(circularly)-402.2(symmetric.)-662.3(The)-402.1(real)-402.1(and)-402.1(imaginary)-402.2(parts)]TJ +T* +(of)Tj +/F7 1 Tf +1.2301 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 101.9178 615.5916 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 111.9253 617.3848 Tm +[(are)-441.3(join)27.2(tly)-441.3(Gaussian)-441.3(with)-441.3(those)-441.3(of)]TJ +/F7 1 Tf +15.5085 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 305.344 615.5916 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 310.0762 617.3848 Tm +0.47 Tc +[(,s)470(o)]TJ +/F11 1 Tf +2.0591 0 TD +0 Tc +(Z)Tj +/F1 1 Tf +1.2922 0 TD +[(is)-441.3(join)27.2(tly)-441.3(Gaussian)-441.3(with)-441.3(circularly-)]TJ +-22.6631 -1.2083 TD +[(symmetric)-325.4(comp)-27.3(onen)27.2(ts.)-434.9(On)-325.4(the)-325.3(other)-325.3(hand,)-325.6(for)]TJ +/F7 1 Tf +20.6211 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 333.7405 601.1458 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 342.3622 602.939 Tm +[(real)-325.3(\(or)-325.4(appro)27.2(ximately)-325.4(real\),)]TJ +/F7 1 Tf +12.4802 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 499.5776 601.1458 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 507.6304 602.939 Tm +(=)Tj +/F7 1 Tf +1.0393 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 528.0688 601.1458 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 588.4932 Tm +(\(or)Tj +/F7 1 Tf +1.546 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 105.6946 586.6999 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 113.7484 588.4932 Tm +()Tj +/F7 1 Tf +1.0555 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 134.3801 586.6999 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 139.1123 588.4932 Tm +[(\).)-424.7(When)]TJ +/F7 1 Tf +3.9013 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 193.7654 586.6999 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 202.0224 588.4932 Tm +[(is)-294.9(pure)-294.8(imaginary)-295(\(or)-294.8(close)-294.9(to)-294.8(pure)-294.9(imaginary\),)]TJ +/F7 1 Tf +20.1637 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 451.0954 586.6999 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 459.3524 588.4932 Tm +[(is)-294.8(the)-294.9(negativ)27.2(e)]TJ +-31.7982 -1.2083 TD +(of)Tj +/F7 1 Tf +1.0884 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 100.2251 572.254 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 108.54 574.0474 Tm +(\(or)Tj +/F7 1 Tf +1.5508 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 135.0914 572.254 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 143.1452 574.0474 Tm +0.2777 Tc +()Tj +/F7 1 Tf +1.8333 0 TD +0 Tc +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 173.075 572.254 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 177.8072 574.0474 Tm +[(\).)-426.3(Th)27.2(us)]TJ +/F11 1 Tf +3.5328 0 TD +(Z)Tj +/F1 1 Tf +1.1506 0 TD +[(do)-27.2(esnt)-299.7(app)-27.2(ear)-299.6(to)-299.7(ha)27.1(v)27.3(e)-299.7(the)-299.7(required)-299.7(circular)-299.7(symmetry)-299.8(\(w)27.2(e)]TJ +-12.9315 -1.2083 TD +[(justify)-326.5(this)-326.4(more)-326.4(precisely)-326.5(later\).)]TJ +0 -1.5417 TD +[(The)-311(co)27.2(v)54.4(ariance)-311(matrix)-311.1(for)-311(this)-311.1(example)-311.1(is)-311(easily)-311.1(calculated)-311.1(to)-311.1(b)-27.2(e)]TJ +/F12 1 Tf +27.8347 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 420.0289 539.3773 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 430.6302 541.1707 Tm +(=)Tj +/F16 1 Tf +1.0393 0.81 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 449.2324 546.4757 Tm +0.3542 Tc +(10)Tj +0 -1.1829 TD +(01)Tj +/F16 1 Tf +11.9552 0 0 11.9552 461.7196 550.8543 Tm +0 Tc +()Tj +/F1 1 Tf +0.4167 -0.81 TD +[(.)-430(This)-311.1(is)-311(also)]TJ +-32.4128 -1.2083 TD +[(the)-321.5(co)27.2(v)54.4(ariance)-321.5(function)-321.5(of)-321.5(t)27.2(w)27.2(o)-321.5(iid)-321.4(unit)-321.5(v)54.4(ariance)-321.5(complex)-321.5(rvs.)-433.5(The)-321.5(p)-27.2(oin)27.2(t)-321.5(o)0(f)-321.4(this)-321.5(example,)]TJ +T* +[(then,)-279.1(is)-267.3(rst)-267.3(that)-267.2(individual)-267.4(circular)-267.4(symmetry)-267.3(among)-267.4(the)-267.2(comp)-27.2(onen)27.2(ts)-267.3(of)-267.2(a)-267.3(random)-267.4(v)27.2(ector)]TJ +T* +[(is)-460.5(not)-460.5(enough)-460.5(to)-460.5(pro)27.1(vide)-460.4(o)27.2(v)27.2(erall)-460.4(circular)-460.5(symmetry)81.5(,)-494(and)-460.4(second)-460.5(that)-460.5(complex)-460.5(join)27.2(tly-)]TJ +T* +[(Gaussian)-326.5(random)-326.5(v)27.2(ectors)-326.4(are)-326.4(not)-326.4(fully)-326.5(sp)-27.1(ecied)-326.5(b)27.2(y)-326.4(their)-326.4(co)27.2(v)54.4(ariance)-326.5(matrices.)]TJ +0 -2.7462 TD +[(W)81.6(e)-322.5(ha)27.1(v)27.2(e)-322.5(no)27.2(w)-322.5(seen)-322.5(that)-322.6(there)-322.5(is)-322.5(something)-322.5(wrong)-322.5(with)-322.5(the)-322.5(con)27.2(v)27.2(e)0(n)27.1(tional)-322.5(wisdom)-322.6(and)-322.5(also)]TJ +0 -1.2083 TD +[(that)-444.2(circular)-444.3(symmetry)-444.3(for)-444.2(random)-444.3(v)27.2(ectors)-444.2(is)-444.2(more)-444.2(subtle)-444.3(than)-444.2(circular)-444.3(symmetry)-444.3(for)]TJ +T* +[(individual)-370.7(random)-370.7(v)54.4(ariables.)-568(T)81.6(o)-370.7(mak)27.2(e)-370.7(matters)-370.7(w)27.2(orse,)-381.8(w)27.2(e)-370.7(no)27.2(w)-370.7(sho)27.2(w)-370.6(that)-370.7(the)-370.7(co)27.2(v)54.4(ariance)]TJ +T* +[(matrix)-335.1(is)]TJ +/F14 1 Tf +4.1842 0 TD +(always)Tj +/F1 1 Tf +3.1927 0 TD +[(defectiv)27.1(e)-335(i)0(n)-335(determining)-335.1(circular)-335.1(symmetry)81.5(.)-461.1(I)0(n)-335(particular,)-337.3(for)-335(an)27.1(y)-335(zero-)]TJ +-7.3768 -1.2083 TD +[(mean)-326.4(complex)-326.5(random)-326.4(v)27.2(ector)]TJ +/F11 1 Tf +12.9738 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +(,)Tj +/F12 1 Tf +0.5983 0 TD +(K)Tj +/F8 1 Tf +7.9701 0 0 7.9701 259.6922 390.4707 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 263.6204 392.7403 Tm +-0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 271.2179 390.4707 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 282.4 392.7731 Tm +[(is)-326.5(the)-326.3(same)-326.4(as)]TJ +/F12 1 Tf +6.3265 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 366.0942 390.9798 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 373.3748 392.7731 Tm +[(.)-435.2(T)81.7(o)-326.4(see)-326.4(this,)]TJ +/F12 1 Tf +-12.8634 -1.9607 TD +(K)Tj +/F8 1 Tf +7.9701 0 0 7.9701 227.6503 367.0307 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 231.5786 369.3001 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 239.1761 367.0307 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 249.7773 369.333 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([\()Tj +/F7 1 Tf +0.6527 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 282.406 374.2695 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 290.8214 369.333 Tm +(Z)Tj +/F1 1 Tf +0.851 0 TD +(\)\()Tj +/F7 1 Tf +0.7615 0 TD +(e)Tj +/F10 1 Tf +7.9701 0 0 7.9701 315.5248 374.2695 Tm +()Tj +/F8 1 Tf +0.8264 0 TD +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 330.5265 369.333 Tm +(Z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 340.7004 374.2695 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 345.4326 369.333 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 349.9846 374.2695 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 354.8214 369.333 Tm +0.2778 Tc +(]=)Tj +/F12 1 Tf +1.5891 0 TD +0 Tc +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 381.8789 367.5397 Tm +(Z)Tj +/F7 1 Tf +11.9552 0 0 11.9552 389.1597 369.333 Tm +(.)Tj +/F1 1 Tf +10.7638 0 TD +(\(1\))Tj +-36.6907 -2.294 TD +[(It)-360.4(is)-360.5(no)27.2(w)-360.4(time)-360.4(to)-360.4(dig)-360.5(ourselv)27.2(es)-360.4(out)-360.4(from)-360.4(this)-360.4(m)27.2(uddle)-360.4(of)-360.4(con)27.2(v)27.2(e)0(n)27.1(tional)-360.4(wisdom.)-537.3(Although)]TJ +0 -1.2083 TD +[(the)-497.2(co)27.2(v)54.4(ariance)-497.3(matrix)]TJ +/F14 1 Tf +10.1137 0 TD +[(do)50(es)]TJ +/F1 1 Tf +2.3798 0 TD +[(fully)-497.2(sp)-27.2(ecify)-497.2(the)-497.2(distribution)-497.2(of)-497.2(a)-497.2(zero-mean)-497.3(real)-497.3(join)27.2(tly-)]TJ +-12.4935 -1.2083 TD +[(Gaussian)-404(random)-404(v)27.2(ector,)-423.3(there)-404(is)-404(another)-404(matrix,)-423.4(called)-404(the)-403.9(pseudo-co)27.1(v)54.4(ariance)-404(matrix,)]TJ +/F12 1 Tf +T* +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 89.3569 296.7771 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 100.1923 298.5703 Tm +(=)Tj +/F12 1 Tf +1.0589 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +0.142 Tc +(ZZ)Tj +/F13 1 Tf +5.9776 0 0 5.9776 143.4242 302.9091 Tm +0 Tc +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 148.26 298.5703 Tm +[(],)-340.8(that)-337.9(is)-338(needed,)-340.9(along)-337.9(with)]TJ +/F12 1 Tf +12.4285 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 304.9056 296.7771 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 312.1853 298.5703 Tm +[(,)-340.8(t)0(o)-337.9(s)0(p)-27.1(ecify)-338(the)-337.9(distribution)-338(of)-337.9(an)-337.9(arbitrary)]TJ +-19.4883 -1.2083 TD +[(complex)-384.7(join)27.2(tly-Gaussian)-384.7(random)-384.6(v)27.2(ector.)-609.7(F)81.6(o)0(r)-384.6(the)-384.5(example)-384.7(ab)-27.2(o)27.2(v)27.2(e)0(,)]TJ +/F12 1 Tf +28.9412 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 435.3535 282.3313 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 447.1382 284.1245 Tm +(=)Tj +/F16 1 Tf +1.1383 0.81 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 466.924 289.4296 Tm +0.3541 Tc +(01)Tj +0 -1.1829 TD +(10)Tj +/F16 1 Tf +11.9552 0 0 11.9552 479.4112 293.8082 Tm +0 Tc +()Tj +/F1 1 Tf +0.4167 -0.81 TD +[(,)-399.1(whereas)]TJ +-33.8927 -1.2083 TD +[(for)-326.5(the)-326.4(case)-326.4(of)-326.4(t)27.2(w)27.2(o)-326.3(iid)-326.4(complex)-326.5(rvs,)]TJ +/F12 1 Tf +15.623 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 276.1325 267.8854 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 286.7338 269.6786 Tm +0.2778 Tc +[(=0)277.8(.)]TJ +-17.3593 -1.5417 TD +0 Tc +[(The)-356.5(probabilit)27.1(y)-356.6(densit)27.2(y)-356.5(o)0(f)-356.6(a)-356.5(complex)-356.6(random)-356.5(v)27.2(ector)]TJ +/F11 1 Tf +22.9303 0 TD +(Z)Tj +/F1 1 Tf +1.18 0 TD +0.3291 Tc +(=\()Tj +/F7 1 Tf +1.4714 0 TD +0 Tc +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 393.0451 249.4545 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 397.7773 251.2478 Tm +0.1667 Tc +[(,...)-166.7(,Z)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 434.0035 249.4545 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 439.6394 251.2478 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 444.1923 255.5866 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 453.2902 251.2478 Tm +[(is)-356.5(dened)-356.6(to)-356.5(b)-27.2(e)]TJ +-31.2911 -1.2083 TD +[(the)-376.3(probabilit)27.1(y)-376.2(densit)27.2(y)-376.3(o)0(f)-376.2(the)-376.3(2)]TJ +/F7 1 Tf +13.6094 0 TD +(n)Tj +/F1 1 Tf +0.9608 0 TD +[(real)-376.3(rvs)]TJ +/F11 1 Tf +3.8858 0 TD +(V)Tj +/F1 1 Tf +1.4145 0 TD +0.3627 Tc +(=\()Tj +/F9 1 Tf +1.505 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 355.9462 235.0087 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 360.6785 236.802 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 414.6431 235.0087 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 420.28 236.802 Tm +(\))Tj +/F7 1 Tf +0.3807 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 451.2747 235.0087 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 456.007 236.802 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.7(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 509.9716 235.0087 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 515.6085 236.802 Tm +(\)\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 524.7134 241.1407 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 529.5492 236.802 Tm +(.)Tj +-37.6698 -1.2083 TD +(If)Tj +/F11 1 Tf +1.0137 0 TD +(Z)Tj +/F1 1 Tf +1.2122 0 TD +[(is)-361.2(zero-mean)-361.4(and)-361.2(complex)-361.3(join)27.2(tly)-361.2(Gaussian,)-370(then)]TJ +/F11 1 Tf +21.4363 0 TD +(V)Tj +/F1 1 Tf +1.413 0 TD +[(is)-361.2(determined)-361.4(b)27.2(y)-361.2(its)-361.2(2)]TJ +/F7 1 Tf +9.4522 0 TD +(n)Tj +/F1 1 Tf +0.9457 0 TD +-0.0272 Tc +[(by)-388.4(2)]TJ +/F7 1 Tf +1.8843 0 TD +0 Tc +(n)Tj +/F1 1 Tf +-37.3573 -1.2083 TD +[(co)27.2(v)54.4(ariance)-369.4(matrix,)-380.1(sa)27.1(y)]TJ +/F12 1 Tf +10.0183 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 207.0296 206.117 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 215.9113 207.9103 Tm +[(.)-564(I)0(t)-369.4(turns)-369.4(out)-369.4(that)]TJ +/F12 1 Tf +8.4926 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 325.5024 206.117 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 337.1975 207.9103 Tm +(and)Tj +/F12 1 Tf +1.9469 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 370.6292 206.117 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 382.3253 207.9103 Tm +[(together)-369.4(sp)-27.2(ecify)]TJ +/F12 1 Tf +7.1902 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 476.3457 206.117 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 485.2274 207.9103 Tm +[(.)-564(I)0(n)-369.4(fact,)]TJ +-33.9625 -1.2083 TD +[(b)27.1(y)-326.4(calculating)-326.5(the)]TJ +/F7 1 Tf +7.9965 0 TD +0.0336 Tc +[(k,)-133(j)]TJ +/F1 1 Tf +1.7692 0 TD +0 Tc +[(elemen)27.2(t)-326.5(o)0(f)]TJ +/F12 1 Tf +4.7326 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 260.5888 191.6712 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 271.7719 193.4645 Tm +(and)Tj +/F12 1 Tf +1.9039 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 304.6894 191.6712 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 311.9701 193.4645 Tm +[(,)-326.3(w)27.2(e)-326.4(see)-326.4(that)]TJ +/F12 1 Tf +-11.8822 -2.3511 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 201.341 163.5637 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 206.4608 165.3569 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 232.2122 163.5637 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 236.5948 165.3569 Tm +[(\)])-833.3(=)]TJ +3.181 0.6765 TD +(1)Tj +ET +274.65 168.568 5.853 -0.478 re +f +BT +11.9552 0 0 11.9552 274.6242 157.1566 Tm +(2)Tj +0.7562 0.6859 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 308.1634 163.5637 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 315.4441 165.3569 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +[(\)\))-222.2(+)]TJ +/F9 1 Tf +1.9676 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 384.1106 163.5637 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 391.3913 165.3569 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +(\)\)])Tj +/F7 1 Tf +1.2003 0 TD +(,)Tj +/F1 1 Tf +7.5533 0 TD +(\(2\))Tj +/F12 1 Tf +-29.1026 -2.3402 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 201.341 135.5866 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 206.4608 137.3799 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 232.2122 135.5866 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 236.5948 137.3799 Tm +[(\)])-833.3(=)]TJ +3.181 0.6765 TD +(1)Tj +ET +274.65 140.608 5.853 -0.478 re +f +BT +11.9552 0 0 11.9552 274.6242 129.1786 Tm +(2)Tj +0.7562 0.686 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 308.1634 135.5866 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 315.4441 137.3799 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +(\)\))Tj +/F9 1 Tf +0.9838 0 TD +0.2222 Tc +()Tj +/F1 1 Tf +1.7222 0 TD +0 Tc +(\()Tj +/F12 1 Tf +0.3808 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 384.3049 135.5866 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 391.5846 137.3799 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133(j)]TJ +/F1 1 Tf +1.4428 0 TD +-0.0001 Tc +(\)\)])Tj +/F7 1 Tf +1.2002 0 TD +0 Tc +(,)Tj +/F1 1 Tf +7.5372 0 TD +(\(3\))Tj +/F12 1 Tf +-29.1026 -2.3403 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 201.341 107.6085 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 206.4608 109.4018 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 232.2122 107.6085 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 236.5948 109.4018 Tm +[(\)])-833.3(=)]TJ +3.181 0.6765 TD +(1)Tj +ET +274.65 112.648 5.853 -0.478 re +f +BT +11.9552 0 0 11.9552 274.6242 101.2005 Tm +(2)Tj +0.7562 0.686 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +1.5 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 317.4615 107.6085 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 324.7422 109.4018 Tm +(\()Tj +/F7 1 Tf +0.3807 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +[(\)\))-222.3(+)]TJ +/F9 1 Tf +1.9676 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 393.4088 107.6085 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 400.6895 109.4018 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0335 Tc +[(k,)-133.2(j)]TJ +/F1 1 Tf +1.4427 0 TD +0 Tc +(\)\)])Tj +/F7 1 Tf +1.2003 0 TD +(,)Tj +/F1 1 Tf +6.7756 0 TD +(\(4\))Tj +/F12 1 Tf +-29.1026 -2.3403 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 201.341 79.6304 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 206.4608 81.4236 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 232.2122 79.6304 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 236.5948 81.4236 Tm +[(\)])-833.3(=)]TJ +3.181 0.6765 TD +(1)Tj +ET +274.65 84.688 5.853 -0.478 re +f +BT +11.9552 0 0 11.9552 274.6242 73.2224 Tm +(2)Tj +0.7562 0.686 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 308.1634 79.6304 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 315.4441 81.4236 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +[(\)\))-222.2(+)]TJ +/F9 1 Tf +1.9676 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 384.1106 79.6304 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 391.3913 81.4236 Tm +(\()Tj +/F7 1 Tf +0.3808 0 TD +0.0336 Tc +[(k,)-133.1(j)]TJ +/F1 1 Tf +1.4428 0 TD +0 Tc +(\)\)])Tj +/F7 1 Tf +1.2003 0 TD +(.)Tj +/F1 1 Tf +7.5533 0 TD +(\(5\))Tj +-17.9645 -2.686 TD +(2)Tj +ET +endstream +endobj +22 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +/F15 23 0 R +/F16 24 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +26 0 obj +<< +/Length 14708 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(Th)27.1(us)-279.9(the)-279.8(co)27.2(v)54.4(ariance)-279.9(of)-279.9(eac)27.2(h)-279.9(pair)-279.9(of)-279.9(the)-279.9(2)]TJ +/F7 1 Tf +17.1494 0 TD +(n)Tj +/F1 1 Tf +0.8643 0 TD +[(rvs,)-289.2(and)-279.9(th)27.2(us)-279.9(the)-279.8(join)27.1(t)-279.9(probabilit)27.1(y)-279.8(distribution)]TJ +-18.0138 -1.2083 TD +(of)Tj +/F11 1 Tf +1.0377 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +[(,)-264.3(i)0(s)-248.9(determined)-248.9(b)27.2(y)]TJ +/F12 1 Tf +7.7617 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 202.6311 691.8058 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 212.8867 693.599 Tm +(and)Tj +/F12 1 Tf +1.8264 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 244.8777 691.8058 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 252.1584 693.599 Tm +[(.)-409.3(I)0(n)-248.9(order)-248.9(for)]TJ +/F11 1 Tf +5.725 0 TD +(Z)Tj +/F1 1 Tf +1.0998 0 TD +(and)Tj +/F7 1 Tf +1.8263 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 361.0102 697.9377 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 369.4257 693.599 Tm +(Z)Tj +/F1 1 Tf +1.0998 0 TD +[(to)-248.9(ha)27.2(v)27.2(e)-248.8(the)-248.9(same)-248.9(distribution,)]TJ +-25.376 -1.2083 TD +[(it)-345.1(is)-345(necessary)-345.1(and)-345(sucien)27.2(t)-345(t)0(o)-345(satisfy)]TJ +/F12 1 Tf +16.6998 0 TD +(K)Tj +/F8 1 Tf +7.9701 0 0 7.9701 286.9081 676.8508 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 290.8364 679.1204 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 298.4349 676.8508 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 309.4147 679.1532 Tm +(=)Tj +/F12 1 Tf +1.071 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 330.2785 677.3599 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 341.6837 679.1532 Tm +(and)Tj +/F12 1 Tf +1.9225 0 TD +(M)Tj +/F8 1 Tf +7.9701 0 0 7.9701 374.8234 676.8508 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 378.7517 679.1204 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 386.3502 676.8508 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 397.33 679.1532 Tm +(=)Tj +/F12 1 Tf +1.071 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 420.2899 677.3599 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 427.5706 679.1532 Tm +[(.)-491(The)-344.9(rst)-345(condition)]TJ +-29.1397 -1.2083 TD +[(is)-392.9(automatically)-393(satised)-392.9(b)27.2(y)-392.9(\(1\),)-409.5(so)]TJ +/F12 1 Tf +15.7502 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 277.6528 662.9141 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 289.606 664.7073 Tm +(=)Tj +/F12 1 Tf +1.1525 0 TD +(M)Tj +/F8 1 Tf +7.9701 0 0 7.9701 313.5402 662.405 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 317.4695 664.6745 Tm +-0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 325.067 662.405 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 337.0441 664.7073 Tm +[(is)-392.9(necessary)-392.9(and)-392.9(sucien)27.2(t)-392.8(for)-392.9(circular)]TJ +-21.5676 -1.2083 TD +[(symmetry)81.5(.)-435.2(O)0(n)-326.4(the)-326.4(other)-326.4(hand)]TJ +/F12 1 Tf +11.4212 -2.2083 TD +(M)Tj +/F8 1 Tf +7.9701 0 0 7.9701 225.8979 621.5582 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 229.8262 623.8276 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 237.4237 621.5582 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 248.0259 623.8605 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(E)Tj +/F1 1 Tf +0.5832 0 TD +([\()Tj +/F7 1 Tf +0.6528 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 280.6545 628.797 Tm +-0.0001 Tc +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 289.069 623.8605 Tm +0 Tc +(Z)Tj +/F1 1 Tf +0.851 0 TD +(\)\()Tj +/F7 1 Tf +0.7616 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 313.7724 628.797 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 322.1878 623.8605 Tm +(Z)Tj +/F1 1 Tf +0.851 0 TD +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 336.9136 628.797 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 341.7494 623.8605 Tm +0.2778 Tc +(]=)Tj +/F7 1 Tf +1.5892 0 TD +0 Tc +(e)Tj +/F6 1 Tf +7.9701 0 0 7.9701 366.1729 628.797 Tm +(2)Tj +/F8 1 Tf +0.5314 0 TD +(i)Tj +/F12 1 Tf +11.9552 0 0 11.9552 378.8224 623.8605 Tm +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 388.9793 622.0673 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 597.4595 Tm +[(Th)27.1(us)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 104.9534 601.7983 Tm +(1)Tj +/F12 1 Tf +11.9552 0 0 11.9552 113.588 597.4595 Tm +(M)Tj +/F8 1 Tf +7.9701 0 0 7.9701 123.744 595.1572 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 127.6722 597.4266 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 135.2707 595.1572 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 145.872 597.4595 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 168.4533 595.6663 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 179.6354 597.4595 Tm +[(if)-326.4(and)-326.4(only)-326.5(if)]TJ +/F12 1 Tf +5.8477 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 259.7031 595.6663 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 270.3044 597.4595 Tm +0.2778 Tc +[(=0)277.8(.)]TJ +-15.9851 -1.5417 TD +0 Tc +[(This)-326.4(is)-326.4(summarized)-326.5(in)-326.4(the)-326.4(follo)27.2(wing)-326.5(theorem:)]TJ +/F5 1 Tf +0 -2.0417 TD +[(Theorem)-375.1(1.)]TJ +/F14 1 Tf +6.1332 0 TD +[(Assume)-427.5(that)]TJ +/F11 1 Tf +5.8068 0 TD +(Z)Tj +/F14 1 Tf +1.1363 0 TD +[(is)-427.5(a)-427.4(c)50(omplex)-427.5(jointly-Gaussian)-427.6(r)50(andom)-427.5(ve)50(ctor.)-682.5(Then)]TJ +/F11 1 Tf +23.0291 0 TD +(Z)Tj +/F14 1 Tf +1.1364 0 TD +(is)Tj +-37.2418 -1.2083 TD +[(cir)49.9(cularly)-254.4(symmetric)-254.4(if)-254.3(and)-254.4(only)-254.4(if)]TJ +/F21 1 Tf +14.4386 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 261.9716 538.3811 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 271.4411 540.1744 Tm +0.2778 Tc +(=0)Tj +/F14 1 Tf +1.5289 0 TD +0 Tc +[(.)-418.1(I)0(n)-254.3(this)-254.4(c)49.9(ase,)-273.4(the)-254.3(distribution)-254.5(of)]TJ +/F11 1 Tf +13.7277 0 TD +(Z)Tj +/F14 1 Tf +0.9632 0 TD +[(is)-254.3(determine)49.9(d)]TJ +-32.2999 -1.2084 TD +(by)Tj +/F21 1 Tf +1.2751 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 102.5036 523.9352 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 108.6516 525.7285 Tm +(.)Tj +/F1 1 Tf +-2.4635 -2.375 TD +[(This)-310.2(theorem)-310.2(explains)-310.2(the)-310.1(ab)-27.2(o)27.2(v)27.2(e)-310.2(example.)-429.8(In)-310.1(the)-310.2(example,)]TJ +/F12 1 Tf +25.3908 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 392.9066 495.5417 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 403.5079 497.335 Tm +(=)Tj +/F16 1 Tf +1.0394 0.81 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 422.1111 502.6401 Tm +0.3541 Tc +(01)Tj +0 -1.1829 TD +(10)Tj +/F16 1 Tf +11.9552 0 0 11.9552 434.5973 507.0187 Tm +0 Tc +()Tj +/F1 1 Tf +0.7268 -0.81 TD +[(and)-310.1(th)27.2(us)]TJ +/F12 1 Tf +4.0255 0 TD +(M)Tj +/F8 1 Tf +7.9701 0 0 7.9701 501.5681 495.0327 Tm +(e)Tj +/F15 1 Tf +5.9776 0 0 5.9776 505.4964 497.3021 Tm +0.0001 Tc +(i)Tj +/F11 1 Tf +7.9701 0 0 7.9701 513.0949 495.0327 Tm +0 Tc +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 523.6962 497.335 Tm +(=)Tj +/F16 1 Tf +-37.1803 -0.4733 TD +()Tj +/F3 1 Tf +10.9091 0 0 10.9091 90.4917 481.873 Tm +(0)Tj +/F22 1 Tf +2.5384 0 TD +(e)Tj +/F6 1 Tf +7.9701 0 0 7.9701 123.2628 485.8311 Tm +(2)Tj +/F8 1 Tf +0.5313 0 TD +(i)Tj +/F22 1 Tf +10.9091 0 0 10.9091 90.4917 468.3148 Tm +(e)Tj +/F6 1 Tf +7.9701 0 0 7.9701 95.5706 472.2729 Tm +(2)Tj +/F8 1 Tf +0.5312 0 TD +(i)Tj +/F3 1 Tf +10.9091 0 0 10.9091 118.1828 468.3148 Tm +(0)Tj +/F16 1 Tf +11.9552 0 0 11.9552 140.8936 491.6762 Tm +()Tj +/F1 1 Tf +0.5278 -1.41 TD +[(.)-792.7(T)0(h)27.2(us,)]TJ +/F11 1 Tf +3.9662 0 TD +(Z)Tj +/F1 1 Tf +1.2965 0 TD +(and)Tj +/F7 1 Tf +2.0231 0 TD +(e)Tj +/F8 1 Tf +7.9701 0 0 7.9701 239.731 479.1572 Tm +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 248.1454 474.8194 Tm +(Z)Tj +/F1 1 Tf +1.2966 0 TD +[(do)-445.5(not)-445.6(ha)27.2(v)27.2(e)-445.6(the)-445.5(same)-445.6(distribution)-445.7(ev)27.2(en)-445.6(though,)-475.4(as)]TJ +-15.4282 -1.7278 TD +[(complex)-326.5(random)-326.5(v)27.2(ectors,)-326.4(they)-326.4(ha)27.2(v)27.2(e)-326.4(the)-326.4(same)-326.4(co)27.2(v)54.4(ariance)-326.5(matrix.)]TJ +0 -1.5417 TD +[(The)-483.7(denition)-483.7(of)-483.7(circular)-483.7(symmetry)-483.7(seems)-483.7(to)-483.6(capture)-483.7(the)-483.7(in)27.2(tuitiv)27.2(e)-483.6(notion)-483.7(of)-483.7(circular)]TJ +0 -1.2083 TD +[(symmetry)-359.4(somewhat)-359.4(b)-27.2(etter)-359.2(than)-359.3(the)-359.3(condition)]TJ +/F12 1 Tf +20.5257 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 334.7437 419.4929 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 346.0144 421.2862 Tm +[(=)-333.7(0)0(,)-367.5(but)-359.3(the)-359.2(latter)-359.4(is)-359.2(often)-359.3(easier)-359.3(to)]TJ +-22.3179 -1.2083 TD +[(w)27.2(ork)-326.4(with.)]TJ +/F5 1 Tf +0 -2.445 TD +[(Example)-322.2(2:)]TJ +/F1 1 Tf +5.8767 0 TD +[(W)81.6(e)-280.4(no)27.2(w)-280.4(giv)27.2(e)-280.4(a)0(n)-280.4(example)-280.4(illustrating)-280.5(the)-280.4(imp)-27.3(ortance)-280.4(of)-280.3(the)-280.4(join)27.1(tly-Gaussian)]TJ +-5.8767 -1.2083 TD +[(requiremen)27(t)-357.5(\(as)-357.5(opp)-27.2(osed)-357.6(to)-357.5(an)-357.5(individually)-357.6(Gaussian)-357.6(requiremen)27.1(t\).)-528.5(Consider)-357.6(a)-357.5(complex)]TJ +T* +[(random)-459.8(2-v)27.2(ector)]TJ +/F11 1 Tf +7.6103 0 TD +(Z)Tj +/F1 1 Tf +1.3107 0 TD +[(for)-459.7(whic)27.2(h)]TJ +/F7 1 Tf +4.564 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 248.4264 346.925 Tm +(1)Tj +/F9 1 Tf +11.9552 0 0 11.9552 259.192 348.7183 Tm +0.5046 Tc +[(C)446.3(N)]TJ +/F1 1 Tf +2.8351 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F1 1 Tf +0.4386 0 TD +[(1\))-459.7(and)]TJ +/F7 1 Tf +3.3673 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 357.0042 346.925 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 367.7689 348.7183 Tm +(=)Tj +/F7 1 Tf +1.2663 0 TD +0.1044 Tc +(UZ)Tj +/F6 1 Tf +7.9701 0 0 7.9701 400.1186 346.925 Tm +0 Tc +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 410.3462 348.7183 Tm +(where)Tj +/F7 1 Tf +2.9619 0 TD +(U)Tj +/F1 1 Tf +1.2292 0 TD +[(is)-459.6(statistically)]TJ +-31.8901 -1.2083 TD +[(indep)-27.3(enden)27.2(t)-382.8(o)0(f)]TJ +/F7 1 Tf +6.7766 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 168.2281 332.4792 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 177.5362 334.2725 Tm +[(and)-382.9(has)-382.8(p)-27.2(ossible)-382.8(v)54.4(alues)]TJ +/F9 1 Tf +10.4742 0 TD +()Tj +/F1 1 Tf +0.7778 0 TD +[(1)-382.8(with)-382.9(probabilit)27.1(y)-382.8(1/2)-382.9(eac)27.2(h.)-604.5(Then)]TJ +/F7 1 Tf +15.438 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 504.6326 332.4792 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 513.9407 334.2725 Tm +(and)Tj +/F7 1 Tf +-36.3643 -1.2083 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 87.213 318.0334 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 96.2401 319.8266 Tm +[(are)-359.3(not)-359.3(join)27.1(tly)-359.3(Gaussian,)-367.6(and)-359.2(in)-359.3(fact)]TJ +/F9 1 Tf +16.1402 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 310.398 318.0334 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 315.1303 319.8266 Tm +[(\))-359.3(and)]TJ +/F9 1 Tf +2.6768 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 368.3318 318.0334 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 373.064 319.8266 Tm +[(\))-359.2(h)0(a)27.1(v)27.2(e)-359.2(a)-359.3(join)27.2(t)-359.3(distribution)-359.3(that)]TJ +-24.5805 -1.2083 TD +[(is)-353.4(concen)27.1(trated)-353.4(on)-353.5(the)-353.3(t)27.2(w)27.2(o)-353.3(diagonal)-353.5(axes.)-516.2(It)-353.3(is)-353.4(easy)-353.4(to)-353.4(see)-353.4(that)]TJ +/F12 1 Tf +27.6305 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 417.5871 303.5876 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 428.7382 305.3808 Tm +(=)Tj +/F16 1 Tf +1.0853 0.81 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 447.8894 310.6859 Tm +0.3541 Tc +(10)Tj +0 -1.1829 TD +(01)Tj +/F16 1 Tf +11.9552 0 0 11.9552 460.3756 315.0645 Tm +0 Tc +()Tj +/F1 1 Tf +0.7701 -0.81 TD +(and)Tj +/F12 1 Tf +1.9309 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 502.8224 303.5876 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 513.9727 305.3808 Tm +0.3238 Tc +(=0)Tj +-36.3669 -1.2083 TD +0 Tc +[(and)-329.6(th)27.2(us)]TJ +/F11 1 Tf +4.0644 0 TD +(Z)Tj +/F1 1 Tf +1.1805 0 TD +[(is)-329.5(circularly)-329.6(symmetric.)-444.8(The)-329.5(corresp)-27.3(onding)-329.6(real)-329.6(random)-329.6(4-v)27.2(ector)]TJ +/F11 1 Tf +28.0354 0 TD +(V)Tj +/F1 1 Tf +1.3813 0 TD +(satises)Tj +/F12 1 Tf +-34.6617 -1.2083 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 87.2608 274.6959 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 99.462 276.4891 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(I)Tj +/F6 1 Tf +7.9701 0 0 7.9701 115.0705 274.6959 Tm +(4)Tj +/F1 1 Tf +11.9552 0 0 11.9552 119.8027 276.4891 Tm +[(,)-311.3(s)0(o)-307.5(the)-307.6(rvs)-307.5(are)-307.6(uncorrelated.)-429(Ho)27.2(w)27.2(e)0(v)27.2(er,)-311.3(they)-307.6(are)-307.6(clearly)-307.6(not)-307.5(indep)-27.3(enden)27.2(t)-307.6(and)-307.5(the)]TJ +-3.3962 -1.2083 TD +[(probabilit)27.1(y)-326.4(densit)27.2(y)-326.4(d)0(o)-27.2(e)0(s)-326.4(not)-326.4(exist.)]TJ +0 -2.7461 TD +[(The)-327(p)-27.2(oin)27.2(t)-327.1(o)0(f)-327(this)-327(example)-327.1(is)-327(that)-327.1(the)-327(join)27.2(t)-327(Gaussian)-327.1(prop)-27.2(ert)27.1(y)-327(i)0(s)-327(imp)-27.3(ortan)27.2(t)-327(i)0(n)-327(the)-327(results)]TJ +0 -1.2083 TD +[(that)-392.7(ha)27.1(v)27.2(e)-392.7(b)-27.2(een)-392.8(deriv)27.2(ed.)-634.2(The)-392.7(stubb)-27.3(orn)-392.8(b)-27.2(eliev)27.2(er)-392.7(in)-392.7(an)-392.7(o)27.2(v)27.2(ersimplied)-392.7(w)27.2(orld)-392.7(migh)27.1(t)-392.7(try)-392.7(to)]TJ +T* +[(think)-361.8(that)-361.7(Examples)-361.9(1)-361.7(and)-361.7(2)-361.8(rely)-361.7(on)-361.8(the)-361.8(lac)27.2(k)-361.7(o)0(f)-361.7(a)-361.8(probabilit)27.1(y)-361.7(densit)27.2(y)81.6(.)-541.2(This)-361.8(is)-361.7(not)-361.8(true,)]TJ +T* +[(and)-352.4(eac)27.2(h)-352.4(example)-352.4(w)27.2(ould)-352.3(lead)-352.5(to)-352.4(the)-352.3(same)-352.4(conclusion)-352.5(if)-352.3(w)27.2(e)-352.4(mo)-27.2(died)]TJ +/F11 1 Tf +29.5888 0 TD +(Z)Tj +/F1 1 Tf +1.2034 0 TD +[(b)27.2(y)-352.4(adding)-352.4(a)-352.4(nice)]TJ +-30.7922 -1.2083 TD +[(random)-379.9(v)27.2(ector)]TJ +/F11 1 Tf +6.6345 0 TD +(Y)Tj +/F9 1 Tf +1.4322 0 TD +0.3686 Tc +[(C)310.2(N)]TJ +/F1 1 Tf +2.6992 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +0.1667 Tc +(,)Tj +/F1 1 Tf +0.8969 0 TD +0 Tc +[(\).)-595.3(This)-379.8(w)27.2(ould)-379.8(yield)-379.8(a)-379.8(true)-379.8(probabilit)27.1(y)-379.7(densit)27.2(y)-379.8(and)-379.7(sligh)27.1(tly)]TJ +-12.5331 -1.2083 TD +[(complicate)-326.5(but)-326.4(not)-326.4(c)27.2(hange)-326.4(the)-326.4(issues)-326.4(discussed.)]TJ +ET +79.17 146.888 181.438 -0.398 re +f +BT +/F17 1 Tf +6.9738 0 0 6.9738 92.6635 139.1462 Tm +(1)Tj +/F3 1 Tf +9.9626 0 0 9.9626 97.1327 135.5307 Tm +[(Note)-358.8(that)-358.8(the)-358.9(statemen)27.8(t)]TJ +/F20 1 Tf +11.0522 0 TD +(M)Tj +/F19 1 Tf +6.9738 0 0 6.9738 215.9591 133.5103 Tm +(e)Tj +/F18 1 Tf +4.9813 0 0 4.9813 219.739 135.5027 Tm +-0.0001 Tc +(i)Tj +/F11 1 Tf +6.9738 0 0 6.9738 227.0874 133.5103 Tm +0 Tc +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 236.7113 135.5307 Tm +(=)Tj +/F20 1 Tf +1.0981 0 TD +(M)Tj +/F11 1 Tf +6.9738 0 0 6.9738 256.3686 134.0363 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 266.3771 135.5307 Tm +[(if)-358.9(and)-358.8(only)-358.9(if)]TJ +/F20 1 Tf +6.0743 0 TD +(M)Tj +/F11 1 Tf +6.9738 0 0 6.9738 335.6105 134.0363 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 345.2344 135.5307 Tm +[(=)-320.3(0)-358.9(is)-358.9(v)55.6(alid)-358.9(whether)-358.8(or)-358.8(not)]TJ +/F11 1 Tf +12.3458 0 TD +(Z)Tj +/F3 1 Tf +1.2098 0 TD +[(is)-358.9(Gaussian.)]TJ +-40.2588 -1.2 TD +[(Similarly)-333.3(\(1\))-333.3(is)-333.4(v)55.6(alid)-333.4(whether)-333.3(or)-333.3(not)]TJ +/F11 1 Tf +16.1251 0 TD +(Z)Tj +/F3 1 Tf +1.1843 0 TD +[(is)-333.3(Gaussian.)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 303.0745 49.312 Tm +(3)Tj +ET +endstream +endobj +27 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F3 6 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +/F15 23 0 R +/F16 24 0 R +/F17 28 0 R +/F18 29 0 R +/F19 30 0 R +/F20 31 0 R +/F21 32 0 R +/F22 33 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +35 0 obj +<< +/Length 10793 +>> +stream
+BT +/F5 1 Tf +17.2154 0 0 17.2154 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(2)-1125(Linear)-915.1(transformations)-915(of)-915.1(circularly-symmetric)]TJ +1.6875 -1.2731 TD +[(Gaussian)-375(v)31.3(ectors)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 655.8575 Tm +[(Circular)-251.5(symmetry)-251.5(can)-251.5(also)-251.5(b)-27.2(e)-251.4(c)27.2(haracterized)-251.6(as)-251.5(the)-251.4(result)-251.5(of)-251.4(a)-251.5(linear)-251.5(transformation)-251.5(\(in)]TJ +/F23 1 Tf +36.8388 0 TD +(C)Tj +/F1 1 Tf +0.7222 0 TD +(\))Tj +-37.561 -1.2083 TD +(of)Tj +/F7 1 Tf +1.0402 0 TD +(m)Tj +/F1 1 Tf +1.108 0 TD +[(iid)-251.5(random)-251.5(v)54.4(ariables,)-266.5(eac)27.2(h)]TJ +/F9 1 Tf +11.2531 0 TD +0.0583 Tc +(CN)Tj +/F1 1 Tf +1.5527 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F1 1 Tf +0.4387 0 TD +[(1\).)-410.2(Th)27.1(us)-251.5(let)]TJ +/F11 1 Tf +5.2976 0 TD +(W)Tj +/F9 1 Tf +1.624 0 TD +0.2778 Tc +[(C)219.5(N)]TJ +/F1 1 Tf +2.6082 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F12 1 Tf +0.4386 0 TD +(I)Tj +/F8 1 Tf +7.9701 0 0 7.9701 406.3911 639.6185 Tm +(m)Tj +/F1 1 Tf +11.9552 0 0 11.9552 414.3801 641.4117 Tm +[(\).)-410.2(That)-251.5(is,)]TJ +/F7 1 Tf +4.6326 0 TD +(W)Tj +/F6 1 Tf +7.9701 0 0 7.9701 480.8149 639.6185 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 485.5472 641.4117 Tm +0.1667 Tc +[(,...)-166.6(,W)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 524.812 639.6185 Tm +0 Tc +(m)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 626.9659 Tm +[(are)-386.6(iid)-386.5(and)-386.5(ha)27.2(v)27.2(e)-386.5(iid)-386.5(real)-386.5(and)-386.5(imaginary)-386.5(parts,)-401.6(th)27.2(us)-386.5(consisting)-386.5(collectiv)27.1(ely)-386.5(of)-386.5(2)]TJ +/F7 1 Tf +33.9189 0 TD +(n)Tj +/F1 1 Tf +0.9709 0 TD +[(iid)-386.5(real)]TJ +-34.8898 -1.2083 TD +[(rvs,)-282(eac)27.3(h)]TJ +/F9 1 Tf +4.2572 0 TD +(N)Tj +/F1 1 Tf +0.9678 0 TD +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +(,)Tj +/F6 1 Tf +7.9701 0 0 7.9701 158.5116 617.2264 Tm +(1)Tj +ET +158.49 615.688 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 158.5116 608.3975 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 163.9412 612.5201 Tm +[(\).)-416.6(Let)]TJ +/F12 1 Tf +2.768 0 TD +(A)Tj +/F1 1 Tf +0.9178 0 TD +[(b)-27.2(e)-270.8(an)-270.8(arbitrary)]TJ +/F7 1 Tf +6.6873 0 TD +(m)Tj +/F1 1 Tf +1.1272 0 TD +-0.0271 Tc +(by)Tj +/F7 1 Tf +1.3044 0 TD +0 Tc +(n)Tj +/F1 1 Tf +0.8553 0 TD +[(complex)-270.8(matrix)-270.9(and)-270.8(let)]TJ +/F11 1 Tf +10.1133 0 TD +(Z)Tj +/F1 1 Tf +1.1287 0 TD +(=)Tj +/F12 1 Tf +1.0393 0 TD +(A)Tj +/F11 1 Tf +0.6469 0 TD +(W)Tj +/F1 1 Tf +1.3463 0 TD +[(.)-416.7(Then)]TJ +/F12 1 Tf +-28.2003 -2.1979 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 168.8259 584.4503 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 179.4272 586.2437 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F12 1 Tf +0.2719 0 TD +(A)Tj +/F11 1 Tf +0.647 0 TD +0.1863 Tc +(WW)Tj +/F10 1 Tf +7.9701 0 0 7.9701 242.0015 591.1801 Tm +0 Tc +()Tj +/F12 1 Tf +11.9552 0 0 11.9552 246.2635 586.2437 Tm +(A)Tj +/F10 1 Tf +7.9701 0 0 7.9701 253.9985 591.1801 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 258.2595 586.2437 Tm +0.2778 Tc +(]=)Tj +/F12 1 Tf +1.5892 0 TD +-0.0001 Tc +(AA)Tj +/F10 1 Tf +7.9701 0 0 7.9701 292.7273 591.1801 Tm +0 Tc +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 296.9893 586.2437 Tm +(;)Tj +/F12 1 Tf +2.397 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 335.8018 584.4503 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 346.403 586.2437 Tm +(=)Tj +/F12 1 Tf +1.0393 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F12 1 Tf +0.272 0 TD +(A)Tj +/F11 1 Tf +0.647 0 TD +0.1862 Tc +(WW)Tj +/F13 1 Tf +5.9776 0 0 5.9776 408.9774 591.1801 Tm +0 Tc +(T)Tj +/F12 1 Tf +11.9552 0 0 11.9552 413.8142 586.2437 Tm +(A)Tj +/F13 1 Tf +5.9776 0 0 5.9776 421.5482 591.1801 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 426.3851 586.2437 Tm +0.2778 Tc +(]=0)Tj +-29.0406 -2.1023 TD +0 Tc +[(Th)27.1(us)]TJ +/F11 1 Tf +2.4806 0 TD +(Z)Tj +/F1 1 Tf +1.1773 0 TD +[(is)-326.4(circularly)-326.4(symmetric)-326.5(and)-326.4(denoted)-326.5(b)27.2(y)]TJ +/F9 1 Tf +17.0373 0 TD +0.0583 Tc +(CN)Tj +/F1 1 Tf +1.5527 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F12 1 Tf +0.4387 0 TD +-0.0001 Tc +(AA)Tj +/F10 1 Tf +7.9701 0 0 7.9701 376.2969 565.4496 Tm +0 Tc +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 380.5589 561.1108 Tm +(\),)Tj +-25.2074 -1.5417 TD +[(As)-275.6(explained)-275.6(in)-275.5(greater)-275.6(detail)-275.6(in)-275.6(Section)-275.6(7.11.1)-275.6(of)-275.6(PDC08,)-285.8(the)-275.6(class)-275.6(of)-275.5(co)27.2(v)54.4(ariance)-275.5(matrices)]TJ +0 -1.2083 TD +[(\(real)-411.8(or)-411.8(complex\))-411.8(is)-411.8(the)-411.8(same)-411.8(as)-411.8(the)-411.7(class)-411.8(of)-411.7(nonnegativ)27.1(e-denite)-411.8(matrices.)-691.4(Eac)27.2(h)-411.8(suc)27.2(h)]TJ +T* +(matrix)Tj +/F12 1 Tf +3.1823 0 TD +(K)Tj +/F1 1 Tf +1.0005 0 TD +[(can)-326.5(b)-27.2(e)-326.4(represen)27.1(ted)-326.4(as)]TJ +/F12 1 Tf +12.257 -2.1022 TD +(K)Tj +/F1 1 Tf +0.952 0 TD +(=)Tj +/F12 1 Tf +1.0393 0 TD +(Q)Tj +/F1 1 Tf +0.7222 0 TD +()Tj +/F12 1 Tf +0.6797 0 TD +(Q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 324.9405 493.593 Tm +()Tj +/F6 1 Tf +0.8265 0 TD +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 517.8431 488.6566 Tm +(\(6\))Tj +-36.6907 -2.1022 TD +[(where)-298.8()-298.6(i)0(s)-298.6(diagonal)-298.8(with)-298.7(nonnegativ)27.1(e)-298.7(terms)-298.7(whic)27.1(h)-298.6(are)-298.7(the)-298.7(eigen)27.2(v)54.4(alues)-298.7(of)]TJ +/F12 1 Tf +31.0978 0 TD +(K)Tj +/F1 1 Tf +0.6742 0 TD +[(.)-425.9(The)-298.7(columns)]TJ +-31.772 -1.2083 TD +(of)Tj +/F12 1 Tf +1.2396 0 TD +(Q)Tj +/F1 1 Tf +1.173 0 TD +[(are)-450.7(orthonormal)-450.9(eigen)27.1(v)27.2(ectors)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 259.0316 453.4167 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 269.1527 449.078 Tm +[(of)-450.8(those)-450.8(eigen)27.2(v)54.4(alues.)-808.4(By)-450.8(c)27.2(h)0(o)-27.2(osing)]TJ +/F12 1 Tf +15.5062 0 TD +(R)Tj +/F1 1 Tf +1.1197 0 TD +(=)Tj +/F12 1 Tf +1.2511 0 TD +(Q)Tj +/F9 1 Tf +0.7222 0.8467 TD +()Tj +ET +501.45 459.688 8.125 -0.478 re +f +BT +/F1 1 Tf +11.9552 0 0 11.9552 501.4715 449.078 Tm +()Tj +/F12 1 Tf +0.6796 0 TD +(Q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 518.2307 453.4167 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 529.5492 449.078 Tm +(,)Tj +-37.6698 -1.2083 TD +[(w)27.2(e)-403.3(see)-403.4(that)]TJ +/F11 1 Tf +5.3768 0 TD +(Z)Tj +/F1 1 Tf +1.2597 0 TD +(=)Tj +/F12 1 Tf +1.1703 0 TD +(R)Tj +/F11 1 Tf +0.6302 0 TD +(W)Tj +/F1 1 Tf +1.7496 0 TD +[(has)-403.3(the)-403.3(co)27.2(v)54.4(ariance)-403.4(matrix)]TJ +/F12 1 Tf +11.655 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 348.3796 432.8388 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 360.5469 434.6321 Tm +(=)Tj +/F12 1 Tf +1.1703 0 TD +(RR)Tj +/F10 1 Tf +7.9701 0 0 7.9701 389.606 438.9708 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 393.868 434.6321 Tm +[(.)-665.9(This)-403.3(means)-403.4(that)-403.3(for)]TJ +/F14 1 Tf +10.0962 0 TD +(any)Tj +/F1 1 Tf +-36.4168 -1.2083 TD +[(co)27.2(v)54.4(ariance)-432.8(matrix)]TJ +/F12 1 Tf +8.1277 0 TD +(K)Tj +/F1 1 Tf +0.6742 0 TD +[(,)-459.3(there)-432.8(is)-432.7(a)-432.8(matrix)]TJ +/F12 1 Tf +8.6419 0 TD +(R)Tj +/F1 1 Tf +1.0629 0 TD +[(suc)27.1(h)-432.7(that)-432.8(the)-432.7(random)-432.9(v)27.2(ector)]TJ +/F11 1 Tf +13.076 0 TD +(Z)Tj +/F1 1 Tf +1.3097 0 TD +(=)Tj +/F12 1 Tf +1.2204 0 TD +(R)Tj +/F11 1 Tf +0.6302 0 TD +(W)Tj +/F1 1 Tf +1.779 0 TD +(has)Tj +-36.522 -1.2083 TD +[(co)27.2(v)54.4(ariance)]TJ +/F12 1 Tf +4.7327 0 TD +(K)Tj +/F1 1 Tf +1.0005 0 TD +[(and)-326.4(pseudo-co)27.1(v)54.4(ariance)-326.5(0.)-435.2(This)-326.4(is)-326.4(summed)-326.4(up)-326.4(in)-326.4(the)-326.4(follo)27.1(wing)-326.4(theorem.)]TJ +/F5 1 Tf +-5.7332 -1.9507 TD +[(Theorem)-375.1(2.)]TJ +/F14 1 Tf +6.1332 0 TD +[(A)-316.1(n)0(e)50(c)50(essary)-316.2(and)-316.2(sucient)-316.2(c)50(ondition)-316.3(for)-316.2(a)-316.2(r)50(andom)-316.2(ve)50(ctor)-316.3(to)-316.2(b)50(e)-316.2(a)-316.2(cir)50(cularly-)]TJ +-6.1332 -1.2083 TD +[(symmetric)-378.8(jointly-Gaussian)-378.9(r)50(andom)-378.8(ve)50(ctor)-378.8(is)-378.7(that)-378.8(it)-378.7(has)-378.8(the)-378.7(form)]TJ +/F11 1 Tf +28.594 0 TD +(Z)Tj +/F1 1 Tf +1.0397 0 TD +(=)Tj +/F21 1 Tf +1.0925 0 TD +(A)Tj +/F11 1 Tf +0.647 0 TD +(W)Tj +/F14 1 Tf +1.5387 0 TD +[(wher)50(e)]TJ +/F11 1 Tf +2.7913 0 TD +(W)Tj +/F14 1 Tf +1.5387 0 TD +(is)Tj +-37.2418 -1.2083 TD +[(iid)-350.1(c)50(omplex)-350(Gaussian)-350.1(and)]TJ +/F21 1 Tf +11.3318 0 TD +(A)Tj +/F14 1 Tf +0.997 0 TD +[(is)-350(an)-350(arbitr)49.9(ary)-350(c)50(omplex)-350(matrix.)]TJ +/F1 1 Tf +-12.3288 -2.284 TD +[(W)81.6(e)-238.7(no)27.2(w)-238.6(h)0(a)27.2(v)27.2(e)-238.6(three)-238.6(equiv)54.3(alen)27.2(t)-238.6(c)27.2(haracterizations)-238.8(for)-238.6(circularly-symmetric)-238.8(Gaussian)-238.6(random)]TJ +0 -1.2083 TD +[(v)27.2(ectors,)-306(rst,)-306(the)-300.8(denition)-300.8(in)-300.8(terms)-300.9(of)-300.8(phase)-300.9(in)27.2(v)54.4(ariance,)-306(second,)-306(in)-300.9(terms)-300.8(of)-300.8(zero)-300.8(pseudo-)]TJ +T* +[(co)27.2(v)54.4(ariance,)-444.9(and)-421.2(third,)-444.9(in)-421.2(terms)-421.2(of)-421.2(linear)-421.2(transformations)-421.3(of)-421.2(iid)-421.2(Gaussian)-421.3(v)27.2(ectors.)-719.6(One)]TJ +T* +[(adv)54.3(an)27.2(tage)-343.6(of)-343.5(the)-343.6(third)-343.5(c)27.2(haracterization)-343.6(is)-343.5(that)-343.6(the)-343.6(join)27.2(tly-Gaussian)-343.6(requiremen)27.1(t)-343.6(i)0(s)-343.5(auto-)]TJ +T* +[(matically)-289.3(met,)-296.6(whereas)-289.2(the)-289.2(other)-289.2(t)27.2(w)27.2(o)-289.2(dep)-27.2(end)-289.1(on)-289.2(that)-289.2(as)-289.1(a)-289.2(separate)-289.3(requiremen)27.1(t.)-422.7(Another)]TJ +T* +[(adv)54.3(an)27.2(tage)-298.2(of)-298.2(the)-298.2(third)-298.3(c)27.2(haracterization)-298.4(is)-298.2(that)-298.2(the)-298.3(usual)-298.3(motiv)54.4(ation)-298.3(for)-298.2(mo)-27.2(deling)-298.3(random)]TJ +T* +[(v)27.2(ectors)-386.2(as)-386.2(circularly)-386.3(symmetric)-386.2(is)-386.2(that)-386.2(they)-386.2(are)-386.2(linear)-386.2(transformations)-386.3(of)-386.2(essen)27.2(tially)-386.2(iid)]TJ +T* +[(complex)-326.5(Gaussian)-326.4(random)-326.5(v)27.2(ectors.)]TJ +/F5 1 Tf +17.2154 0 0 17.2154 79.2 181.3698 Tm +[(3)-1125(The)-276.4(real)-276.4(and)-276.4(imaginary)-276.4(parts)-276.4(of)-276.4(circularly)-276.4(symmet-)]TJ +1.6875 -1.2731 TD +[(ric)-375(random)-375(v)31.3(ectors)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 129.1825 Tm +[(Since)-269.2(the)-269.1(probabilit)27.1(y)-269(densit)27.1(y)-269.1(o)0(f)-269(a)-269.1(complex)-269.1(random)-269.1(v)54.4(ariable)-269.1(or)-269.1(v)27.2(ector)-269.1(is)-269(dened)-269.1(in)-269(terms)-269.1(of)]TJ +0 -1.2083 TD +[(the)-258.9(real)-258.9(and)-258.9(imaginary)-259(parts)-258.9(of)-258.9(that)-258.9(v)54.4(ariable)-259(or)-258.8(v)27.2(ector,)-272.5(w)27.3(e)-258.9(no)27.2(w)-258.9(pause)-258.9(to)-258.9(discuss)-258.9(these)-258.9(rela-)]TJ +T* +[(tionships.)-415.8(The)-267.8(ma)-54.4(jor)-267.8(reason)-267.8(for)-267.8(using)-267.8(complex)-267.9(v)27.3(ector)-267.9(spaces)-267.9(and)-267.7(complex)-267.8(random)-267.9(v)27.2(ectors)]TJ +ET +79.17 90.609 181.438 -0.398 re +f +BT +/F17 1 Tf +6.9738 0 0 6.9738 92.6635 82.8155 Tm +(2)Tj +/F3 1 Tf +9.9626 0 0 9.9626 97.1327 79.2 Tm +[(A)-333.4(complex)-333.3(matrix)-333.2(with)-333.3(orthonormal)-333.3(columns)-333.3(is)-333.3(called)-333.4(a)-333.3(unitary)-333.3(matrix.)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 303.0745 49.312 Tm +(4)Tj +ET +endstream +endobj +36 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F3 6 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +/F17 28 0 R +/F21 32 0 R +/F23 37 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +39 0 obj +<< +/Length 19359 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(is)-389(to)-389(a)27.2(v)27.2(oid)-389(all)-389(the)-388.9(detail)-389.1(of)-388.9(the)-389(real)-389(and)-388.9(imaginary)-389(parts,)-404.6(but)-389(our)-388.9(in)27.2(tuition)-389(comes)-389(from)]TJ +/F23 1 Tf +0 -1.2083 TD +(R)Tj +/F6 1 Tf +7.9701 0 0 7.9701 87.8346 697.9377 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 96.3268 693.599 Tm +(and)Tj +/F23 1 Tf +1.892 0 TD +(R)Tj +/F6 1 Tf +7.9701 0 0 7.9701 127.5806 697.9377 Tm +(3)Tj +/F1 1 Tf +11.9552 0 0 11.9552 132.3128 693.599 Tm +[(,)-316.8(and)-314.6(the)-314.5(ma)-54.4(jor)-314.6(source)-314.5(of)-314.5(confusion)-314.6(in)-314.5(treating)-314.6(complex)-314.5(random)-314.6(v)27.3(ectors)-314.6(comes)]TJ +-4.4427 -1.2083 TD +[(from)-408.4(assuming)-408.4(that)]TJ +/F23 1 Tf +8.9333 0 TD +(C)Tj +/F8 1 Tf +7.9701 0 0 7.9701 194.6331 683.4919 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 205.1507 679.1532 Tm +[(is)-408.4(roughly)-408.4(the)-408.4(same)-408.3(as)]TJ +/F23 1 Tf +10.2993 0 TD +(R)Tj +/F8 1 Tf +7.9701 0 0 7.9701 336.9156 683.4919 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 342.5515 679.1532 Tm +[(.)-681.1(This)-408.4(assumption)-408.4(causes)-408.4(additional)]TJ +-22.0283 -1.2083 TD +[(confusion)-326.5(when)-326.4(dealing)-326.5(with)-326.5(circular)-326.4(symmetry)81.5(.)]TJ +0 -1.5417 TD +(Let)Tj +/F11 1 Tf +1.7859 0 TD +(Z)Tj +/F1 1 Tf +1.2092 0 TD +[(b)-27.2(e)-358.2(a)-358.2(random)-358.2(complex)]TJ +/F7 1 Tf +9.701 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector)]TJ +/F11 1 Tf +3.2957 0 TD +(Z)Tj +/F1 1 Tf +1.1828 0 TD +0.3319 Tc +(=\()Tj +/F7 1 Tf +1.4743 0 TD +0 Tc +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 317.1487 644.4832 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 321.881 646.2765 Tm +0.1667 Tc +[(,...)-166.6(,)0(Z)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 358.1061 644.4832 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 363.743 646.2765 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 368.2949 650.6152 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 377.4127 646.2765 Tm +[(and)-358.2(let)-358.2(the)-358.2(corresp)-27.3(onding)-358.2(real)]TJ +-24.9443 -1.2083 TD +[(random)-402.7(2)]TJ +/F7 1 Tf +4.1561 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector)]TJ +/F11 1 Tf +3.3401 0 TD +(V)Tj +/F1 1 Tf +1.4543 0 TD +[(consist)-402.7(of)-402.7(the)-402.6(real)-402.7(and)-402.6(imaginary)-402.7(comp)-27.3(onen)27.2(ts)-402.6(of)]TJ +/F11 1 Tf +21.542 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +[(,)-421.7(tak)27.2(en)-402.6(in)-402.6(the)]TJ +-31.9279 -1.2083 TD +(order)Tj +/F11 1 Tf +2.5567 0 TD +(V)Tj +/F1 1 Tf +1.3296 0 TD +0.2778 Tc +(=\()Tj +/F9 1 Tf +1.4201 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 163.8376 615.5916 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 168.5699 617.3848 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 222.5345 615.5916 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 228.1714 617.3848 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 259.1661 615.5916 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 263.8984 617.3848 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 317.863 615.5916 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 323.4999 617.3848 Tm +(\)\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 332.6047 621.7236 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 337.4406 617.3848 Tm +(.)Tj +-21.6008 -1.5417 TD +[(W)81.6(e)-370.8(start)-370.7(b)27.1(y)-370.7(relating)-370.8(the)-370.8(2)]TJ +/F7 1 Tf +11.3784 0 TD +(n)Tj +/F1 1 Tf +0.9552 0 TD +-0.0272 Tc +[(by)-398(2)]TJ +/F7 1 Tf +1.8939 0 TD +0 Tc +(n)Tj +/F1 1 Tf +0.9552 0 TD +[(real)-370.8(co)27.2(v)54.4(ariance)-370.8(matrix)]TJ +/F12 1 Tf +9.9519 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 387.749 597.1606 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 400.8538 598.9539 Tm +(=)Tj +/F12 1 Tf +1.1148 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +0.1862 Tc +(VV)Tj +/F13 1 Tf +5.9776 0 0 5.9776 449.5562 603.2927 Tm +0 Tc +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 454.392 598.9539 Tm +[(])-370.8(t)0(o)-370.7(the)]TJ +/F7 1 Tf +3.6145 0 TD +(n)Tj +/F1 1 Tf +0.9552 0 TD +-0.0272 Tc +(by)Tj +/F7 1 Tf +1.4043 0 TD +0 Tc +(n)Tj +/F1 1 Tf +-37.3573 -1.2083 TD +(matrix)Tj +/F12 1 Tf +3.2272 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 125.8421 582.7148 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 137.3579 584.5081 Tm +(=)Tj +/F12 1 Tf +1.1158 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F11 1 Tf +0.272 0 TD +0.1421 Tc +(ZZ)Tj +/F10 1 Tf +7.9701 0 0 7.9701 181.2692 588.8468 Tm +0 Tc +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 185.5312 584.5081 Tm +[(].)-570(The)-371.3(\(real\))-371.4(co)27.2(v)54.4(ariance)-371.4(matrix)]TJ +/F12 1 Tf +13.8868 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 359.6095 582.7148 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 372.9295 584.5081 Tm +[(can)-371.4(then)-371.3(b)-27.3(e)-371.3(expressed)-371.3(in)-371.4(blo)-27.2(c)27.3(k)]TJ +-24.5693 -1.2083 TD +[(form)-326.4(in)-326.4(terms)-326.4(of)-326.4(the)-326.4(\(complex\))-326.5(co)27.2(v)54.4(ariance)-326.5(matrix)]TJ +/F12 1 Tf +21.4925 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 344.2062 568.269 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 351.4869 570.0623 Tm +(.)Tj +/F12 1 Tf +-13.0908 -3.3958 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 203.0446 527.6713 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 215.2468 529.4645 Tm +(=)Tj +/F16 1 Tf +1.0393 2.01 TD +()Tj +0 -1.8 TD +()Tj +/F12 1 Tf +1.0833 1.0067 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 302.1211 548.3487 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 306.9579 544.01 Tm +(\))Tj +/F12 1 Tf +2.1932 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 394.676 548.3487 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 399.5128 544.01 Tm +(\))Tj +/F12 1 Tf +-13.2904 -2.4167 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 302.1211 519.457 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 306.9579 515.1183 Tm +(\))Tj +/F12 1 Tf +2.1932 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 394.676 519.457 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 399.5128 515.1183 Tm +(\))Tj +/F16 1 Tf +0.7974 3.21 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +-27.5903 -3.5502 TD +[(Assume)-373.6(in)-373.5(what)-373.5(follo)27.1(ws)-373.5(that)]TJ +/F11 1 Tf +12.7901 0 TD +(Z)Tj +/F1 1 Tf +1.2244 0 TD +[(is)-373.5(circularly)-373.5(symmetric.)-576.5(The)-373.5(pseudo-co)27.1(v)54.4(ariance)-373.5(matrix,)]TJ +/F12 1 Tf +-14.0145 -1.2083 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 89.3569 473.2922 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 101.8281 475.0854 Tm +[(is)-434.1(then)-434.3(zero,)-461.2(so)-434.2(expressing)-434.2(\(2\),)-461.2(in)-434.1(matrix)-434.3(form,)-461.2(w)27.3(e)-434.2(get)]TJ +/F12 1 Tf +24.5705 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F9 1 Tf +0.272 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(Z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 457.071 479.4232 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 461.9069 475.0854 Tm +[(\)])-461.2(=)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 491.0396 479.7928 Tm +(1)Tj +ET +491.01 478.288 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 491.0396 470.9629 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 496.4693 475.0854 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3807 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 517.7166 473.2922 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 524.9963 475.0854 Tm +0.0001 Tc +(\).)Tj +-37.289 -1.2083 TD +0 Tc +[(Using)-326.4(\(3\),)-326.4(\(4\),)-326.4(and)-326.4(\(5\))-326.4(in)-326.4(the)-326.4(same)-326.4(w)27.2(a)27.2(y)81.6(,)]TJ +/F12 1 Tf +17.3906 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 295.1671 458.8464 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 307.9502 460.6396 Tm +[(can)-326.5(b)-27.2(e)-326.4(expressed)-326.4(as)]TJ +/F12 1 Tf +-7.3131 -3.3958 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 228.5808 418.2486 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 240.7831 420.0419 Tm +(=)Tj +/F16 1 Tf +1.0393 2.01 TD +()Tj +0 -1.8 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 267.3554 439.2946 Tm +(1)Tj +ET +267.33 437.848 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 267.3554 430.4648 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 272.785 434.5873 Tm +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 294.0314 432.7941 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 301.3121 434.5873 Tm +(\))Tj +/F9 1 Tf +2.1933 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 338.0274 439.2946 Tm +(1)Tj +ET +338.01 437.848 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 338.0274 430.4648 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 343.4571 434.5873 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 364.7034 432.7941 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 371.9841 434.5873 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 267.3554 410.403 Tm +(1)Tj +ET +267.33 408.928 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 267.3554 401.5731 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 272.785 405.6956 Tm +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 294.0314 403.9024 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 301.3121 405.6956 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 333.3778 410.403 Tm +(1)Tj +ET +1 i +333.33 408.45 4.234 0.478 re +f +BT +7.9701 0 0 7.9701 333.3778 401.5731 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 338.8075 405.6956 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 360.0538 403.9024 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 367.3345 405.6956 Tm +(\))Tj +/F16 1 Tf +1.1863 3.21 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +11.4031 -0.21 TD +(\(7\))Tj +-36.6907 -3.4383 TD +[(It)-304.2(can)-304(then)-304.1(b)-27.2(e)-304.2(v)27.3(eried)-304.1(b)27.1(y)-304.1(matrix)-304.1(m)27.1(ultiplication)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 320.5539 383.2737 Tm +(3)Tj +/F1 1 Tf +11.9552 0 0 11.9552 328.9216 378.936 Tm +[(with)-304.1(\(7\))-304.1(that)-304.2(if)]TJ +/F12 1 Tf +6.7377 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 417.5313 377.1427 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 428.4474 378.936 Tm +[(is)-304(non-singular,)-308.7(then)]TJ +/F12 1 Tf +-29.2131 -1.2083 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 87.2608 369.4376 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0302 TD +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 102.4817 364.4901 Tm +[(is)-326.4(also)-326.4(non-singular)-326.4(and)-326.4(its)-326.4(in)27.2(v)27.2(erse)-326.4(is)-326.4(giv)27.2(en)-326.4(in)-326.5(blo)-27.2(c)27.3(k)-326.4(form)-326.4(b)27.2(y)]TJ +/F12 1 Tf +9.4983 -3.4188 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 224.0956 328.5659 Tm +()Tj +/F6 1 Tf +0.8265 0 TD +(1)Tj +/F11 1 Tf +-0.8265 -1.0303 TD +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 238.7357 323.6175 Tm +(=)Tj +/F16 1 Tf +1.0393 2.01 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +1.0833 1.0067 TD +(2)Tj +/F9 1 Tf +0.4896 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 291.212 343.1113 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 302.5305 338.1629 Tm +(\))Tj +/F9 1 Tf +2.1933 0 TD +()Tj +/F1 1 Tf +0.7778 0 TD +(2)Tj +/F9 1 Tf +0.4896 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3807 0 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 365.1497 343.1113 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 376.4692 338.1629 Tm +(\))Tj +-9.3982 -2.4167 TD +(2)Tj +/F9 1 Tf +0.4896 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 291.212 314.2196 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 302.5305 309.2712 Tm +2.2014 Tc +(\)2)Tj +/F9 1 Tf +3.0718 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 360.5011 314.2196 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 371.8197 309.2712 Tm +(\))Tj +/F16 1 Tf +1.1863 3.21 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +11.0279 -0.21 TD +(\(8\))Tj +-36.6907 -3.6736 TD +[(W)81.6(e)-441.7(next)-441.7(relate)-441.7(the)-441.7(eigen)27.2(v)54.4(alue,)-470.5(eigen)27.1(v)27.2(ector)-441.6(pairs)-441.7(of)]TJ +/F12 1 Tf +22.7968 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 359.7988 277.9058 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 372.3596 279.6991 Tm +[(to)-441.7(those)-441.7(of)]TJ +/F12 1 Tf +5.2198 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 442.8234 277.9058 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 451.7041 279.6991 Tm +[(.)-781(Let)]TJ +/F7 1 Tf +2.9224 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 493.4705 277.9058 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 503.1332 279.6991 Tm +0.0272 Tc +[(be)-414.5(a)27.2(n)]TJ +-35.4603 -1.2083 TD +0 Tc +[(eigen)27.1(v)54.4(alue)-219.4(of)]TJ +/F12 1 Tf +5.5792 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 153.9596 263.46 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 163.8615 265.2533 Tm +[(and)-219.3(let)]TJ +/F11 1 Tf +3.1041 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 208.5898 263.46 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 216.2919 265.2533 Tm +0.2778 Tc +(=\()Tj +/F7 1 Tf +1.4202 0 TD +0 Tc +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 238.4608 263.46 Tm +(1)Tj +/F8 1 Tf +0.5312 0 TD +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 247.0765 265.2533 Tm +0.1667 Tc +[(,...)-166.6(,q)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 280.4802 263.46 Tm +0 Tc +(nj)Tj +/F1 1 Tf +11.9552 0 0 11.9552 290.0005 265.2533 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 294.5524 269.591 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 302.0105 265.2533 Tm +[(b)-27.2(e)-219.3(a)-219.3(corresp)-27.3(onding)-219.3(eigen)27.1(v)27.2(ector,)-240.7(c)27.2(hosen)-219.3(so)-219.3(that)]TJ +-18.6372 -1.2083 TD +[(the)-382.5(set)-382.4(of)-382.5(eigen)27.2(v)27.2(ectors)-382.5(is)-382.5(orthonormal.)-603.5(Let)]TJ +/F11 1 Tf +19.0294 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 314.0264 249.0142 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 322.8693 250.8075 Tm +0.3732 Tc +(=\()Tj +/F9 1 Tf +1.5156 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 359.3654 249.0142 Tm +(1)Tj +/F8 1 Tf +0.5313 0 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 367.9811 250.8075 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +(,...)Tj +/F9 1 Tf +1.7546 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 411.8875 249.0142 Tm +(nj)Tj +/F1 1 Tf +11.9552 0 0 11.9552 421.4077 250.8075 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 449.5811 249.0142 Tm +(1)Tj +/F8 1 Tf +0.5312 0 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 458.1968 250.8075 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 509.34 249.0142 Tm +(nj)Tj +/F1 1 Tf +11.9552 0 0 11.9552 518.8603 250.8075 Tm +(\)\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 527.9642 255.1452 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 236.3616 Tm +[(b)-27.3(e)-326.3(the)-326.4(corresp)-27.3(onding)-326.5(eigen)27.2(v)27.2(ector)-326.5(expressed)-326.4(as)-326.4(a)-326.4(real)-326.4(2)]TJ +/F7 1 Tf +23.1952 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector.)]TJ +-23.7797 -1.5417 TD +[(W)81.6(e)-304.8(no)27.2(w)-304.8(sho)27.2(w)-304.8(that)]TJ +/F11 1 Tf +8.1872 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 184.4045 216.1375 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 192.4304 217.9307 Tm +[(is)-304.8(an)-304.8(eigen)27.1(v)27.2(ector)-304.8(of)]TJ +/F12 1 Tf +8.4595 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 301.6249 216.1375 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 314.1499 217.9307 Tm +[(with)-304.8(the)-304.8(eigen)27.2(v)54.4(alue)]TJ +/F7 1 Tf +8.53 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 422.9559 216.1375 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 427.3385 217.9307 Tm +(/)Tj +/F1 1 Tf +0.4896 0 TD +[(2.)-427.9(Using)-304.8(\(7\))-304.8(\(whic)27.1(h)]TJ +ET +79.17 206.769 181.438 -0.398 re +f +BT +/F17 1 Tf +6.9738 0 0 6.9738 92.6635 198.6869 Tm +(3)Tj +/F3 1 Tf +9.9626 0 0 9.9626 97.1327 195.0715 Tm +[(In)-379.7(more)-379.6(detail,)]TJ +/F20 1 Tf +6.959 0 TD +(I)Tj +/F19 1 Tf +6.9738 0 0 6.9738 169.2294 193.5771 Tm +(n)Tj +/F3 1 Tf +9.9626 0 0 9.9626 178.1898 195.0715 Tm +(=)Tj +/F20 1 Tf +1.1327 0 TD +(K)Tj +/F11 1 Tf +6.9738 0 0 6.9738 196.3935 193.5771 Tm +(Z)Tj +/F20 1 Tf +9.9626 0 0 9.9626 202.8254 195.0715 Tm +(K)Tj +/F24 1 Tf +6.9738 0 0 6.9738 209.7444 199.3335 Tm +()Tj +/F17 1 Tf +0.8929 0 TD +(1)Tj +/F11 1 Tf +-0.8929 -1.0337 TD +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 224.2232 195.0715 Tm +[(implies)-379.6(that)]TJ +/F9 1 Tf +5.6537 0 TD +()Tj +/F3 1 Tf +0.7223 0 TD +(\()Tj +/F20 1 Tf +0.3888 0 TD +(K)Tj +/F11 1 Tf +6.9738 0 0 6.9738 298.5375 193.5771 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 304.9704 195.0715 Tm +(\))Tj +/F9 1 Tf +0.3889 0 TD +()Tj +/F3 1 Tf +0.7222 0 TD +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F24 1 Tf +6.9738 0 0 6.9738 326.8324 199.3335 Tm +()Tj +/F17 1 Tf +0.8929 0 TD +(1)Tj +/F11 1 Tf +-0.8929 -1.0337 TD +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 337.5283 195.0715 Tm +(\))Tj +/F9 1 Tf +0.642 0 TD +0.2531 Tc +()Tj +/F3 1 Tf +1.7531 0 TD +0 Tc +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F11 1 Tf +6.9738 0 0 6.9738 372.1833 193.5771 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 378.6152 195.0715 Tm +(\))Tj +/F9 1 Tf +0.3889 0 TD +()Tj +/F3 1 Tf +0.7223 0 TD +(\()Tj +/F20 1 Tf +0.3888 0 TD +(K)Tj +/F24 1 Tf +6.9738 0 0 6.9738 400.4782 199.3335 Tm +()Tj +/F17 1 Tf +0.8929 0 TD +(1)Tj +/F11 1 Tf +-0.8929 -1.0337 TD +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 411.1741 195.0715 Tm +0.355 Tc +(\)=)Tj +/F20 1 Tf +1.8766 0 TD +0 Tc +(I)Tj +/F19 1 Tf +6.9738 0 0 6.9738 432.6376 193.5771 Tm +(n)Tj +/F3 1 Tf +9.9626 0 0 9.9626 441.8431 195.0715 Tm +(and)Tj +/F9 1 Tf +1.9908 0 TD +()Tj +/F3 1 Tf +0.7222 0 TD +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F11 1 Tf +6.9738 0 0 6.9738 479.6653 193.5771 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 486.0972 195.0715 Tm +(\))Tj +/F9 1 Tf +0.3889 0 TD +()Tj +/F3 1 Tf +0.7222 0 TD +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F24 1 Tf +6.9738 0 0 6.9738 507.9602 199.3335 Tm +()Tj +/F17 1 Tf +0.8929 0 TD +(1)Tj +/F11 1 Tf +-0.8929 -1.0337 TD +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 518.6561 195.0715 Tm +0.2531 Tc +(\)+)Tj +/F9 1 Tf +-44.1104 -1.2 TD +0 Tc +()Tj +/F3 1 Tf +0.7223 0 TD +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F11 1 Tf +6.9738 0 0 6.9738 97.1885 181.6219 Tm +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 103.6214 183.1163 Tm +(\))Tj +/F9 1 Tf +0.3889 0 TD +()Tj +/F3 1 Tf +0.7222 0 TD +(\()Tj +/F20 1 Tf +0.3889 0 TD +(K)Tj +/F24 1 Tf +6.9738 0 0 6.9738 125.4834 187.3783 Tm +()Tj +/F17 1 Tf +0.8929 0 TD +(1)Tj +/F11 1 Tf +-0.8929 -1.0337 TD +(Z)Tj +/F3 1 Tf +9.9626 0 0 9.9626 136.1793 183.1163 Tm +[(\))-277.8(=)-277.8(0)0(.)-444.4(With)-333.3(this,)-333.3(it)-333.3(is)-333.4(seen)-333.3(that)-333.3(the)-333.3(pro)-27.8(duct)-333.3(of)-333.3(\(6\))-333.3(and)-333.3(\(7\))-333.3(is)]TJ +/F20 1 Tf +26.8862 0 TD +(I)Tj +/F17 1 Tf +6.9738 0 0 6.9738 406.8045 181.6219 Tm +(2)Tj +/F19 1 Tf +0.5694 0 TD +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 303.0745 49.312 Tm +(5)Tj +ET +endstream +endobj +40 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F3 6 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F16 24 0 R +/F17 28 0 R +/F19 30 0 R +/F20 31 0 R +/F23 37 0 R +/F24 41 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +43 0 obj +<< +/Length 21939 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(dep)-27.2(ends)-326.4(on)-326.5(the)-326.3(circular)-326.5(symmetry)-326.5(of)]TJ +/F11 1 Tf +16.0582 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +(\),)Tj +/F12 1 Tf +-8.9356 -3.1712 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 182.5853 668.3387 Tm +(V)Tj +11.9552 0 0 11.9552 191.467 670.132 Tm +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 198.7925 668.3387 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 213.1377 670.132 Tm +(=)Tj +/F16 1 Tf +1.5948 2.0101 TD +()Tj +0 -1.8001 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.3512 689.3848 Tm +(1)Tj +ET +246.33 687.928 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.3512 680.5549 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.7818 684.6775 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.0281 682.8842 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 280.3088 684.6775 Tm +(\))Tj +/F9 1 Tf +2.1933 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 317.0232 689.3848 Tm +(1)Tj +ET +317.01 687.928 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 317.0232 680.5549 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 322.4528 684.6775 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 343.6991 682.8842 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 350.9799 684.6775 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.3512 660.4932 Tm +(1)Tj +ET +246.33 659.008 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.3512 651.6633 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.7818 655.7858 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.0281 653.9926 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 280.3088 655.7858 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 312.3736 660.4932 Tm +(1)Tj +ET +312.33 659.008 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 312.3736 651.6633 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 317.8042 655.7858 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 339.0506 653.9926 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 346.3312 655.7858 Tm +(\))Tj +/F16 1 Tf +1.1863 3.2101 TD +()Tj +0 -1.8001 TD +()Tj +0.8333 1.8001 TD +()Tj +0 -1.8001 TD +()Tj +/F9 1 Tf +1.0833 1.0067 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 404.2321 682.8842 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 408.6147 684.6775 Tm +(\))Tj +/F9 1 Tf +-2.1068 -2.4167 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 404.2321 653.9926 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 408.6147 655.7858 Tm +(\))Tj +/F16 1 Tf +0.7974 3.2101 TD +()Tj +0 -1.8001 TD +()Tj +/F1 1 Tf +-17.1483 -5.96 TD +(=)Tj +/F16 1 Tf +1.5948 2.0101 TD +()Tj +0 -1.8001 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.3512 620.6426 Tm +(1)Tj +ET +246.33 619.168 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.3512 611.8127 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.7818 615.9352 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.0281 614.142 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 280.3088 615.9352 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 305.6658 614.142 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 310.0473 615.9352 Tm +(\))Tj +/F9 1 Tf +0.603 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 330.407 620.6426 Tm +(1)Tj +ET +330.45 619.168 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 330.407 611.8127 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 335.8366 615.9352 Tm +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 357.084 614.142 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 364.3636 615.9352 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 389.7206 614.142 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 394.1031 615.9352 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.4488 591.751 Tm +(1)Tj +ET +246.45 590.248 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.4488 582.921 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.8785 587.0436 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3807 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.1248 585.2503 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 280.4055 587.0436 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 305.7624 585.2503 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 310.144 587.0436 Tm +0.2223 Tc +(\)+)Tj +/F6 1 Tf +7.9701 0 0 7.9701 330.3103 591.751 Tm +0 Tc +(1)Tj +ET +330.33 590.248 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 330.3103 582.921 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 335.74 587.0436 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 356.9863 585.2503 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 364.267 587.0436 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 389.6239 585.2503 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 394.0065 587.0436 Tm +(\))Tj +/F16 1 Tf +0.8055 3.2101 TD +()Tj +0 -1.8001 TD +()Tj +/F1 1 Tf +-15.9344 -6.0859 TD +(=)Tj +/F16 1 Tf +1.5948 2.01 TD +()Tj +0 -1.8 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.3512 550.394 Tm +(1)Tj +ET +246.33 548.968 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.3512 541.5651 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.7818 545.6877 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.0281 543.8944 Tm +(Z)Tj +11.9552 0 0 11.9552 280.3088 545.6877 Tm +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 287.9263 543.8944 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 292.3088 545.6877 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 246.3512 521.5024 Tm +(1)Tj +ET +246.33 520.048 4.234 -0.478 re +f +BT +7.9701 0 0 7.9701 246.3512 512.6735 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 251.7818 516.796 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F12 1 Tf +0.3808 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 273.0281 515.0027 Tm +(Z)Tj +11.9552 0 0 11.9552 280.3088 516.796 Tm +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 287.9263 515.0027 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 292.3088 516.796 Tm +(\))Tj +/F16 1 Tf +0.7974 3.21 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +0.9444 -0.21 TD +(=)Tj +/F16 1 Tf +1.0393 2.01 TD +()Tj +0 -1.8 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 339.7061 551.7709 Tm +()Tj +/F15 1 Tf +5.9776 0 0 5.9776 344.6456 550.5554 Tm +(j)Tj +ET +339.69 548.968 8.843 -0.478 re +f +BT +/F6 1 Tf +7.9701 0 0 7.9701 342.0095 541.5651 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 349.7435 545.6877 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 370.5485 543.8944 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 374.931 545.6877 Tm +(\))Tj +/F8 1 Tf +7.9701 0 0 7.9701 339.7061 521.3729 Tm +()Tj +/F15 1 Tf +5.9776 0 0 5.9776 344.6456 520.1574 Tm +(j)Tj +ET +339.69 518.488 8.843 -0.478 re +f +BT +/F6 1 Tf +7.9701 0 0 7.9701 342.0095 511.1671 Tm +(2)Tj +/F9 1 Tf +11.9552 0 0 11.9552 349.7435 515.2897 Tm +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 370.5485 513.4964 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 374.931 515.2897 Tm +(\))Tj +/F16 1 Tf +0.7974 3.336 TD +()Tj +0 -1.8 TD +()Tj +/F1 1 Tf +1.1111 -0.21 TD +(=)Tj +/F7 1 Tf +1.306 0.6765 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 420.1893 537.4366 Tm +(j)Tj +ET +413.37 534.328 11.211 -0.478 re +f +BT +/F1 1 Tf +11.9552 0 0 11.9552 416.0399 522.941 Tm +(2)Tj +/F11 1 Tf +0.8137 0.686 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 433.0929 529.349 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 517.8431 531.1422 Tm +(\(9\))Tj +-36.6907 -3.2417 TD +[(In)-310.5(the)-310.6(p)-27.2(e)0(n)27.2(ultimate)-310.6(step,)-313.7(w)27.2(e)-310.5(used)-310.6(the)-310.5(facts)-310.5(that)]TJ +/F7 1 Tf +20.357 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 329.3997 490.5943 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 337.4944 492.3876 Tm +[(is)-310.5(real)-310.5(and)-310.6(that)]TJ +/F11 1 Tf +6.8504 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 427.0107 490.5943 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 435.1044 492.3876 Tm +[(is)-310.5(an)-310.5(eigen)27.2(v)27.2(ector)-310.5(of)]TJ +/F12 1 Tf +-29.7699 -1.2083 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 87.2608 476.1484 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 94.5405 477.9417 Tm +(.)Tj +-1.2832 -1.5417 TD +[(This)-337.2(sp)-27.2(ecies)]TJ +/F7 1 Tf +6.0487 0 TD +(n)Tj +/F1 1 Tf +0.9216 0 TD +[(of)-337.1(the)-337.2(eigen)27.2(v)54.4(alue/eigen)27.1(v)27.2(ector)-337.1(pairs)-337.2(of)]TJ +/F12 1 Tf +16.2967 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 365.4207 457.7176 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 374.3024 459.5108 Tm +[(,)-339.8(but)-337.1(what)-337.1(ab)-27.2(out)-337.2(the)-337.1(rest?)-467.4(W)81.7(e)]TJ +-24.6841 -1.2083 TD +[(next)-331.2(sho)27.2(w)-331(that)-331.1(the)-331.1(eigen)27.1(v)54.4(alues)-331.1(of)]TJ +/F12 1 Tf +14.6447 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 262.3392 443.2718 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 275.1781 445.065 Tm +[(come)-331.1(in)-331(pairs.)-449.3(F)81.6(o)0(r)-331.1(eac)27.2(h)-331(eigen)27.2(v)54.4(alue)]TJ +/F7 1 Tf +15.0972 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 462.4957 443.2718 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 470.8364 445.065 Tm +(of)Tj +/F12 1 Tf +1.1198 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 492.2839 443.2718 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 499.5637 445.065 Tm +[(,)-332.3(there)]TJ +-35.1617 -1.2083 TD +[(are)-397.4(t)27.2(w)27.2(o)-397.4(eigen)27.2(v)54.4(alues)-397.3(of)]TJ +/F12 1 Tf +9.945 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 206.1539 428.826 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 215.0356 430.6192 Tm +[(,)-415.1(eac)27.2(h)-397.4(equal)-397.5(to)]TJ +/F7 1 Tf +6.8838 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 304.1614 428.826 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 308.543 430.6192 Tm +(/)Tj +/F1 1 Tf +0.4896 0 TD +[(2.)-648.2(The)-397.4(corresp)-27.3(onding)-397.4(eigen)27.1(v)27.2(ectors)-397.4(can)-397.4(b)-27.2(e)]TJ +-19.6732 -1.2083 TD +[(c)27.2(hosen)-405.8(as)]TJ +/F11 1 Tf +4.4942 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 140.254 414.3801 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 149.4864 416.1733 Tm +(and)Tj +/F11 1 Tf +1.9832 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 185.6149 414.3801 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 194.8473 416.1733 Tm +(where)Tj +/F11 1 Tf +2.908 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 242.0304 414.3801 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 251.3475 416.1733 Tm +0.4128 Tc +(=\()Tj +/F9 1 Tf +1.5552 0 TD +0 Tc +()Tj +/F1 1 Tf +1.5 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 297.615 414.3801 Tm +(1)Tj +/F8 1 Tf +0.5312 0 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 306.2307 416.1733 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +1.5 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 369.0999 414.3801 Tm +(nj)Tj +/F1 1 Tf +11.9552 0 0 11.9552 378.6202 416.1733 Tm +(\))Tj +/F7 1 Tf +0.3807 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 409.2214 414.3801 Tm +(1)Tj +/F8 1 Tf +0.5312 0 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 417.8381 416.1733 Tm +(\))Tj +/F7 1 Tf +0.3807 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 471.4082 414.3801 Tm +(nj)Tj +/F1 1 Tf +11.9552 0 0 11.9552 480.9285 416.1733 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 485.4805 420.5111 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 490.3163 416.1733 Tm +[(.)-673.2(I)0(t)-405.7(can)]TJ +-34.3882 -1.2083 TD +[(b)-27.3(e)-373.1(seen)-373.1(that)]TJ +/F11 1 Tf +5.7214 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 160.0189 399.9342 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 168.8618 401.7275 Tm +[(is)-373.1(the)-373.2(represen)27.1(tation)-373.2(of)]TJ +/F7 1 Tf +10.3702 0 TD +(i)Tj +/F11 1 Tf +0.3341 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 304.4503 399.9342 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 313.2932 401.7275 Tm +[(as)-373.1(a)-373.2(real)-373.2(2)]TJ +/F7 1 Tf +4.5519 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector.)-575.5(It)-373.2(can)-373.1(also)-373.2(b)-27.2(e)-373.2(v)27.2(eried)]TJ +-24.7173 -1.2083 TD +[(directly)-380.8(that)]TJ +/F11 1 Tf +5.7933 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 155.7848 385.4885 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 164.7183 387.2817 Tm +(and)Tj +/F11 1 Tf +1.9583 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 200.5479 385.4885 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 209.4814 387.2817 Tm +[(\(as)-380.7(v)27.2(ectors)-380.8(in)]TJ +/F23 1 Tf +6.212 0 TD +(R)Tj +/F6 1 Tf +7.9701 0 0 7.9701 292.3806 391.6194 Tm +(2)Tj +/F8 1 Tf +0.5313 0 TD +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 302.2516 387.2817 Tm +[(\))-380.7(are)-380.7(orthonormal.)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 397.8491 391.6194 Tm +(4)Tj +/F1 1 Tf +11.9552 0 0 11.9552 409.7325 387.2817 Tm +[(Next,)-394.3(the)-380.7(calculation)-380.8(in)]TJ +-27.6477 -1.2083 TD +[(\(9\),)-289.4(with)]TJ +/F11 1 Tf +3.9966 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 134.3053 371.0426 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 142.0364 372.8358 Tm +[(replaced)-280.2(b)27.2(y)]TJ +/F11 1 Tf +5.1297 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 215.7798 371.0426 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 220.1624 372.8358 Tm +[(,)-289.3(sho)27.2(ws)-280.2(that)]TJ +/F11 1 Tf +5.4027 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 297.1706 371.0426 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 304.9016 372.8358 Tm +[(is)-280.1(an)-280.1(eigen)27.2(v)27.2(ector)-280.2(of)]TJ +/F12 1 Tf +8.3608 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 412.9166 371.0426 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 425.1467 372.8358 Tm +[(with)-280.1(eigen)27.1(v)54.4(alue)]TJ +/F7 1 Tf +6.8159 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 513.4606 371.0426 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 517.8431 372.8358 Tm +(/)Tj +/F1 1 Tf +0.4896 0 TD +(2.)Tj +-37.1803 -1.2083 TD +[(Finally)81.5(,)-388.4(let)]TJ +/F11 1 Tf +5.0482 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 147.1691 356.5967 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 156.0468 358.39 Tm +(and)Tj +/F11 1 Tf +1.9536 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 187.0197 356.5967 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 196.6356 358.39 Tm +[(b)-27.2(e)-376(orthonormal)-376.1(eigen)27.1(v)27.2(ectors)-376.1(of)]TJ +/F12 1 Tf +13.7218 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 368.7412 356.5967 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 376.0219 358.39 Tm +[(.)-584.1(Then)-376.1(the)-376(corresp)-27.3(onding)-376.1(real)]TJ +-24.8279 -1.2083 TD +(2)Tj +/F7 1 Tf +0.4896 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ectors)]TJ +/F11 1 Tf +3.6501 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 143.0037 342.151 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 151.2887 343.9442 Tm +(and)Tj +/F11 1 Tf +1.9039 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 181.3758 342.151 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 190.397 343.9442 Tm +[(are)-326.5(orthonormal,)-326.5(as)-326.4(sho)27.2(wn)-326.4(b)27.1(y)]TJ +/F11 1 Tf +-1.4615 -2.0754 TD +(r)Tj +/F13 1 Tf +5.9776 0 0 5.9776 180.2511 324.0688 Tm +(T)Tj +/F8 1 Tf +7.9701 0 0 7.9701 180.2511 316.1774 Tm +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 185.0869 319.1322 Tm +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 192.4124 317.339 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 200.8528 319.1322 Tm +(=)Tj +/F9 1 Tf +1.0393 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F13 1 Tf +5.9776 0 0 5.9776 234.0832 324.0688 Tm +(T)Tj +/F8 1 Tf +7.9701 0 0 7.9701 234.0832 316.1774 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 238.9191 319.1322 Tm +(\))Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 264.277 317.339 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 269.3958 319.1322 Tm +0.2222 Tc +(\)+)Tj +/F9 1 Tf +1.5868 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F13 1 Tf +5.9776 0 0 5.9776 309.1716 324.0688 Tm +(T)Tj +/F8 1 Tf +7.9701 0 0 7.9701 309.1716 316.1774 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 314.0075 319.1322 Tm +(\))Tj +/F9 1 Tf +0.3807 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 339.3644 317.339 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 344.4842 319.1322 Tm +0.2778 Tc +(\)=)Tj +/F9 1 Tf +1.6979 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 385.5871 324.8 Tm +()Tj +/F8 1 Tf +0 -1.0955 TD +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 389.9696 319.1322 Tm +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 397.5871 317.339 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 402.7068 319.1322 Tm +0.2778 Tc +(\)=)Tj +/F7 1 Tf +1.6979 0 TD +0 Tc +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 428.1903 317.339 Tm +-0.0007 Tc +(j,k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 295.4172 Tm +0 Tc +[(Similarly)81.5(,)-642.2(\()]TJ +/F11 1 Tf +5.0484 0 TD +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 146.8802 293.6239 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 151.2627 295.4172 Tm +(,)Tj +/F11 1 Tf +0.4387 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 168.9245 293.6239 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 174.0443 295.4172 Tm +[(\))-579.1(are)-579.1(orthonormal)-579.1(and)-579(\()]TJ +/F11 1 Tf +11.2373 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 320.806 293.6239 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 325.1885 295.4172 Tm +(,)Tj +/F11 1 Tf +0.4386 0 TD +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 342.8503 293.6239 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 347.9701 295.4172 Tm +[(\))-579(are)-579.1(orthonormal.)-1193.2(Th)27.2(us)-579.1(the)-579(set)]TJ +-22.4815 -1.2083 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(r)Tj +/F6 1 Tf +7.9701 0 0 7.9701 91.0785 279.1781 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 95.8107 280.9713 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F11 1 Tf +2.3599 0 TD +0 Tc +(r)Tj +/F8 1 Tf +7.9701 0 0 7.9701 131.3504 279.1781 Tm +(n)Tj +/F7 1 Tf +11.9552 0 0 11.9552 136.9863 280.9713 Tm +(,)Tj +/F11 1 Tf +0.4387 0 TD +(m)Tj +/F6 1 Tf +7.9701 0 0 7.9701 154.6481 279.1781 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 159.3803 280.9713 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F11 1 Tf +2.3599 0 TD +0 Tc +(m)Tj +/F8 1 Tf +7.9701 0 0 7.9701 200.012 279.1781 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 205.6478 280.9713 Tm +[(\))-326.4(i)0(s)-326.4(a)0(n)-326.5(orthonormal)-326.5(set)-326.4(and)-326.4(spans)]TJ +/F23 1 Tf +14.7635 0 TD +(R)Tj +/F6 1 Tf +7.9701 0 0 7.9701 390.7826 285.3091 Tm +(2)Tj +/F8 1 Tf +0.5312 0 TD +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 400.6526 280.9713 Tm +(.)Tj +/F5 1 Tf +17.2154 0 0 17.2154 79.2 237.4486 Tm +[(4)-1125(The)-700.2(probabilit)31.3(y)-700.2(densit)31.3(y)-700.2(o)0(f)-700.2(circularly-symmetric)]TJ +1.6875 -1.2731 TD +[(Gaussian)-375(v)31.3(ectors)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 185.2612 Tm +[(Assuming)-281.6(that)]TJ +/F12 1 Tf +6.5302 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 165.329 183.468 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 175.9751 185.2612 Tm +[(is)-281.5(p)-27.2(ositiv)27.1(e)-281.5(denite,)-290.6(all)-281.6(its)-281.5(eignev)54.4(alues)]TJ +/F7 1 Tf +15.9176 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 373.1009 183.468 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 377.8332 185.2612 Tm +0.1667 Tc +[(,...)-166.7(,)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 412.8748 183.468 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 421.877 185.2612 Tm +[(are)-281.5(p)-27.2(ositiv)27.1(e,)-290.5(so)-281.5(all)-281.5(the)]TJ +-28.6635 -1.2083 TD +[(eigen)27.1(v)54.4(alues)-367.4(of)]TJ +/F12 1 Tf +6.2615 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 162.1171 169.0222 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 175.3893 170.8154 Tm +[(are)-367.4(also)-367.3(p)-27.2(ositiv)27.1(e)-367.3(and)]TJ +/F12 1 Tf +9.2863 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 294.4688 169.0222 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 307.741 170.8154 Tm +[(is)-367.3(p)-27.3(ositiv)27.2(e)-367.3(denite.)-558.1(The)-367.4(probabilit)27.1(y)-367.3(densit)27.2(y)]TJ +-19.1165 -1.2083 TD +(of)Tj +/F11 1 Tf +1.0897 0 TD +(Z)Tj +/F1 1 Tf +1.1518 0 TD +[(is)-300.9(dened)-300.9(as)-300.9(the)-300.8(join)27.1(t)-300.8(probabilit)27.1(y)-300.9(densit)27.2(y)-300.9(o)0(f)-300.8(its)-300.9(real)-300.9(and)-300.9(imaginary)-301(parts,)-306(so)-300.9(it)-300.8(is)-300.9(the)]TJ +-2.2415 -1.2083 TD +[(probabilit)27.1(y)-326.4(densit)27.2(y)-326.4(asso)-27.3(ciated)-326.4(with)]TJ +/F11 1 Tf +15.2749 0 TD +(V)Tj +/F1 1 Tf +1.0518 0 TD +[(.)-435.2(Since)-326.4(this)-326.5(is)-326.4(join)27.2(tly)-326.4(Gaussian)-326.5(and)-326.4(non-singular,)]TJ +/F7 1 Tf +-5.9153 -2.5732 TD +(f)Tj +/F11 1 Tf +7.9701 0 0 7.9701 209.4396 109.3669 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 218.3203 111.1601 Tm +(\()Tj +/F11 1 Tf +0.3808 0 TD +(v)Tj +/F1 1 Tf +0.6432 0 TD +0.2778 Tc +(\)=)Tj +4.9794 0.6765 TD +0 Tc +(1)Tj +ET +252.09 114.328 81.923 -0.478 re +f +BT +11.9552 0 0 11.9552 252.0578 101.2971 Tm +(\(2)Tj +/F7 1 Tf +0.8704 0 TD +()Tj +/F1 1 Tf +0.5913 0 TD +(\))Tj +/F8 1 Tf +7.9701 0 0 7.9701 274.0852 104.7511 Tm +(n)Tj +/F16 1 Tf +11.9552 0 0 11.9552 279.7211 111.5188 Tm +( )Tj +ET +291.69 112.048 42.304 -0.478 re +f +BT +/F1 1 Tf +11.9552 0 0 11.9552 291.6762 101.2971 Tm +(det\()Tj +/F12 1 Tf +1.7408 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 320.547 99.5038 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 329.4277 101.2971 Tm +(\))Tj +0.6475 0.825 TD +(exp)Tj +/F9 1 Tf +1.7626 0.6765 TD +()Tj +/F11 1 Tf +0.7778 0 TD +(v)Tj +/F13 1 Tf +5.9776 0 0 5.9776 375.2299 123.5865 Tm +(T)Tj +/F12 1 Tf +11.9552 0 0 11.9552 380.0667 119.2478 Tm +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 388.1266 124.1963 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(V)Tj +11.9552 0 0 11.9552 399.4451 119.2478 Tm +(v)Tj +ET +358.29 114.328 48.896 -0.478 re +f +BT +/F1 1 Tf +11.9552 0 0 11.9552 379.7619 102.9599 Tm +(2)Tj +11.0603 0.6859 TD +(\(10\))Tj +ET +79.17 90.609 181.438 -0.398 re +f +BT +/F17 1 Tf +6.9738 0 0 6.9738 92.6635 82.8155 Tm +(4)Tj +/F3 1 Tf +9.9626 0 0 9.9626 97.1327 79.2 Tm +[(One)-333.4(could)-333.2(equally)-333.4(w)27.8(ell)-333.4(replace)]TJ +/F11 1 Tf +13.6417 0 TD +(r)Tj +/F19 1 Tf +6.9738 0 0 6.9738 239.1452 77.7056 Tm +(j)Tj +/F3 1 Tf +9.9626 0 0 9.9626 246.664 79.2 Tm +(with)Tj +/F22 1 Tf +2.2778 0 TD +(e)Tj +/F19 1 Tf +6.9738 0 0 6.9738 273.9955 82.8155 Tm +(i)Tj +/F11 1 Tf +9.9626 0 0 9.9626 282.1031 79.2 Tm +(r)Tj +/F19 1 Tf +6.9738 0 0 6.9738 288.2072 77.7056 Tm +(j)Tj +/F3 1 Tf +9.9626 0 0 9.9626 295.726 79.2 Tm +[(for)-333.4(an)27.8(y)-333.3(real)]TJ +/F22 1 Tf +5.3667 0 TD +()Tj +/F3 1 Tf +0.9292 0 TD +[(and)-333.3(replace)]TJ +/F11 1 Tf +5.3361 0 TD +(m)Tj +/F19 1 Tf +6.9738 0 0 6.9738 421.9597 77.7056 Tm +(j)Tj +/F3 1 Tf +9.9626 0 0 9.9626 429.4785 79.2 Tm +(with)Tj +/F22 1 Tf +2.2778 0 TD +(e)Tj +/F19 1 Tf +6.9738 0 0 6.9738 456.81 82.8155 Tm +(i)Tj +/F11 1 Tf +9.9626 0 0 9.9626 464.9176 79.2 Tm +(m)Tj +/F19 1 Tf +6.9738 0 0 6.9738 475.2648 77.7056 Tm +(j)Tj +/F3 1 Tf +9.9626 0 0 9.9626 479.463 79.2 Tm +(.)Tj +/F1 1 Tf +11.9552 0 0 11.9552 303.0745 49.312 Tm +(6)Tj +ET +endstream +endobj +44 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F3 6 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F15 23 0 R +/F16 24 0 R +/F17 28 0 R +/F19 30 0 R +/F22 33 0 R +/F23 37 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +46 0 obj +<< +/Length 16003 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(This)-441.9(can)-441.8(b)-27.2(e)-441.9(expressed)-441.8(directly)-441.9(in)-441.9(terms)-441.9(of)-441.8(the)-441.8(complex)-441.9(random)]TJ +/F7 1 Tf +28.6808 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector)]TJ +/F11 1 Tf +3.3792 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +[(.)-781.5(F)81.6(or)-441.8(an)27.2(y)]TJ +-33.4956 -1.2083 TD +[(sample)-306.6(v)54.4(alue)]TJ +/F11 1 Tf +5.759 0 TD +(z)Tj +/F1 1 Tf +0.936 0 TD +(of)Tj +/F11 1 Tf +1.0952 0 TD +(Z)Tj +/F1 1 Tf +0.8509 0 TD +[(,)-310.5(the)-306.5(corresp)-27.3(onding)-306.6(real)-306.5(2)]TJ +/F7 1 Tf +10.891 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector)-306.5(is)]TJ +/F11 1 Tf +4.2087 0 TD +(v)Tj +/F13 1 Tf +5.9776 0 0 5.9776 377.7046 697.9377 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 385.861 693.599 Tm +0.2778 Tc +(=\()Tj +/F9 1 Tf +1.4202 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F11 1 Tf +0.3807 0 TD +(z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 423.5507 697.9377 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 428.3866 693.599 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F11 1 Tf +0.3808 0 TD +(z)Tj +/F13 1 Tf +5.9776 0 0 5.9776 458.8952 697.9377 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 463.731 693.599 Tm +[(\)\).)-428.6(Using)-306.5(this)]TJ +-32.1644 -1.2083 TD +[(and)-326.4(the)-326.4(expression)-326.5(in)-326.4(\(8\))-326.4(for)]TJ +/F12 1 Tf +12.5223 0 TD +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 236.9664 684.1017 Tm +()Tj +/F6 1 Tf +0.8265 0 TD +(1)Tj +/F11 1 Tf +-0.8265 -1.0304 TD +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 248.2859 679.1532 Tm +(,)Tj +/F11 1 Tf +0.65 -1.7863 TD +(v)Tj +/F13 1 Tf +5.9776 0 0 5.9776 263.748 662.7347 Tm +(T)Tj +/F12 1 Tf +11.9552 0 0 11.9552 268.5838 657.7982 Tm +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 276.6446 662.7467 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(V)Tj +11.9552 0 0 11.9552 287.9631 657.7982 Tm +(v)Tj +/F1 1 Tf +0.9211 0 TD +0.2778 Tc +(=2)Tj +/F11 1 Tf +1.5289 0 TD +0 Tc +(z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 324.7781 662.7347 Tm +()Tj +/F12 1 Tf +11.9552 0 0 11.9552 329.0401 657.7982 Tm +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 337.0999 662.7467 Tm +()Tj +/F6 1 Tf +0.8265 0 TD +(1)Tj +/F11 1 Tf +-0.8265 -1.0303 TD +(Z)Tj +11.9552 0 0 11.9552 348.4194 657.7982 Tm +(z)Tj +/F1 1 Tf +13.682 0 TD +(\(11\))Tj +-36.2011 -1.7862 TD +[(Establishing)-311.5(this)-311.5(equalit)27.1(y)-311.4(also)-311.4(uses)-311.5(the)-311.4(fact)-311.4(that)]TJ +/F11 1 Tf +20.8694 0 TD +(z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 336.2222 640.7821 Tm +()Tj +/F12 1 Tf +11.9552 0 0 11.9552 340.4842 636.4443 Tm +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 348.5439 641.3918 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +11.9552 0 0 11.9552 359.8625 636.4443 Tm +(z)Tj +/F1 1 Tf +0.9409 0 TD +[(is)-311.4(real.)-430.3(W)81.6(e)-311.4(no)27.2(w)-311.4(recall)-311.5(that)-311.4(eac)27.2(h)]TJ +-24.4172 -1.2083 TD +[(eigen)27.1(v)54.4(alue)]TJ +/F7 1 Tf +4.6782 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 141.9577 620.2053 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 150.2416 621.9985 Tm +(of)Tj +/F12 1 Tf +1.1152 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 171.6334 620.2053 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 182.8155 621.9985 Tm +[(corresp)-27.3(onds)-326.4(to)-326.4(t)27.2(w)27.3(o)-326.4(eigen)27.1(v)54.4(alues,)-326.5(b)-27.2(oth)]TJ +/F7 1 Tf +16.0637 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 381.6877 620.2053 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 386.0693 621.9985 Tm +(/)Tj +/F1 1 Tf +0.4896 0 TD +[(2,)-326.4(of)]TJ +/F12 1 Tf +2.2032 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 426.3213 620.2053 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 435.202 621.9985 Tm +0.4352 Tc +[(.T)435.2(h)462.4(u)435.2(s)]TJ +-15.8762 -1.7863 TD +0 Tc +(det\()Tj +/F12 1 Tf +1.7407 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 274.2705 598.8503 Tm +(V)Tj +/F1 1 Tf +11.9552 0 0 11.9552 283.1512 600.6436 Tm +0.2778 Tc +(\)=2)Tj +/F6 1 Tf +7.9701 0 0 7.9701 309.3031 605.5801 Tm +0 Tc +(2)Tj +/F8 1 Tf +0.5312 0 TD +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 319.1731 600.6436 Tm +(\(det)Tj +/F12 1 Tf +1.9074 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 350.0364 598.8503 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 357.317 600.6436 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 361.869 605.5801 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 511.9901 600.6436 Tm +(\(12\))Tj +-36.2011 -1.7863 TD +[(Substituting)-326.5(these)-326.4(relations)-326.4(in)27.1(to)-326.4(\(10\),)-326.4(w)27.2(e)-326.4(get)-326.4(an)-326.5(expression)-326.5(for)]TJ +/F7 1 Tf +27.0628 0 TD +(f)Tj +/F11 1 Tf +7.9701 0 0 7.9701 408.5111 577.4954 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 419.6932 579.2887 Tm +[(in)-326.4(terms)-326.4(of)]TJ +/F12 1 Tf +4.9828 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 487.3236 577.4954 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 494.6042 579.2887 Tm +(.)Tj +/F7 1 Tf +-23.312 -2.2322 TD +(f)Tj +/F11 1 Tf +7.9701 0 0 7.9701 221.6757 550.8094 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 228.9564 552.6028 Tm +(\()Tj +/F11 1 Tf +0.3808 0 TD +(z)Tj +/F1 1 Tf +0.6294 0 TD +0.2778 Tc +(\)=)Tj +3.8702 0.6766 TD +0 Tc +(1)Tj +ET +262.53 555.808 55.401 -0.478 re +f +BT +/F7 1 Tf +11.9552 0 0 11.9552 262.5275 544.4025 Tm +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 269.597 547.8566 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 277.2254 544.4025 Tm +(det\()Tj +/F12 1 Tf +1.7408 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 306.0962 542.6093 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 313.3768 544.4025 Tm +(\))Tj +0.6474 0.6859 TD +(exp\()Tj +/F9 1 Tf +1.8768 0 TD +()Tj +/F11 1 Tf +0.7778 0 TD +(z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 360.3776 557.5392 Tm +()Tj +/F12 1 Tf +11.9552 0 0 11.9552 364.6386 552.6028 Tm +(K)Tj +/F10 1 Tf +7.9701 0 0 7.9701 372.6994 557.5512 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F11 1 Tf +-0.8264 -1.0303 TD +(Z)Tj +11.9552 0 0 11.9552 384.0179 552.6028 Tm +(z)Tj +/F1 1 Tf +0.6294 0 TD +[(\))-9694.1(\(13\))]TJ +-26.1262 -2.3472 TD +[(Note)-257(that)-256.9(\(10\))-256.9(is)-256.9(v)54.4(alid)-256.9(for)-256.9(an)27.1(y)-256.9(join)27.2(tly-Gaussian)-257(2)]TJ +/F7 1 Tf +20.4643 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ector,)-270.9(whereas)-257(\(11\))-256.9(and)-256.9(\(12\),)-270.7(and)-257(th)27.3(us)]TJ +-21.0488 -1.2084 TD +[(\(13\),)-309.8(dep)-27.2(end)-305.6(on)-305.7(circular)-305.7(symmetry)81.5(.)-428.3(Next,)-309.9(supp)-27.2(ose)-305.7(an)-305.6(arbitrary)-305.8(random)-305.7(v)27.2(ector)]TJ +/F11 1 Tf +33.6998 0 TD +(Z)Tj +/F1 1 Tf +1.1566 0 TD +[(has)-305.7(the)]TJ +-34.8564 -1.2083 TD +[(densit)27.1(y)-243.7(i)0(n)-243.8(\()-0.1(13\).)-407.7(W)81.6(e)-243.7(ha)27.2(v)27.2(e)-243.8(seen)-243.8(that)-243.8(there)-243.8(is)-243.8(a)-243.8(circularly-symmetric)-244(Gaussian)-243.8(random)-243.9(v)27.2(ector)]TJ +T* +[(with)-370.3(the)-370.2(co)27.2(v)54.4(ariance)-370.3(matrix)]TJ +/F12 1 Tf +12.0068 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 230.8045 479.4112 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 238.0842 481.2045 Tm +[(,)-381.2(and)-370.2(this)-370.3(also)-370.2(has)-370.2(the)-370.2(densit)27.2(y)-370.2(i)0(n)-370.2(\()-0.1(13\).)-566.7(Since)-370.2(the)-370.2(densit)27.2(y)]TJ +-13.29 -1.2083 TD +[(fully)-294.4(describ)-27.2(es)-294.3(whether)]TJ +/F11 1 Tf +10.0597 0 TD +(Z)Tj +/F1 1 Tf +1.1453 0 TD +[(is)-294.3(circularly-symmetric)-294.5(join)27.2(tly)-294.3(Gaussian,)-300.8(w)27.2(e)-294.3(conclude)-294.3(that)-294.3(\(13\))]TJ +-11.2049 -1.2083 TD +[(is)-403.8(a)-403.8(necessary)-403.8(and)-403.8(sucien)27.2(t)-403.8(condition)-403.8(for)-403.8(a)-403.8(non-singular)-403.9(complex)-403.8(random)-403.8(v)27.2(ector)-403.8(to)-403.7(b)-27.2(e)]TJ +T* +[(circularly-symmetric)-326.6(join)27.1(tly)-326.4(Gaussian.)-435.3(The)-326.4(follo)27.1(wing)-326.4(theorem)-326.4(summarizes)-326.5(this.)]TJ +/F5 1 Tf +0 -1.6798 TD +[(Theorem)-375.1(3.)]TJ +/F14 1 Tf +6.1332 0 TD +[(Assume)-273.9(that)]TJ +/F11 1 Tf +5.4998 0 TD +(Z)Tj +/F14 1 Tf +0.9827 0 TD +[(is)-274(a)-273.9(c)50(omplex)-274(r)50(andom)]TJ +/F7 1 Tf +8.8583 0 TD +(n)Tj +/F14 1 Tf +0.5845 0 TD +[(-ve)50(ctor)-273.9(with)-273.9(an)-274(arbitr)50(ary)-273.9(non-singular)]TJ +-22.0585 -1.2083 TD +[(c)50(ovarianc)49.9(e)]TJ +/F21 1 Tf +4.8126 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 144.795 401.5452 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 150.943 403.3385 Tm +[(.)-450(Then)-350.1(\(13\))-350(is)-350(a)-350(n)0(e)50(c)50(essary)-350.1(and)-350(sucient)-350(c)50(ondition)-350.1(for)]TJ +/F11 1 Tf +23.6378 0 TD +(Z)Tj +/F14 1 Tf +1.0588 0 TD +[(to)-350.1(b)50(e)]TJ +/F9 1 Tf +2.3751 0 TD +0.0583 Tc +(CN)Tj +/F1 1 Tf +1.5527 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F21 1 Tf +0.4386 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 516.8618 401.5452 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 523.0097 403.3385 Tm +(\))Tj +/F14 1 Tf +0.3807 0 TD +(.)Tj +/F1 1 Tf +-37.5036 -2.0132 TD +(If)Tj +/F12 1 Tf +0.9187 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 98.2446 377.4774 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 108.7083 379.2707 Tm +[(is)-266.4(singular,)-278.4(then)-266.4(one)-266.4(or)-266.3(more)-266.4(comp)-27.3(onen)27.2(ts)-266.3(of)]TJ +/F11 1 Tf +18.6687 0 TD +(Z)Tj +/F1 1 Tf +1.1173 0 TD +[(are)-266.4(deterministic)-266.5(linear)-266.4(com)27.2(binations)]TJ +-22.2542 -1.2083 TD +[(of)-305.2(the)-305.3(other)-305.2(comp)-27.3(onen)27.2(ts,)-309.5(so)-305.2(the)-305.3(most)-305.3(con)27.2(v)27.2(enien)27.2(t)-305.2(w)27.2(a)27.2(y)-305.2(of)-305.3(sp)-27.2(ecifying)]TJ +/F11 1 Tf +28.5698 0 TD +(Z)Tj +/F1 1 Tf +1.1562 0 TD +[(is)-305.3(b)27.2(y)-305.2(rst)-305.3(remo)27.1(ving)]TJ +-29.7259 -1.2083 TD +[(comp)-27.3(onen)27.2(ts)-281.7(of)]TJ +/F11 1 Tf +6.4164 0 TD +(Z)Tj +/F1 1 Tf +1.1326 0 TD +[(that)-281.7(are)-281.6(deterministic)-281.7(linear)-281.7(com)27.2(binations)-281.7(of)-281.6(the)-281.7(remaining)-281.7(comp)-27.2(onen)27.1(ts)]TJ +-7.549 -1.2083 TD +[(and)-326.4(using)-326.5(\(13\))-326.4(for)-326.4(the)-326.4(remaining)-326.5(comp)-27.3(onen)27.2(ts.)]TJ +0 -1.5417 TD +[(As)-524.4(with)-524.4(real)-524.3(join)27.2(tly-Gaussian)-524.4(random)-524.4(v)27.2(ectors,)-573.9(it)-524.3(is)-524.3(often)-524.3(more)-524.4(insigh)27.2(tful)-524.3(to)-524.4(express)]TJ +0 -1.2083 TD +[(the)-442.1(probabilit)27.1(y)-442(densit)27.2(y)-442(i)0(n)-442(terms)-442(of)-442(the)-442.1(eigen)27.2(v)54.4(alues)-442(and)-442(eigenfunctions)-442.2(of)]TJ +/F12 1 Tf +32.4906 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 475.6902 301.2633 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 482.9709 303.0566 Tm +[(.)-782(Letting)]TJ +/F7 1 Tf +-33.7738 -1.2083 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 86.0294 286.8174 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 90.7616 288.6107 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 125.8032 286.8174 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 135.2877 288.6107 Tm +[(b)-27.2(e)-321.8(the)-321.9(eigen)27.2(v)54.4(alues)-321.9(of)]TJ +/F12 1 Tf +9.1805 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 253.1029 286.8174 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 264.2311 288.6107 Tm +[(\(rep)-27.2(eated)-321.9(as)-321.9(necessary\))-322(and)]TJ +/F11 1 Tf +12.1832 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 417.5024 286.8174 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 422.2346 288.6107 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F11 1 Tf +2.3599 0 TD +0 Tc +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 458.0663 286.8174 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 467.5507 288.6107 Tm +[(b)-27.2(e)-321.8(the)-321.9(corre-)]TJ +-32.4839 -1.2083 TD +[(sp)-27.2(onding)-326.5(eigenfunctions,)-326.5(w)27.2(e)-326.4(can)-326.4(use)-326.4(\(6\))-326.4(t)0(o)-326.4(express)]TJ +/F12 1 Tf +21.9495 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 349.6697 272.3716 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 360.8518 274.1649 Tm +(as)Tj +/F12 1 Tf +-8.1664 -2.5483 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 271.2807 241.9068 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 281.882 243.7001 Tm +(=)Tj +/F8 1 Tf +7.9701 0 0 7.9701 300.3726 258.644 Tm +(n)Tj +/F16 1 Tf +11.9552 0 0 11.9552 294.3073 255.0575 Tm +(\012)Tj +/F8 1 Tf +7.9701 0 0 7.9701 295.5895 229.863 Tm +(j)Tj +/F6 1 Tf +0.4874 0 TD +(=1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 313.5691 243.7001 Tm +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 320.3975 241.9068 Tm +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 324.7791 243.7001 Tm +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 332.3975 241.9068 Tm +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 336.7801 243.7001 Tm +(q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 344.3975 249.3679 Tm +()Tj +/F8 1 Tf +0 -1.0956 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 210.2466 Tm +[(Substituting)-326.5(this)-326.4(in)27.1(to)-326.4(\(13,)]TJ +/F7 1 Tf +9.0995 -2.6612 TD +(f)Tj +/F11 1 Tf +7.9701 0 0 7.9701 193.7564 176.6376 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 201.0361 178.4309 Tm +(\()Tj +/F11 1 Tf +0.3808 0 TD +(z)Tj +/F1 1 Tf +0.6294 0 TD +0.2778 Tc +(\)=)Tj +3.8702 0.6765 TD +0 Tc +(1)Tj +ET +234.57 181.648 55.401 -0.478 re +f +BT +/F7 1 Tf +11.9552 0 0 11.9552 234.6082 170.2306 Tm +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 241.6777 173.6836 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 249.3061 170.2306 Tm +(det\()Tj +/F12 1 Tf +1.7408 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 278.1768 168.4373 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 285.4575 170.2306 Tm +(\))Tj +0.6474 0.6859 TD +(exp)Tj +/F16 1 Tf +1.6626 1.71 TD +()Tj +/F9 1 Tf +0.7917 -1.71 TD +()Tj +/F16 1 Tf +0.9444 0.95 TD +(\012)Tj +/F8 1 Tf +7.9701 0 0 7.9701 340.522 164.5938 Tm +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 353.0909 178.4309 Tm +(z)Tj +/F10 1 Tf +7.9701 0 0 7.9701 360.6157 183.3673 Tm +()Tj +/F11 1 Tf +11.9552 0 0 11.9552 364.8777 178.4309 Tm +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 372.4962 176.6376 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 376.8777 178.4309 Tm +()Tj +/F10 1 Tf +7.9701 0 0 7.9701 383.7061 183.3794 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F8 1 Tf +-0.8264 -1.0053 TD +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 395.0257 178.4309 Tm +(q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 402.6431 184.0987 Tm +()Tj +/F8 1 Tf +0 -1.0955 TD +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 407.0257 178.4309 Tm +(z)Tj +/F16 1 Tf +0.6294 1.71 TD +()Tj +/F1 1 Tf +-28.0507 -4.6952 TD +(Expressing)Tj +/F11 1 Tf +4.9515 0 TD +(q)Tj +/F10 1 Tf +7.9701 0 0 7.9701 146.0135 148.4085 Tm +()Tj +/F8 1 Tf +0 -1.0955 TD +(j)Tj +/F11 1 Tf +11.9552 0 0 11.9552 150.396 142.7418 Tm +(z)Tj +/F1 1 Tf +0.96 0 TD +[(as)-330.5(the)-330.6(pro)-54.4(jection)-330.6(of)]TJ +/F11 1 Tf +8.6713 0 TD +(z)Tj +/F1 1 Tf +0.96 0 TD +(on)Tj +/F11 1 Tf +1.3641 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 300.9425 140.9484 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 305.325 142.7418 Tm +(,)Tj +/F14 1 Tf +0.6035 0 TD +(i.e.)Tj +/F1 1 Tf +1.3501 0 TD +0.3315 Tc +[(,a)331.5(s)]TJ +/F9 1 Tf +1.8099 0 TD +0 Tc +()Tj +/F11 1 Tf +0.3888 0 TD +(z)Tj +/F7 1 Tf +0.6295 0 TD +(,)Tj +/F11 1 Tf +0.4386 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 375.3544 140.9484 Tm +(j)Tj +/F9 1 Tf +11.9552 0 0 11.9552 379.737 142.7418 Tm +()Tj +/F1 1 Tf +0.3888 0 TD +[(,)-331.6(and)-330.6(recalling)-330.6(that)-330.6(det)]TJ +/F12 1 Tf +10.0847 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 513.0103 140.9484 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 523.6962 142.7418 Tm +(=)Tj +/F16 1 Tf +-37.1803 -0.4583 TD +(\015)Tj +/F8 1 Tf +7.9701 0 0 7.9701 90.4917 124.808 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 96.8657 128.2959 Tm +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 103.6941 126.5025 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 108.0767 128.2959 Tm +[(,)-326.4(this)-326.4(b)-27.2(ecomes)]TJ +/F7 1 Tf +8.5643 -2.7196 TD +(f)Tj +/F11 1 Tf +7.9701 0 0 7.9701 216.2331 93.9895 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 223.5138 95.7828 Tm +(\()Tj +/F11 1 Tf +0.3807 0 TD +(z)Tj +/F1 1 Tf +0.6295 0 TD +0.2777 Tc +(\)=)Tj +/F8 1 Tf +7.9701 0 0 7.9701 260.9584 110.7268 Tm +0 Tc +(n)Tj +/F16 1 Tf +11.9552 0 0 11.9552 255.8894 107.1402 Tm +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 256.1754 81.9456 Tm +(j)Tj +/F6 1 Tf +0.4874 0 TD +(=1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 280.5669 103.8705 Tm +(1)Tj +ET +274.41 98.968 18.279 -0.478 re +f +BT +/F7 1 Tf +11.9552 0 0 11.9552 274.3542 87.5816 Tm +0.0358 Tc +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 288.2521 85.7881 Tm +0 Tc +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 295.8217 95.7828 Tm +(exp)Tj +/F16 1 Tf +1.6626 0.81 TD +()Tj +/F9 1 Tf +0.4583 -0.81 TD +(|)Tj +/F11 1 Tf +1.4445 0 TD +(z)Tj +/F7 1 Tf +0.6294 0 TD +(,)Tj +/F11 1 Tf +0.4387 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 358.8334 93.9895 Tm +(j)Tj +/F9 1 Tf +11.9552 0 0 11.9552 363.216 95.7828 Tm +(|)Tj +/F6 1 Tf +7.9701 0 0 7.9701 371.1861 100.7183 Tm +(2)Tj +/F7 1 Tf +11.9552 0 0 11.9552 375.9183 95.7828 Tm +()Tj +/F10 1 Tf +7.9701 0 0 7.9701 382.7467 100.7303 Tm +()Tj +/F6 1 Tf +0.8264 0 TD +(1)Tj +/F8 1 Tf +-0.8264 -1.0052 TD +(j)Tj +/F16 1 Tf +11.9552 0 0 11.9552 394.0653 105.4665 Tm +()Tj +/F1 1 Tf +9.8639 -0.81 TD +(\(14\))Tj +-17.4749 -3.8871 TD +(7)Tj +ET +endstream +endobj +47 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +/F16 24 0 R +/F21 32 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +49 0 obj +<< +/Length 17623 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(This)-445.7(is)-445.6(the)-445.7(densit)27.1(y)-445.6(o)0(f)]TJ +/F7 1 Tf +9.9962 0 TD +(n)Tj +/F1 1 Tf +1.0302 0 TD +[(indep)-27.2(enden)27.2(t)-445.6(circularly-symmetric)-445.8(Gaussian)-445.8(random)-445.7(v)54.4(ariables,)]TJ +-11.0263 -1.2083 TD +(\()Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F11 1 Tf +0.3889 0 TD +(Z)Tj +/F7 1 Tf +0.8509 0 TD +(,)Tj +/F11 1 Tf +0.4387 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 111.4381 691.8058 Tm +(1)Tj +/F9 1 Tf +11.9552 0 0 11.9552 116.1703 693.599 Tm +()Tj +/F7 1 Tf +0.3888 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F11 1 Tf +0.3889 0 TD +(Z)Tj +/F7 1 Tf +0.851 0 TD +(,)Tj +/F11 1 Tf +0.4386 0 TD +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 176.7173 691.8058 Tm +(n)Tj +/F9 1 Tf +11.9552 0 0 11.9552 182.3532 693.599 Tm +()Tj +/F1 1 Tf +0.3889 0 TD +[(\))-344.5(with)-344.4(v)54.4(ariances)]TJ +/F7 1 Tf +7.2129 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 280.0628 691.8058 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 284.795 693.599 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 319.8376 691.8058 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 329.592 693.599 Tm +[(resp)-27.2(ectiv)27.2(ely)81.5(.)-489.3(I)0(n)-344.5(other)-344.5(w)27.2(ords,)-349(expressing)]TJ +/F11 1 Tf +-20.9443 -1.2083 TD +(Z)Tj +/F1 1 Tf +1.3222 0 TD +[(in)-471.2(the)-471.2(orthonormal)-471.3(basis)]TJ +/F9 1 Tf +11.4153 0 TD +({)Tj +/F11 1 Tf +0.5 0 TD +(q)Tj +/F6 1 Tf +7.9701 0 0 7.9701 245.073 677.3599 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 249.8052 679.1532 Tm +0.1667 Tc +[(,...)-166.6(,)]TJ +/F11 1 Tf +2.36 0 TD +0 Tc +(q)Tj +/F8 1 Tf +7.9701 0 0 7.9701 285.6369 677.3599 Tm +(n)Tj +/F9 1 Tf +11.9552 0 0 11.9552 291.2737 679.1532 Tm +(})Tj +/F1 1 Tf +0.5 0 TD +[(,)-507.3(the)-471.2(v)54.4(ariables)-471.3(in)-471.2(this)-471.2(basis)-471.2(are)-471.2(indep)-27.2(enden)27.2(t)]TJ +-18.2391 -1.2083 TD +[(circularly-symmetric)-407.4(Gaussian)-407.3(random)-407.3(v)54.4(ariables)-407.3(with)-407.2(v)54.4(ariances)]TJ +/F7 1 Tf +27.8808 0 TD +()Tj +/F6 1 Tf +7.9701 0 0 7.9701 419.3474 662.9141 Tm +(1)Tj +/F7 1 Tf +11.9552 0 0 11.9552 424.0797 664.7073 Tm +0.1667 Tc +[(,...)-166.7(,)]TJ +/F8 1 Tf +7.9701 0 0 7.9701 459.1223 662.9141 Tm +0 Tc +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 464.7582 664.7073 Tm +[(.)-677.6(This)-407.3(is)-407.1(the)]TJ +-32.2503 -1.2083 TD +[(same)-417(as)-416.9(the)-416.9(analogous)-417(result)-416.9(for)-417(join)27.2(tly-Gaussian)-417(real)-416.9(random)-417(v)27.2(ectors)-416.9(whic)27.1(h)-416.9(s)0(a)27.1(y)0(s)-416.8(that)]TJ +T* +[(there)-251.8(is)-251.8(alw)27.1(a)27.2(y)0(s)-251.8(a)0(n)-251.8(orthonormal)-251.9(basis)-251.8(in)-251.8(whic)27.2(h)-251.8(the)-251.8(v)54.4(ariables)-251.9(are)-251.7(Gaussian)-251.8(and)-251.8(indep)-27.2(enden)27.2(t.)]TJ +T* +[(This)-315(analogy)-315(forms)-315(the)-314.9(simplest)-315(w)27.2(a)27.2(y)-314.9(to)-315(\(sort)-315(of)-69.7(\))-314.9(visualize)-315(circularly-symmetric)-315.1(Gaussian)]TJ +T* +[(v)27.2(ectors)-413.8()-413.8(they)-413.7(ha)27.1(v)27.2(e)-413.7(the)-413.7(same)-413.8(kind)-413.8(of)-413.7(elliptical)-413.8(symmetry)-413.9(as)-413.7(the)-413.7(real)-413.8(case,)-435.6(except)-413.8(that)]TJ +T* +[(here,)-342.5(eac)27.2(h)-339.2(complex)-339.3(random)-339.3(v)54.4(ariable)-339.2(is)-339.2(also)-339.2(circularly)-339.3(symmetric.)-473.8(It)-339.2(should)-339.2(b)-27.2(e)-339.2(clear)-339.2(that)]TJ +T* +[(\(14\))-358.8(is)-358.8(also)-358.9(an)-358.8(if-and-only-if)-358.9(condition)-358.9(for)-358.9(circularly-symmetric)-359(join)27.2(tly-Gaussian)-358.9(random)]TJ +T* +[(v)27.2(ectors.)]TJ +/F5 1 Tf +17.2154 0 0 17.2154 79.2 519.6683 Tm +[(5)-1125(Linear)-349.6(functionals)-349.6(of)-349.6(circularly-symmetric)-349.6(random)]TJ +1.6875 -1.2731 TD +[(v)31.3(ectors)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 467.4799 Tm +(Let)Tj +/F11 1 Tf +1.7344 0 TD +(Z)Tj +/F9 1 Tf +1.1287 0 TD +0.2778 Tc +[(C)219.5(N)]TJ +/F1 1 Tf +2.6083 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F12 1 Tf +0.4386 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 168.3218 465.6866 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 175.6015 467.4799 Tm +[(\).)-428.6(If)-306.6(some)-306.7(other)-306.7(random)-306.7(v)27.2(ector)]TJ +/F11 1 Tf +13.4991 0 TD +(Y)Tj +/F1 1 Tf +1.3703 0 TD +[(can)-306.6(b)-27.2(e)-306.7(expressed)-306.7(as)]TJ +/F11 1 Tf +8.6409 0 TD +(Y)Tj +/F1 1 Tf +1.3413 0 TD +(=)Tj +/F12 1 Tf +1.0393 0 TD +(B)Tj +/F11 1 Tf +0.6498 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +[(,)-310.6(then)]TJ +/F11 1 Tf +-35.4553 -1.2083 TD +(Y)Tj +/F1 1 Tf +1.4208 0 TD +[(is)-357.3(also)-357.2(a)-357.3(circularly-symmetric)-357.4(join)27.2(tly-Gaussian)-357.4(random)-357.3(v)27.2(ector.)-527.8(T)81.6(o)-357.2(see)-357.3(this,)-365(represen)27.1(t)]TJ +/F11 1 Tf +-1.4208 -1.2083 TD +(Z)Tj +/F1 1 Tf +1.1971 0 TD +(as)Tj +/F11 1 Tf +1.2219 0 TD +(Z)Tj +/F1 1 Tf +1.1623 0 TD +(=)Tj +/F12 1 Tf +1.0729 0 TD +(A)Tj +/F11 1 Tf +0.6469 0 TD +(W)Tj +/F1 1 Tf +1.6924 0 TD +(where)Tj +/F11 1 Tf +2.8483 0 TD +(W)Tj +/F9 1 Tf +1.6576 0 TD +0.3114 Tc +[(C)253.1(N)]TJ +/F1 1 Tf +2.6418 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +0.1667 Tc +(,I)Tj +/F1 1 Tf +0.9492 0 TD +0 Tc +[(\).)-494.3(Then)]TJ +/F11 1 Tf +3.7235 0 TD +(Y)Tj +/F1 1 Tf +1.3749 0 TD +(=)Tj +/F12 1 Tf +1.0729 0 TD +(BA)Tj +/F11 1 Tf +1.2968 0 TD +(W)Tj +/F1 1 Tf +1.3462 0 TD +0.351 Tc +[(,s)351(o)]TJ +/F11 1 Tf +1.8449 0 TD +0 Tc +(Y)Tj +/F9 1 Tf +1.3749 0 TD +0.3114 Tc +[(C)253.1(N)]TJ +/F1 1 Tf +2.6418 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F12 1 Tf +0.4386 0 TD +(BK)Tj +/F11 1 Tf +7.9701 0 0 7.9701 476.9485 436.795 Tm +(Z)Tj +/F12 1 Tf +11.9552 0 0 11.9552 484.2292 438.5883 Tm +(B)Tj +/F10 1 Tf +7.9701 0 0 7.9701 491.998 442.927 Tm +()Tj +/F1 1 Tf +11.9552 0 0 11.9552 496.2601 438.5883 Tm +[(\).)-494.3(This)]TJ +-34.8853 -1.2083 TD +[(helps)-281.6(sho)27.2(w)-281.6(w)0(h)27.1(y)-281.6(circular)-281.6(symmetry)-281.6(is)-281.6(imp)-27.2(ortan)27.2(t)-281.6()-281.6(i)0(t)-281.6(i)0(s)-281.6(i)0(n)27.2(v)54.4(arian)27.1(t)-281.6(t)0(o)-281.6(linear)-281.6(transformations.)]TJ +0 -1.5417 TD +(If)Tj +/F12 1 Tf +1.042 0 TD +(B)Tj +/F1 1 Tf +1.0395 0 TD +[(is)-389.5(1)-389.6(b)27.2(y)]TJ +/F7 1 Tf +3.35 0 TD +(n)Tj +/F1 1 Tf +0.9741 0 TD +(\()Tj +/F14 1 Tf +0.3807 0 TD +(i.e.)Tj +/F1 1 Tf +1.35 0 TD +[(,)-405.3(i)0(f)-389.6(i)0(t)-389.6(i)0(s)-389.6(a)-389.5(ro)27.2(w)-389.6(v)27.2(ector)]TJ +/F11 1 Tf +9.5479 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 297.9208 410.0504 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 302.7567 405.7115 Tm +[(\))-389.6(then)]TJ +/F7 1 Tf +3.0638 0 TD +(Y)Tj +/F1 1 Tf +1.171 0 TD +(=)Tj +/F11 1 Tf +1.1468 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 374.398 410.0504 Tm +(T)Tj +/F11 1 Tf +11.9552 0 0 11.9552 379.2349 405.7115 Tm +(Z)Tj +/F1 1 Tf +1.2405 0 TD +[(is)-389.5(a)-389.6(complex)-389.7(rv.)-624.7(Suc)27.2(h)-389.5(rvs)]TJ +-26.3372 -1.2083 TD +[(are)-384.1(called)]TJ +/F14 1 Tf +4.5216 0 TD +[(line)49.9(ar)-403(functionals)]TJ +/F1 1 Tf +7.9323 0 TD +(of)Tj +/F11 1 Tf +1.1728 0 TD +(Z)Tj +/F1 1 Tf +0.851 0 TD +[(.)-608.2(T)0(h)27.1(u)0(s)-384.1(all)-384.1(linear)-384.1(functionals)-384.2(of)-384.1(a)-384.1(circularly-symmetric)]TJ +-14.4778 -1.2083 TD +[(join)27.1(tly)-326.4(Gaussian)-326.4(random)-326.5(v)27.2(ector)-326.5(are)-326.4(circularly-symmetric)-326.6(Gaussian)-326.5(rvs.)]TJ +0 -1.5417 TD +[(Con)27.1(v)27.2(ersely)81.6(,)-518.2(w)27.2(e)-479.7(n)0(o)27.1(w)-479.8(w)27.2(a)0(n)27.2(t)-479.8(to)-479.8(sho)27.2(w)-479.8(that)-479.8(if)-479.8(all)-479.8(linear)-479.9(functionals)-479.8(of)-479.8(a)-479.8(complex)-479.8(random)]TJ +0 -1.2083 TD +[(v)27.2(ector)]TJ +/F11 1 Tf +3.0091 0 TD +(Z)Tj +/F1 1 Tf +1.2488 0 TD +[(are)-398(circularly-symmetric)-398.1(Gaussian,)-415.9(then)]TJ +/F11 1 Tf +17.7343 0 TD +(Z)Tj +/F1 1 Tf +1.2488 0 TD +[(m)27.1(ust)-397.9(also)-398(b)-27.2(e)-397.9(circularly-symmetric)]TJ +-23.2411 -1.2084 TD +[(and)-473.5(join)27.2(tly-Gaussian.)-876.5(The)-473.5(question)-473.5(of)-473.4(b)-27.2(eing)-473.5(join)27.1(tly)-473.4(Gaussian)-473.6(can)-473.5(b)-27.2(e)-473.4(separated)-473.6(from)]TJ +T* +[(that)-373.1(of)-373.1(b)-27.2(eing)-373.1(circularly)-373.2(symmetric.)-575.2(Th)27.1(us)-373.1(assume)-373.1(that)-373.1(for)-373.1(all)-373.1(complex)]TJ +/F7 1 Tf +30.6286 0 TD +(n)Tj +/F1 1 Tf +0.5845 0 TD +[(-v)27.2(ectors)]TJ +/F11 1 Tf +3.6968 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 503.8556 319.3903 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 508.6914 315.0515 Tm +[(,)-384.7(the)]TJ +-35.9252 -1.2083 TD +[(complex)-405.8(rv)]TJ +/F11 1 Tf +5.2176 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 148.8797 304.9444 Tm +(T)Tj +/F11 1 Tf +11.9552 0 0 11.9552 153.7156 300.6057 Tm +(Z)Tj +/F1 1 Tf +1.2567 0 TD +[(is)-405.7(complex)-405.7(Gaussian.)-673.2(Lo)-27.1(oking)-405.7(at)]TJ +/F11 1 Tf +14.9253 0 TD +(V)Tj +/F1 1 Tf +1.4574 0 TD +(and)Tj +/F11 1 Tf +1.9833 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 395.6095 304.9444 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 405.2952 300.6057 Tm +[(as)-405.7(real)-405.7(2)]TJ +/F7 1 Tf +3.7542 0 TD +(n)Tj +/F1 1 Tf +0.9902 0 TD +[(v)27.2(ectors,)]TJ +/F11 1 Tf +3.6948 0 TD +(V)Tj +/F1 1 Tf +1.4645 0 TD +(=)Tj +-37.1803 -1.2083 TD +(\()Tj +/F9 1 Tf +0.3808 0 TD +()Tj +/F1 1 Tf +0.7223 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 104.9514 284.3666 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 109.6837 286.1599 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 163.6483 284.3666 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 169.2852 286.1599 Tm +(\))Tj +/F7 1 Tf +0.3807 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 200.28 284.3666 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 205.0122 286.1599 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 258.9768 284.3666 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 264.6137 286.1599 Tm +(\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 269.1656 290.4986 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 277.8252 286.1599 Tm +(and)Tj +/F11 1 Tf +1.8973 0 TD +(r)Tj +/F13 1 Tf +5.9776 0 0 5.9776 307.8346 290.4986 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 315.991 286.1599 Tm +0.2778 Tc +(=\()Tj +/F9 1 Tf +1.4202 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(b)Tj +/F6 1 Tf +7.9701 0 0 7.9701 351.1323 284.3666 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 355.8645 286.1599 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +0.1667 Tc +[(,...)-166.6(,)]TJ +/F9 1 Tf +2.3599 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(b)Tj +/F8 1 Tf +7.9701 0 0 7.9701 406.7945 284.3666 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 412.4304 286.1599 Tm +(\))Tj +/F7 1 Tf +0.3808 0 TD +(,)Tj +/F9 1 Tf +0.4387 0 TD +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3808 0 TD +(b)Tj +/F6 1 Tf +7.9701 0 0 7.9701 440.3906 284.3666 Tm +(1)Tj +/F1 1 Tf +11.9552 0 0 11.9552 445.1228 286.1599 Tm +(\))Tj +/F7 1 Tf +0.5475 0 TD +0.1667 Tc +[(...)-166.6(,)]TJ +/F9 1 Tf +1.9212 0 TD +0 Tc +()Tj +/F1 1 Tf +0.7222 0 TD +(\()Tj +/F7 1 Tf +0.3807 0 TD +(b)Tj +/F8 1 Tf +7.9701 0 0 7.9701 492.801 284.3666 Tm +(n)Tj +/F1 1 Tf +11.9552 0 0 11.9552 498.4369 286.1599 Tm +(\)\))Tj +/F13 1 Tf +5.9776 0 0 5.9776 507.5417 290.4986 Tm +(T)Tj +/F1 1 Tf +11.9552 0 0 11.9552 512.3776 286.1599 Tm +0.3212 Tc +[(,w)348.5(e)]TJ +-36.2335 -1.2083 TD +0 Tc +[(see)-341(that)]TJ +/F11 1 Tf +3.7337 0 TD +(r)Tj +/F13 1 Tf +5.9776 0 0 5.9776 131.1631 276.0528 Tm +(T)Tj +/F11 1 Tf +11.9552 0 0 11.9552 135.999 271.7141 Tm +(V)Tj +/F1 1 Tf +1.3928 0 TD +[(is)-341(a)-341(Gaussian)-341(random)-341.1(v)54.4(ariable)-341.1(for)-341.1(all)]TJ +/F11 1 Tf +16.227 0 TD +(b)Tj +/F1 1 Tf +0.6108 0 TD +[(.)-479(Since)]TJ +/F11 1 Tf +3.3223 0 TD +(r)Tj +/F1 1 Tf +0.9537 0 TD +[(can)-341(b)-27.2(e)-341(arbitrarily)-341.2(c)27.3(hosen)]TJ +-27.2577 -1.2083 TD +[(b)27.1(y)-259.7(c)27.3(h)0(o)-27.2(osing)-259.8(the)-259.7(real)-259.8(and)-259.7(imaginary)-259.8(comp)-27.3(onen)27.2(ts)-259.8(of)]TJ +/F11 1 Tf +21.3997 0 TD +(b)Tj +/F1 1 Tf +0.6108 0 TD +[(,)-273.1(w)27.3(e)-259.7(see)-259.8(that)-259.8(all)-259.7(real)-259.8(linear)-259.8(functionals)]TJ +-22.0106 -1.2083 TD +(of)Tj +/F11 1 Tf +1.1761 0 TD +(V)Tj +/F1 1 Tf +1.4391 0 TD +[(are)-387.4(Gaussian.)-617.9(It)-387.3(is)-387.4(kno)27.2(wn)-387.3(for)-387.4(real)-387.3(random)-387.4(v)27.3(ectors)-387.4(\(see)-387.3(for)-387.3(example)-387.3(Section)-387.4(7.3.6)]TJ +-2.6152 -1.2083 TD +[(of)-385.6(PDC08\))-385.6(that)]TJ +/F11 1 Tf +7.2215 0 TD +(V)Tj +/F1 1 Tf +1.4373 0 TD +[(is)-385.5(join)27.1(tly)-385.5(Gaussian)-385.6(if)-385.5(all)-385.5(its)-385.5(linear)-385.6(functionals)-385.6(are)-385.6(Gaussian)-385.5(random)]TJ +-8.6588 -1.2083 TD +[(v)54.4(ariables.)-691.2(Th)27.2(us)]TJ +/F11 1 Tf +7.2607 0 TD +(Z)Tj +/F1 1 Tf +1.2627 0 TD +[(is)-411.6(complex)-411.8(join)27.1(tly)-411.7(Gaussian)-411.8(if)-411.7(all)-411.7(its)-411.7(linear)-411.8(functionals)-411.7(are)-411.7(complex)]TJ +-8.5233 -1.2083 TD +[(Gaussian)-326.5(random)-326.5(v)54.4(ariables.)]TJ +0 -1.5417 TD +[(W)81.6(e)-387.1(could)-387.1(no)27.2(w)-387(sho)27.2(w)-387(that)]TJ +/F11 1 Tf +11.1878 0 TD +(Z)Tj +/F1 1 Tf +1.238 0 TD +[(is)-387(also)-387(circularly)-387.1(symmetric)-387.2(and)-387(join)27.1(tly)-387.1(Gaussian)-387.1(if)]TJ +/F11 1 Tf +22.6044 0 TD +(b)Tj +/F13 1 Tf +5.9776 0 0 5.9776 505.2952 185.3927 Tm +(T)Tj +/F11 1 Tf +11.9552 0 0 11.9552 510.131 181.054 Tm +(Z)Tj +/F1 1 Tf +1.238 0 TD +(is)Tj +-37.2836 -1.2083 TD +[(circularly-symmetric)-254.5(Gaussian)-254.3(for)-254.2(all)]TJ +/F11 1 Tf +15.8634 0 TD +(b)Tj +/F1 1 Tf +0.6108 0 TD +[(,)-268.6(but)-254.3(it)-254.2(is)-254.3(just)-254.3(as)-254.2(easy)81.6(,)-268.7(and)-254.2(yields)-254.3(a)-254.3(sligh)27.2(tly)-254.3(stronger)]TJ +-16.4743 -1.2083 TD +[(result,)-308.2(to)-303.6(sho)27.2(w)-303.5(that)]TJ +/F11 1 Tf +8.6549 0 TD +(Z)Tj +/F9 1 Tf +1.1287 0 TD +0.2778 Tc +[(C)219.5(N)]TJ +/F1 1 Tf +2.6082 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +(,)Tj +/F12 1 Tf +0.4387 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 251.0565 150.3691 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 258.3372 152.1624 Tm +0.3036 Tc +[(\)i)303.6(f)]TJ +/F11 1 Tf +1.5591 0 TD +0 Tc +(Z)Tj +/F1 1 Tf +1.1545 0 TD +[(is)-303.5(join)27.2(tly)-303.6(Gaussian)-303.7(and,)-308.1(in)-303.5(addition,)-308.3(the)-303.5(limited)]TJ +-17.6977 -1.2083 TD +[(set)-351.1(of)-351.1(linear)-351.1(functionals)]TJ +/F7 1 Tf +10.4452 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 212.0857 135.9233 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 219.3255 137.7166 Tm +(+)Tj +/F7 1 Tf +1.0006 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 239.3006 135.9233 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 248.6167 137.7166 Tm +[(is)-351.1(circularly)-351.1(symmetric)-351.2(Gaussian)-351.2(for)-351.1(all)]TJ +/F7 1 Tf +17.2846 0 TD +0.0019 Tc +[(j,)-164.7(k)]TJ +/F1 1 Tf +1.3884 0 TD +0.5093 Tc +[(.I)509.3(f)]TJ +/F7 1 Tf +1.7847 0 TD +0 Tc +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 501.2045 135.9233 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 508.4443 137.7166 Tm +(+)Tj +/F7 1 Tf +1.0006 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 528.4185 135.9233 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 79.2 123.2708 Tm +[(is)-438.5(circularly)-438.5(symmetric)-438.6(for)-438.5(all)]TJ +/F7 1 Tf +13.4907 0 TD +(j)Tj +/F1 1 Tf +0.4613 0 TD +[(,)-466.4(then)]TJ +/F12 1 Tf +3.0808 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F7 1 Tf +0.2719 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 301.9268 127.6094 Tm +(2)Tj +/F8 1 Tf +-0.1077 -0.9151 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 306.659 123.2708 Tm +[(])-468.5(=)-468.5(0)0(,)-466.4(s)0(o)-438.5(that)-438.5(the)-438.4(main)-438.5(diagonal)-438.5(of)]TJ +/F12 1 Tf +16.3607 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 512.4095 121.4775 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 524.9315 123.2708 Tm +(is)Tj +-37.2836 -1.2083 TD +[(zero.)-551.4(If)-365.1(in)-365.1(addition,)]TJ +/F7 1 Tf +8.9453 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 194.1549 107.0316 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 201.5083 108.8248 Tm +(+)Tj +/F7 1 Tf +1.0102 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 221.597 107.0316 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 231.0824 108.8248 Tm +[(is)-365(circularly)-365.2(symmetric,)-374.9(then)]TJ +/F12 1 Tf +12.7413 0 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([\()Tj +/F7 1 Tf +0.6528 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 406.1958 107.0316 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 413.5502 108.8248 Tm +(+)Tj +/F7 1 Tf +1.0102 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 433.6389 107.0316 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 438.7587 108.8248 Tm +(\))Tj +/F6 1 Tf +7.9701 0 0 7.9701 443.3106 113.1637 Tm +(2)Tj +/F1 1 Tf +11.9552 0 0 11.9552 448.0428 108.8248 Tm +[(])-343.7(=)-343.7(0)0(.)-551.3(But)-365.1(since)]TJ +/F12 1 Tf +-30.8522 -1.2083 TD +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F7 1 Tf +0.272 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 98.2964 98.7179 Tm +(2)Tj +/F8 1 Tf +-0.1077 -0.9151 TD +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 103.0286 94.3791 Tm +0.3416 Tc +(]=)Tj +/F12 1 Tf +1.7167 0 TD +0 Tc +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F7 1 Tf +0.272 0 TD +(Z)Tj +/F6 1 Tf +7.9701 0 0 7.9701 142.6481 98.7179 Tm +(2)Tj +/F8 1 Tf +-0.1076 -0.9344 TD +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 147.3803 94.3791 Tm +0.3416 Tc +[(]=0)341.6(,)-31.6(2)]TJ +/F12 1 Tf +3.3411 0 TD +0 Tc +(E)Tj +/F1 1 Tf +0.5833 0 TD +([)Tj +/F7 1 Tf +0.272 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 205.5611 92.5857 Tm +(j)Tj +/F7 1 Tf +11.9552 0 0 11.9552 209.9437 94.3791 Tm +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 217.9557 92.5857 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 223.0755 94.3791 Tm +[(])-341.6(=)-341.5(0.)-547.6(Th)27.1(us)-363.9(the)]TJ +/F7 1 Tf +7.2677 0 TD +0.0019 Tc +[(j,)-164.7(k)]TJ +/F1 1 Tf +1.7523 0 TD +0 Tc +[(elemen)27.2(t)-363.9(o)0(f)]TJ +/F12 1 Tf +4.8075 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 398.5415 92.5857 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 409.9059 94.3791 Tm +0.3416 Tc +[(=0)341.6(.)-206(T)341.6(h)368.8(u)341.6(s)-22.3(i)341.6(f)]TJ +/F7 1 Tf +5.8653 0 TD +0 Tc +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 488.0399 92.5857 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 495.3833 94.3791 Tm +(+)Tj +/F7 1 Tf +1.0093 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 515.462 92.5857 Tm +(k)Tj +/F1 1 Tf +11.9552 0 0 11.9552 524.9315 94.3791 Tm +(is)Tj +-18.5574 -3.7697 TD +(8)Tj +ET +endstream +endobj +50 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F10 13 0 R +/F11 14 0 R +/F12 15 0 R +/F13 16 0 R +/F14 17 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +52 0 obj +<< +/Length 6565 +>> +stream
+BT +/F1 1 Tf +11.9552 0 0 11.9552 79.2 708.0448 Tm +0 g +/GS1 gs +0 Tc +0 Tw +[(circularly)-326.5(symmetric)-326.4(for)-326.5(all)]TJ +/F7 1 Tf +11.9458 0 TD +0.0018 Tc +[(j,)-164.9(k)]TJ +/F1 1 Tf +1.3884 0 TD +0 Tc +[(,)-326.3(i)0(t)-326.4(follo)27.1(ws)-326.4(that)]TJ +/F12 1 Tf +6.9139 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 331.4261 706.2516 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 342.0274 708.0448 Tm +[(=)-277.8(0)-326.3(and)]TJ +/F11 1 Tf +3.7592 0 TD +(Z)Tj +/F1 1 Tf +1.1773 0 TD +[(is)-326.5(circularly)-326.4(symmetric.)]TJ +/F6 1 Tf +7.9701 0 0 7.9701 520.8359 712.3836 Tm +(5)Tj +/F5 1 Tf +17.2154 0 0 17.2154 79.2 664.1266 Tm +[(6)-1125(Summary)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 79.2 633.8561 Tm +[(In)-326.5(summary)81.5(,)-326.3(w)27.2(e)-326.4(h)0(a)27.2(v)27.2(e)-326.4(pro)27.2(v)27.2(e)0(d)-326.4(the)-326.4(follo)27.2(wing)-326.4(theorem.)]TJ +/F5 1 Tf +0 -2.0417 TD +[(Theorem)-375.1(4.)]TJ +/F14 1 Tf +6.1332 0 TD +[(A)-465.3(c)50(omplex)-465.6(r)50(andom)-465.5(ve)50(ctor)]TJ +/F11 1 Tf +11.6887 0 TD +(Z)Tj +/F14 1 Tf +1.1744 0 TD +(is)Tj +/F9 1 Tf +1.1655 0 TD +0.0583 Tc +(CN)Tj +/F1 1 Tf +1.5527 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8704 0 TD +(,)Tj +/F21 1 Tf +0.4387 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 362.5106 607.6543 Tm +(Z)Tj +/F1 1 Tf +11.9552 0 0 11.9552 368.6585 609.4476 Tm +(\))Tj +/F14 1 Tf +0.8463 0 TD +[(if)-465.5(and)-465.5(only)-465.5(if)-465.5(any)-465.5(one)-465.6(of)-465.5(the)]TJ +-25.0583 -1.2083 TD +[(fol)-50.1(lowing)-350(c)50(onditions)-350.1(is)-350.1(satise)50(d.)]TJ +/F9 1 Tf +0.9143 -2.375 TD +()Tj +/F11 1 Tf +0.9896 0 TD +(Z)Tj +/F14 1 Tf +1.0589 0 TD +[(is)-350(jointly)-350(Gaussian)-350.2(and)-350(has)-350(the)-350(same)-350(distribution)-350.2(as)]TJ +/F7 1 Tf +22.6444 0 TD +()Tj +/F8 1 Tf +7.9701 0 0 7.9701 390.0663 570.947 Tm +-0.0001 Tc +(i)Tj +/F11 1 Tf +11.9552 0 0 11.9552 398.4807 566.6082 Tm +0 Tc +(Z)Tj +/F14 1 Tf +1.0589 0 TD +[(for)-350(al)-50(l)-350(r)50(e)50(a)0(l)]TJ +/F7 1 Tf +4.825 0 TD +()Tj +/F14 1 Tf +0.5796 0 TD +(.)Tj +/F9 1 Tf +-32.2557 -2.0417 TD +()Tj +/F11 1 Tf +0.9896 0 TD +(Z)Tj +/F14 1 Tf +1.0589 0 TD +[(is)-350(zer)50(o-me)49.9(an)-350(jointly)-350(Gaussian)-350.1(and)-350(the)-350(pseudo-c)49.9(ovarianc)49.9(e)-350(matrix)]TJ +/F21 1 Tf +27.7445 0 TD +(M)Tj +/F11 1 Tf +7.9701 0 0 7.9701 456.4673 540.4065 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 466.7995 542.1998 Tm +[(is)-350(zer)50(o.)]TJ +/F9 1 Tf +-31.5068 -2.0417 TD +()Tj +/F11 1 Tf +0.9896 0 TD +(Z)Tj +/F14 1 Tf +1.1696 0 TD +[(c)50(a)0(n)-460.7(b)50(e)-460.7(expr)50(esse)50(d)-460.7(a)0(s)]TJ +/F11 1 Tf +8.9552 0 TD +(Z)Tj +/F1 1 Tf +1.1916 0 TD +(=)Tj +/F21 1 Tf +1.2443 0 TD +(A)Tj +/F11 1 Tf +0.6469 0 TD +(W)Tj +/F14 1 Tf +1.6207 0 TD +[(wher)50(e)]TJ +/F11 1 Tf +2.8732 0 TD +(W)Tj +/F14 1 Tf +1.6207 0 TD +[(is)-460.7(a)-460.7(v)0(e)50(ctor)-460.7(of)-460.7(statistic)49.9(al)-50(ly)-460.7(indep)50(endent)]TJ +-19.322 -1.2083 TD +[(c)50(omp)49.9(onents,)-350(al)-50(l)]TJ +/F9 1 Tf +6.9751 0 TD +0.0584 Tc +(CN)Tj +/F1 1 Tf +1.5528 0 TD +0 Tc +(\(0)Tj +/F7 1 Tf +0.8703 0 TD +(,)Tj +/F1 1 Tf +0.4387 0 TD +(1\))Tj +/F14 1 Tf +0.8703 0 TD +(.)Tj +/F9 1 Tf +-11.6968 -2.0417 TD +()Tj +/F14 1 Tf +0.9896 0 TD +[(F)74.9(o)0(r)-373.8(non-singular)]TJ +/F21 1 Tf +7.5613 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 200.4174 477.1437 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 206.5654 478.937 Tm +[(,)-379.8(the)-373.8(pr)50(ob)50(ability)-373.9(density)-374(of)]TJ +/F11 1 Tf +11.6127 0 TD +(Z)Tj +/F14 1 Tf +1.0828 0 TD +[(is)-373.8(given)-373.9(in)-373.8(\(13\).)-521.5(F)74.9(o)0(r)-373.8(singular)]TJ +/F21 1 Tf +13.1043 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 523.0665 477.1437 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 529.2145 478.937 Tm +(,)Tj +-35.7379 -1.2083 TD +[(\(13\))-397.2(gives)-397.2(the)-397.3(density)-397.2(of)]TJ +/F11 1 Tf +10.911 0 TD +(Z)Tj +/F14 1 Tf +1.1061 0 TD +[(after)-397.3(r)50(emoval)-397.2(of)-397.2(the)-397.3(deterministic)49.9(al)-50(ly)-397.3(dep)50(endent)-397.2(c)50(omp)49.9(o-)]TJ +-12.0171 -1.2083 TD +(nents.)Tj +/F9 1 Tf +-0.9896 -2.0417 TD +()Tj +/F14 1 Tf +0.9896 0 TD +[(F)74.9(o)0(r)-373.8(non-singular)]TJ +/F21 1 Tf +7.5613 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 200.4174 423.8436 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 206.5654 425.6368 Tm +[(,)-379.8(the)-373.8(pr)50(ob)50(ability)-373.9(density)-374(of)]TJ +/F11 1 Tf +11.6127 0 TD +(Z)Tj +/F14 1 Tf +1.0828 0 TD +[(is)-373.8(given)-373.9(in)-373.8(\(14\).)-521.5(F)74.9(o)0(r)-373.8(singular)]TJ +/F21 1 Tf +13.1043 0 TD +(K)Tj +/F11 1 Tf +7.9701 0 0 7.9701 523.0665 423.8436 Tm +(Z)Tj +/F14 1 Tf +11.9552 0 0 11.9552 529.2145 425.6368 Tm +(,)Tj +-35.7379 -1.2083 TD +[(\(14\))-397.2(gives)-397.2(the)-397.3(density)-397.2(of)]TJ +/F11 1 Tf +10.911 0 TD +(Z)Tj +/F14 1 Tf +1.1061 0 TD +[(after)-397.3(r)50(emoval)-397.2(of)-397.2(the)-397.3(deterministic)49.9(al)-50(ly)-397.3(dep)50(endent)-397.2(c)50(omp)49.9(o-)]TJ +-12.0171 -1.2083 TD +(nents.)Tj +/F9 1 Tf +-0.9896 -2.0417 TD +()Tj +/F14 1 Tf +0.9896 0 TD +[(A)24.9(l)-50(l)-316(line)50(ar)-316.1(functionals)-316.2(of)]TJ +/F11 1 Tf +10.3786 0 TD +(Z)Tj +/F14 1 Tf +1.0249 0 TD +[(ar)50(e)-316.1(c)50(omplex)-316.1(Gaussian)-316.1(and)]TJ +/F7 1 Tf +11.4085 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 382.6949 370.5435 Tm +(j)Tj +/F1 1 Tf +11.9552 0 0 11.9552 388.8309 372.3367 Tm +(+)Tj +/F7 1 Tf +0.9083 0 TD +(Z)Tj +/F8 1 Tf +7.9701 0 0 7.9701 407.7021 370.5435 Tm +(k)Tj +/F14 1 Tf +11.9552 0 0 11.9552 416.6008 372.3367 Tm +[(is)-316(cir)50(cularly)-316.1(symmetric)]TJ +-26.3183 -1.2083 TD +[(for)-350.1(al)-50(l)]TJ +/F7 1 Tf +2.9626 0 TD +0.0018 Tc +[(j,)-164.9(k)]TJ +/F14 1 Tf +1.3884 0 TD +0 Tc +(.)Tj +/F1 1 Tf +-6.2549 -2.375 TD +[(Note)-454(that)-453.8(either)-454(all)-453.9(or)-453.8(none)-453.9(of)-453.9(these)-453.9(conditions)-454(are)-453.9(satised.)-817.7(The)-454(signicance)-453.9(of)-453.8(the)]TJ +0 -1.2083 TD +[(theorem)-339.1(is)-339(that)-339.1(an)27.1(y)-339(one)-339.1(of)-339(the)-339.1(conditions)-339.2(ma)27.2(y)-339(b)-27.3(e)-339(used)-339.1(to)-339.1(either)-339.1(establish)-339.2(the)-339(circularly-)]TJ +T* +[(symmetric)-326.5(join)27.1(tly-Gaussian)-326.4(prop)-27.2(ert)27.1(y)-326.4(o)0(r)-326.4(t)0(o)-326.4(sho)27.2(w)-326.3(that)-326.4(it)-326.4(do)-27.2(es)-326.4(not)-326.4(hold.)]TJ +ET +79.17 102.489 181.438 -0.398 re +f +BT +/F17 1 Tf +6.9738 0 0 6.9738 92.6635 94.7915 Tm +(5)Tj +/F3 1 Tf +9.9626 0 0 9.9626 97.1327 91.1761 Tm +[(Example)-315.3(2)-315.2(illustrates)-315.3(the)-315.3(strange)-315.2(b)-27.8(eha)27.8(vior)-315.3(p)-27.7(ossible)-315.3(when)]TJ +/F22 1 Tf +25.1556 0 TD +[(v)-35.9(ecZ)]TJ +/F3 1 Tf +2.4884 0 TD +[(is)-315.3(circularly)-315.3(symmetric)-315.2(and)-315.3(individu-)]TJ +-29.444 -1.2 TD +[(ally)-333.4(Gaussian)-333.4(but)-333.3(not)-333.3(join)27.8(tly)-333.3(Gaussian.)]TJ +/F1 1 Tf +11.9552 0 0 11.9552 303.0745 49.312 Tm +(9)Tj +ET +endstream +endobj +53 0 obj +<< +/ProcSet [/PDF /Text ] +/Font << +/F1 4 0 R +/F3 6 0 R +/F5 8 0 R +/F6 9 0 R +/F7 10 0 R +/F8 11 0 R +/F9 12 0 R +/F11 14 0 R +/F12 15 0 R +/F14 17 0 R +/F17 28 0 R +/F21 32 0 R +/F22 33 0 R +>> +/ExtGState << +/GS1 18 0 R +>> +>> +endobj +18 0 obj +<< +/Type /ExtGState +/SA false +/SM 0.02 +/OP false +/op false +/OPM 1 +/BG2 /Default +/UCR2 /Default +/HT /Default +/TR2 /Default +>> +endobj +54 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 699 +/Descent -233 +/Flags 6 +/FontBBox [-34 -251 988 750] +/FontName /CKDJAN+CMR12 +/ItalicAngle 0 +/StemV 65 +/XHeight 474 +/StemH 29 +/CharSet (/R/o/b/e/r/t/G/period/a/l/g/J/n/u/y/one/comma/two/zero/eight/L/equal/parenleft/parenright/c/m/p/x/j/i/hyphen/s/d/v/T/h/f/quoteright/F/w/B/fi/z/q/S/bracketleft/bracketright/I/A/M/seven/P/D/C/O/W/k/plus/\ +three/four/five/ffi/colon/slash/H/E/semicolon/Lambda/six/U/nine/question/N/endash) +/FontFile3 55 0 R +>> +endobj +55 0 obj +<< +/Filter /FlateDecode +/Length 6902 +/Subtype /Type1C +>> +stream
+HtiTW(zAY\Uk$q[F +Da%o6 4QADn@ve@Kt4(*@T̙L&Ɯ3'3?oչ_
At*/?w#[&qIcq˄a%owBQK
E>[C IёQ)ҙ9^8ohJ,64Ĉâe)bb#bY,)M$63BLSmy L RMiO6?L|F2 V[g$2)%U<Cf@ToRh^${~@&+sK{4jݨJc89MvEbpZ:8:b1n4Eޱswi'[(41ct
+TYL&@Z
ҩt{t#aq}!S +Yҙ`1vbb.*cu%ErkcAHϫ٬Z@m{>!^/B< +wN[\wYȁ&.1ZFʠ +Vp#JC,LJX!kτUzXYDbvR+
jr|*vJ@QQ,`aju'qjMVho7XZAr +բt.T Ar`B>giS1)n{JRAyXD2@vX\(d8֕B<$7KR OZ&{OnYyQiY1܋Ruݯ.oVkDp>9`vKדفfnz۪*Dʹao\m`.|pi6ry+f I+jX$$o jZaWܫ*Af</4
£@3i5p"x|xfy?eATF.'CcY7\RW+D!gz!+f|$,2UZ-Wٻ<Ws8-@f[v֒0W+-MQ=k㎨U
9){_(d#`[;ܦ{IVk+Iޟ'Pc\GkVr-Vtg\
ܙpǫH^:0[͑Vp5w`=[wRMi#p<MHrѐ7 @Pwc38_"Z]VJ.9`&]ŰGv¼ +a>]AR\.P/12"SÓٕNJ紺|[i*K@Rz2㚛ُh4_lpR|"gm2𨯹lC> +9!
ٱzSVVVem®x<qGwG4M/FĞ3*9e].Nó_#+)29)RƊҌ,~kp +VY;[gvNӂZ)Ԇ~[MZg=kbhPU(t<3 +7=V_Br/ƺ̥<k4VT;TJo-hPuD?|WiTW]Փhʥ˩L1H.݈kTLQPYF(-ki}if)p +8q#gQt;19V:yE+&gOW{Jغ-͞rG8LpQ\u-:jkLL}V#NE TfXPsD}Ɨiuu&=0@Olj$2TԪs1P +(!9N|;ego +^u$"R.8PJZ)E+4 |7)pZ+ۖGZ6<C7'OFX:.{,r#ǘ{PO
~s>GhÅsPg#c'/:RǟƋNoXSp~ĕl]AK&*Oo:O
0%`#$i)ET3=dI@,:쾆xZN#(pU|>N/R{70tQ'̇@7G܇G|86 +27odH11tZw)9&gpM!]ljwcuX/"1SmA^Xwcu#ѐ2".#8(Xj@K;DiXW&+FSAdѳOoH[沄!'f賃z:̬^gtߠ]p܋'shCV쏦^yƁ64fS,[:v@z9cc-5cЫ9J뚠]"_wݶep:ݛe
6`!(SQ]6k)BM[]űS]Qo=D)z|F\UH~?/e:=E+BXMEQB]Za_VNqvw|=)ׁJ#҇L}*e:v4^Gi̗i`w٥)`Ӌ+O1Xxwf&{RU*KU[ܼ$5g$SVro1f HwRf.3W^̋W%L5Uj| +wpq<epJ
r5JL}ɲ8} R%eri&c&.">&~2lFZkkvJDC +p02pK>FaJrCI`=GH!퉺NA98NZ-Pi~#ۄGn7oq=sP喼D +n+lp'p\-5uXg+
2D GX)7~7}it$mA{Y8`)CᭊlIT-LnjMF挪#黣kFp'3$dZ강o1<۩zODZvRk$?GΨ;qg#cBs#y|>.CK2!rD4ٷR¾ECKSr~~s6@ˇOi iy9Ƃ\dpUa
g{'8۲y +oY&O6MZsTx?tsGLs+h,
jތ;c.]Op#w#1"Id`4%h^<J-5aG>?r0]zbPP
? +^+J@LS#p=J(']J#* TCxJޟ=e(wuZF>E ^.-#a!KoRb3ƣ]h-HG;r7FL+F\-/Dcxm4lS7ggg#J`0ޤl*H|y ߥ8Bj +ʫk8x Vv_rFaE!yJ{i@Z*Zƒx˩s-fd5t"n 8&9q-n-O
Zp}UOOCx'88Z9%:m\{Ĕ +l^{GA?-#c ٌ%B5_쿴WyP7fsP7X]BvRD$@H8B7!7WE:V(nmwu֮{}oֱt:_RccYR^-,8 #cӻE!708sRa~?auÄ[l7+(MEMzߥw?Zg?G@Z@]UwYd̪a$~9Ɔ*|cHğiǏ
x06Ti{2K82MWk<]tGc_9ڝPlkF(jlf,xM]2F~f<p +}KṔ}v + +o&X7JSs1JrSpCeA)$5Kgv}'4@Vj8-}WrfjJK!nT[9]Z"%ۺs-UC{v|=|T8.]f+w a.Do}v̕",p +I/Qg,^+]ﱂ+-|=K&`7+8"<pl*WMIli-|}'-k7 +pz(DTĻ`Ub<GxA֜ǛK3/B@cAo<W^vT㑶)4/5PЫi^B-."Y^HWύޡ?I3
S|,asvӦC[[^Lȴϗ^N\Vmg;]8}fK(ِoV *?`2Q=Ŧb!6/3AA wZ/`@M_(94Lz?!DSV`mf= G`z +K<̲ D!.t/ +eAj}PD~I +'묠~5tne4}?w9Yn:ĦM,STy}6dTC:4W6^<l&}(FKEi^S>G<ľ&J-JJ + +݆nNV_&JI>?8J&03Y^f23O` QW"),92=P&9R.ţ)s!S3veQ}?ͨ +՝ϸ_zominjnME`Rsf$0жBzٞ%@XPo,?J[cP)] +E7@IH1ZѽQqn4 +/pmm쮕㣍Ǧ\)ؑӐnWag+7ov.F;;'%^Gm1D~<"uNGJfP ΡTɟm
X4_.3jjV:|e~/tl-pd`ù)<<gfy +O3_ +endstream +endobj +56 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 704 +/Descent -233 +/Flags 6 +/FontBBox [-33 -250 945 749] +/FontName /CKDJAA+CMR17 +/ItalicAngle 0 +/StemV 53 +/XHeight 474 +/StemH 26 +/CharSet (/C/i/r/c/u/l/a/y/hyphen/S/m/e/t/G/s/n/d/o/v) +/FontFile3 57 0 R +>> +endobj +57 0 obj +<< +/Filter /FlateDecode +/Length 1974 +/Subtype /Type1C +>> +stream
+HU{Pw% :u7 R\mQbEDkRy$ @H +FNk8Z^<{xw_יٝoDνAѱ!,OxO-_kZ(AO<v|jꕈUyG2 +-[BҼ4Qq C+)>rqLij8<'GJyǤyC @MAvz {$y"o *N,!$b@я<<t<WxN^60lPa[z@Hd_;د|;o]F1UZRWɡo80Tz2p +̃2:C֦1O9tH \= +8^]EDnff?L3968F5*C`*]<vPh}h>+tOcp;sNUR:S<%}DNLҳf!7~;8=OL;Y::Y fUKARUPhS9Zlm\c8
n=T[E(0};t~ֵ/4zan%
{Ч7pZΕFi.qZVU6/ϞCTu]}oKݟVBRCxoN9<0W" {D+}9Y[轤1=b6vc#@gBt:nW(@o~V0 u
y5#_:G>P$>:N#sDD,E)Ź@{I}kOCXʄߞ1taBRlrz۳3 +^P_qFNNҺNHuxD-hiPv.[5Q( +Ne'1oᐗ2d~C۪Վ#"I~B_K
hDRqPO
M_1:٤Dd%
x.2uouzj3wNNŎ~dAlPU^:uS@0{j*q^MCsb +XhҎ-%u6I1$^S2ܡ@2 +CgQ+DmV=UfZ_'j6[2sh}!w~1`"/10 +kd>%L_:Q<Vn /t2?kFTVdqjmdD6}c1>9Cu<>NRއTdrBtB\TXVJ;stt+.lB `J#Fi-_vX/w1U*Ⅼǃ` +endstream +endobj +58 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 698 +/Descent -233 +/Flags 6 +/FontBBox [-251 -250 1009 969] +/FontName /CKDJBI+CMR10 +/ItalicAngle 0 +/StemV 69 +/XHeight 474 +/StemH 31 +/CharSet (/A/n/u/m/b/e/r/o/f/a/s/i/c/p/t/l/y/hyphen/G/d/v/h/period/T/w/k/comma/I/g/x/parenleft/parenright/S/seven/eight/one/R/quotedblleft/P/D/C/quotedblright/two/zero/fi/N/equal/plus/W/six/O/q/E/j) +/FontFile3 59 0 R +>> +endobj +59 0 obj +<< +/Filter /FlateDecode +/Length 5637 +/Subtype /Type1C +>> +stream
+H{Tgv\ܱ36jQтx4rQPQ rQZ.BXeAADѨ'DHY?4v=IH$<oشa;#Ekqyk__HGl 6EdV$7xyKK8dk'[U1 BcmCcBIiKmݕJ[D[6A)I̡K a-!xXHv I
C ;r \$YK&G'A&Bm: bqH!#3K$GW%jabaRn2$
~N2L<S÷g>9 s&ee:tsEe}Jyesk
l1;>om6/LmFpk^|$^"SW]^Rejs<xYY(?OsLsb+y/?nچ:|sX-*J?cKm` +цFв*0 +
\E +>f[bccc[[ZyYr#ùQg!.G
k(܊ίW>HUcC +6?KTMt5fY̵KѺ- +7Q9/f'CzєM(^9%Z +5Ld^ߢn[!=/'/O(1<:7&govќM(?Ia9מ+v2,u_2Ҟ<ߒu4wO^;{{һeMkAJ"C˒OO<nO7'61PWz0GٔX{k`%g<s%ց5N6FJ1_[bjBZ?S=Cz.TB鑼oLHn'Kn>4b[ X_U}i3-ҴtUqFb2bmE6ׇ.WFÊOV?p88r!CؐӚ3'pg]Q|c]xV/M+ӳ:Мn*o +w.Gn '{ l͛\M>_Fvu27 3숿76;%.4larKsԙO +,d +Ourm Nhn }`-D"Fx%:47]%F)d}{`'?I;M
kTѠ|3"bGه ;0-G:@8jI+pvrN,By\-6L
ROX?:XeH)L61wD(x9p<?vA<Ǵ_$"n-s\ToN>.o;Έv@gHX0 +;)-T&$y`7ϧ@7"IhQ\;@=,
`VhAtr@Dϴk@/6<Hi4M!}&WuUpex +HAa*UJpB'$tjNRuRO5:23q(Y<jĈ, +
zaz^ٗ6ECD'adu3pN\s80a2gS?G[ww{_QLf4T<hV6
r^pFy.URy9 +^--Z _
uS&5ni< +P*qP3
b6؉wq2Fi&~o +* a9qod^L(xꭻ"ox-CӔi5B47̸#
9Ëܷ,!o 21KY +H}- :4TZ. %Jgzc@L#nVypz8kqiFQ:$
%T5.ѫ8eQ-ֲ\o*=ʤ_f'η|6:5&PV| FM";Kʛ|\,tq 6J%=c(O4cB?\7mUG]b2|Nbi왦$mN1^ݻwp<*ɺ&IR'1G6xŮ綞.E|6XH % +eqPz{,x^Z4#q4_u-(,\IOa"L#,+olˋ.8c>&#>ŞDzd FdJ)MX(Y&ȄSݤšIwMbɢ6Bc6"A60#e˥y{*e:jy~Sw "4<X/pd 4xN/P=vHQ pjJu-Sj&`0lvژnL8&rr^xX9.ST2sk-5A'LFv*֧[iQ :";Ԧ.Vw[t!q;5Q* m߮J1tJk,iأ@MzwQy2ه1.k$ˬ7pKI^@-p ( y-XϹZ"n%ꆵhFS4uPBQXfrM._=~ +B9!CUB .Px6(% e谪JXޟ9'6@hub5*d2 UfꚶeL^}\aqyT-ˊ`Oi=G6!{)V +5z<N'XMc;X2w"ae=X9$Jrq:;&(%Xؚ:d;Nkm86YYPq:;oGGh +O^!.<7@k'8j9l9;|VגbNfFaQmC#;^D}ȕL +md0g`#<hpyTXRee&2rmMKD9B1$ƛKifۻYQJBaۥՀgS`PY? +j܀J +] 9?x4ee'Dž鸶r%567U<̫87GŤfUi ++p
!!vp!y4-j?#.
r[1~0qpSFϧf&cT3j\]@DojmL>ws玍 4&<?=Gf2#Jڻ%_6F,`M=JkFaoNR_+ޱ#6ܙxpVximhg@4>i2O'/.)kئsڐOE',fxAB#iag=%v7N˘G '&pjm1iRv^8E99}g}4m:s4W1뗋 +Rp4;6DZ)fk"q&-;qu%SFKYֵ;pnOc?WZ^^+EYT'Su2G^5Z!YjO֫5&+ +pUVithRcڦ%-*MF +"<]vw˛} +pa(z%0O +d́hR/e;n^z=E%I{#KecD"JT,qNQʅ%ܖQ`c:J`;#XzݚY9 +WYs$Ryl +|r㭃^G-՛>-yƘFe7gQ C&MiGP,\8 +H/rrHFAuPk2'Dqi\4ag.ΌNo`-2嚸VųO1yE9X#ӑ&dׁ?Gg}]Ql«cM3@%d`CmUi{7'eZ{\kǙϳ|Y4cՕOEdzǾ=R(q{8X\
{-QhHCKJeҶdDEZ)#M{E-NƉb5Qp`kn |ًz)u:/E.I QOG wB ouX9Ă~TȆ["7
e"lXsñYl0YP8ZtE +F +A)1苉a5:$Z#mtѴr1|Ġ4`%u%3FCMw6fl < +o.%+uWn`Dl
q|>P_!zD]Q~XW A%)6x{!E8'Nm;;{=sL.9֨0UF%OKJkYkhpn 9*`<g8f{?9,?owrvᢙfqR0±{بbvi?nncx҇\T[%vV^,}3[sɘ +s M
Ś}g{̦!A}?F,6ݘO:
6f7)(<:034LxyN +Ccc +0 +endstream +endobj +60 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 695 +/Descent -233 +/Flags 262150 +/FontBBox [-301 -250 1164 946] +/FontName /CKDJBD+CMBX10 +/ItalicAngle 0 +/StemV 114 +/XHeight 474 +/StemH 47 +/CharSet (/A/b/s/t/r/a/c) +/FontFile3 61 0 R +>> +endobj +61 0 obj +<< +/Filter /FlateDecode +/Length 1016 +/Subtype /Type1C +>> +stream
+H<R{L[eJ1{;
!tK c2-ΎV`2c`] +cc3)L1F2CDd>bII~$EI2+iYx uaҡ'h&@aop^½{(";xC+ua$35-e%XM2ȑbIyBW[jre~eq֒L-/W=A(5:I<Kj/"~j# VtXt? J#UkzC/d9[ci[5ЕwY&huZ Y왢?^AXR!>DZ!D.8Fz~AsGds +)16Kd>_3<3aӰ +$:!hCQ`%Ϋh3jfs8#%ò3nԴkv<laǧ[Qr>͆m8:2|5{i$E ^F#r23q Q3L \ +Pm6+SSusz2,E*P| +endstream +endobj +62 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 696 +/Descent -233 +/Flags 262150 +/FontBBox [-53 -251 1139 750] +/FontName /CKDJCG+CMBX12 +/ItalicAngle 0 +/StemV 109 +/XHeight 474 +/StemH 43 +/CharSet (/one/P/s/e/u/d/o/hyphen/c/v/a/r/i/n/x/m/p/l/E/colon/T/h/period/two/L/t/f/y/G/three/g/four/b/five/six/S) +/FontFile3 63 0 R +>> +endobj +63 0 obj +<< +/Filter /FlateDecode +/Length 3419 +/Subtype /Type1C +>> +stream
+HdTyPwfU{ +%aAq Du˃KAA +r# '3(&QQ61Q ]!V埮u}{$6IJ\q&g)%Β&6o +?&!VKs~i6{5Jcܳo+Ke ǭ`g`"Łִ&sEKTMqb[fcru2Dh$d!]<_ hk,f>/8 Fsv!L$z4qʦFy{1Dv~&g/? ;7n=SsX.iv-T<A^vFpԅ2Ic:YN.co<H!҃E^<.Y2X<8 +>RL +._ 38" +|,oc46L%W ) +!f`)_Eg77JU~k2t_@ez:aSw`J|mn~.4)%y%'ي2sG?3|DsĈWq=m
W<pt LijC#UhSMTx}g/ڮ֯97~,5|OC¹OLCo'իqF+A3(}',:w1 =,Ğhhe11˃Za2+T]"3":!xabj`J. YYQ-]Q;~P.Ra0]Y1pP
KȀw3dX>p #@ +}*+P$oTH%86=)JfT. +ywp`<M,@zS +8(Md<g+&7+pyP6QVn&W%~1SzT$ V~HCC}Q۞=&maKFbY|2ߏ<N䇯Q3s[{(\@'C +t6BTR6*"!
D6BFO +>m%74kZS)l20ݹPJX}4T.iIT[pPUW%nɑ;BLkc&Ey`'M4Ȗ"ƍPՆjCiY`mCf/ygn܉ S&!<{5̆KG$rt3vlE^Ge"M^q==љ_̓0WwT\nnzZ\ݜR_R +bSxO0\@VRF9 +'2mb{cb%`j>Pb|y<a$SDpWzݦQE7!kLd@5 A7j,kO.N+PN>7=t;1z`pFq~{^kYvpʼ-vF +&$oji +ޢ6e76Q6M'L e(dN^T>=mP~!ʂ&|cq.&sDˎ;m"[%u!4<xkĠg;Z˻;c`.,a=WG2b!57P#4͛lh6A<4 {{m +9!LSբt?^Kۮ8\F
L㐣bg^3H9J~i<@'(;gxwY<c= fqXpt1^,D<Qw}RN/V|Mp){+ZH*%7@"
{RM_,lp(=Vs'OUؘ/ۓsU1(,Bꃈ^d2Vv/eEZםL4~ޣw`&$|Yj)$+;}ϙ!5=ׄgm#YvTZ:.UX3;{#>Pʢ*c{O_ w}iil`Z#1'60m=ހS[ԜW<|29Zj R7KdtG9πUl}(9T+0guhSKJ6H 6[o"CÎӣl[%T٭K1vZ``sX契|:[]aè qK&)y8}J~~yQ.&<A6VBo6wLhI"&rYiVN}.&'Ͼ +W7he] +endstream +endobj +64 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 696 +/Descent -233 +/Flags 6 +/FontBBox [-36 -250 1070 750] +/FontName /CKDJDF+CMR8 +/ItalicAngle 0 +/StemV 76 +/XHeight 474 +/StemH 33 +/CharSet (/one/two/zero/four/three/equal/five) +/FontFile3 65 0 R +>> +endobj +65 0 obj +<< +/Length 957 +/Subtype /Type1C +>> +stream
+ +}j_:T]-o}gB(WI&;AxӎtiFvċЋіٕz0T@GP1S"vF}jpcbVs,jf,hjዸ⋈h,t`'<02ZYԨΤ<7#B? +
rGlwYx?{FvťbڽQ"DfVT@htkpozc,MI%ڧ1# :Q?f{kuµ؎׃$Ena}{mltNx~}^v~}cj8f>tjčt>!@vF 㚖|d]UPZl~yyæ]xg]dfUo_mxclVJKtnwyk`107 +Y\{iem;
:Wos| |stt
hw||wttv?oaCy +כ
S%Ffo +endstream +endobj +66 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 699 +/Descent -233 +/Flags 68 +/FontBBox [-30 -250 1026 750] +/FontName /CKDJDB+CMMI12 +/ItalicAngle -14.04 +/StemV 65 +/XHeight 474 +/StemH 22 +/CharSet (/Z/comma/period/k/n/e/phi/slash/j/U/epsilon/m/W/lambda/q/i/delta/f/pi/I/Y/b/epsilon1) +/FontFile3 67 0 R +>> +endobj +67 0 obj +<< +/Filter /FlateDecode +/Length 3305 +/Subtype /Type1C +>> +stream
+Hypw-K$B
LS@@rL08沍m,uYZVCZcp8M0:L@dڒi4$i2v߾}~P$3AQtNwiin^UoWV$_G32̞w?,H^u6ܝsal|t_(WT)j+GJuɋUUiYIMeMEeB-IULRU*畨+:zRVsJy~ڢ^W5(^p +4d!l ?E5A֣H.lFmGPG&2?{7l-(ST8\yJU];|叐W iH7r +mȜɈbZDrqZh3KgNR̖7Gkv4\ў"HBi`AoLN0TVcgvۡC@9B>ÏGHlf>-9Frʂ"lQF:S!~&`A?"~H8ux +E|"J^+xxnѥ/=/<J~\(8᱐`n6j`t8?Ck`uxQ87[s]O柊&[M
g|fއ{xh(0pGpyALpMӈUNfO`<j + +%4,fk5MK͇y-M-}{oXX#B?tcwIw'*
?rudAqxu +(r$^`@Kt"hcӶ\_HI⒪2-AU|(p- oP˥M{pG5S0iUzEw#p02{ՋWC
0mCo'V֖*FwH_)<Rwc#ᢷ<-bk<m:bՐ+ +y?ӌ[M-V1Qm<A"c;_ӎe1jP<.-Y$XbJZR_ +endstream +endobj +68 0 obj +<< +/Type /FontDescriptor +/Ascent 712 +/CapHeight 696 +/Descent -233 +/Flags 68 +/FontBBox [-24 -250 1110 750] +/FontName /CKDJDK+CMMI8 +/ItalicAngle -14.04 +/StemV 78 +/XHeight 474 +/StemH 32 +/CharSet (/n/k/i/phi/e/j/m/lambda/comma) +/FontFile3 69 0 R +>> +endobj +69 0 obj +<< +/Filter /FlateDecode +/Length 1435 +/Subtype /Type1C +>> +stream
+HiPSWKDMWKjN[qUAEF@H$$!IH +%TP2֖3N
>;4_}99sP a8>em;Ha0v$$"nzt)-) iσ/2gPSaqKR*"^IQz +uҷpؼBV9,ARN]YX[̙ +>y5#0CvJ'A0%eKм(=@!x+|AOÌKbldd CK2LԈ¦:
~+Vz+]>o XN! u2z/zLW=tBd@"TZJ%m$bu=-#6OkW}/`TS*s[XL0踩TD-Cr.>:
.¤r-APPPd.kwۻςw! +O_"Vel{P]])KP"O$`YJ|NUe# ]Z$'=KF1w ]"WMW._A׃= +9]Kc#s˩JCntvtde1X VR}ߴLA.H<Adoj7Y'P-;Uø.Mŕd&5"*\ӊm!]l%O=v:"bqyV)Dg+IlTN138bǑ[)ۙElP8e~Uy0jJp~<G.9`;ۯf^H-T:dF*ޡfQ5O$ ǿI#K
:Rg+1e^~'(&&d7;H8EFuCzfpZt& v|U +-ETf[x֫gMi''vJ\."mmnH_||<H:'#?'G +6ќ
Fu^%`LBD!Reb&0_)ʕer,<.kF +HmB +endstream +endobj +70 0 obj +<< +/Type /FontDescriptor +/Ascent 0 +/CapHeight 749 +/Descent 0 +/Flags 68 +/FontBBox [-29 -960 1116 775] +/FontName /CKDJEF+CMSY10 +/ItalicAngle -14.035 +/StemV 85 +/StemH 40 +/CharSet (/Rfractur/Ifractur/lessequal/similar/C/N/approxequal/minus/plusminus/radical/angbracketleft/angbracketright/bar/braceleft/braceright/bullet) +/FontFile3 71 0 R +>> +endobj +71 0 obj +<< +/Filter /FlateDecode +/Length 2103 +/Subtype /Type1C +>> +stream
+HT{TWBe'[3TqEZkmmACy'<HfyLȋwA`"Gnm-v9{ō}̹s}\C$Bj% id.;
a_ '*k Ml"~7AM$.|:wՆBEQ47#5KȖ+~fed* +iY;2\VP$͖gdeKycI^~XjTdfŋE-͑rLYT"jcގ,dn
O+QdrYnYx<BLh<^"/ 1#4cy +ĂX/r{5Y;'zxBu!BۂymaN<x3TTAx.7l< +Վ3 UXē'' |4g
pAZHc!9ߜ=o=60JsޠISrB'"ͨõ*m6Or7ݛąp-x!2.f&m
p2|c?:fa=e/[_Yk,#Z6 @$):~--GI{-'6]+p3W0iot켽k N:7Pla*$j6婹 r.2%@T-.JϺ;KEDq6?^f9fω@~]Xv)onq.^8)Ք`u:pDip&\N9]Jbޠ#FK"XP8Kzn|4?6d,:gx.Ljd{+Cds&-V^bAVčy(B(EBD!_FH
zYq/.Eee3)РgRz1(O,[Ébѻ(¹ؑT$Ҁd484MWy\.0bT6pN¦ɭƴzvu=vh)/ɇ +PTb5>P
}>P[ԡw7o4z}g'1"pRf3A@i +5ة.T6'P;+6qX,L.dDX UZ51i( +ۺ~?|}Ϯ6ܝ!o95껷Adp 63n^>vZ|H=ոI +c54b$ +endstream +endobj +72 0 obj +<< +/Type /FontDescriptor +/Ascent 0 +/CapHeight 749 +/Descent 0 +/Flags 68 +/FontBBox [-30 -955 1185 779] +/FontName /CKDJGJ+CMSY8 +/ItalicAngle -14.035 +/StemV 89 +/StemH 46 +/CharSet (/dagger/asteriskmath/minus) +/FontFile3 73 0 R +>> +endobj +73 0 obj +<< +/Length 579 +/Subtype /Type1C +>> +stream
+ + +endstream +endobj +74 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 695 +/Descent -233 +/Flags 262212 +/FontBBox [-29 -250 1274 754] +/FontName /CKDJCM+CMBXTI10 +/ItalicAngle -14.04 +/StemV 107 +/XHeight 474 +/StemH 47 +/CharSet (/Z/V/Y/W/q/r/m/v/z/b) +/FontFile3 75 0 R +>> +endobj +75 0 obj +<< +/Filter /FlateDecode +/Length 1621 +/Subtype /Type1C +>> +stream
+HOmj-RO6F^"E
Yڤ$\1` l`n|BNˤEei,֦R5e[f;{=s~=QUhϭ= +R R-yxBHO$>)Oٻ/?w& kcy53k^GMn<~~?@QuДDŽ76a
5l2k:-5Bk+Wۯ`$tHs?M"Vo,|k'DMHO hjrCpvf$^uo'(gBq9)H{Q?:v9.IB,j1h%tɶv@d-0"G<|oi1qz=2P$[a#Tռp⯉oOi3uěv5k-#hQ*F7yon}/Y_9!yj: +sqhtVVvo
wy3bX53@
Xg$)S:|s-B)bƷ6f8[kyxtԈc8N[O?[FQ"E0:_Л;_nuuCهKCݠQ5d2cݸA)9<Þ'1{y=B-`Vx-1n;^r؝?g_b%;\O'`;^'$eBЖie|/_ +u0h#lqc`+9\_ߍi<To!%4D"#@^6MQ#)ؤdUR3{>nE3#{W+\c3\G%h%SG2.cX~g?fݡd\Ö,Ь&MzPMos xH1)mxJs%]]'K\!v}ıHԃ*o˻663,1D^r:9,&TOG + +endstream +endobj +76 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 707 +/Descent -233 +/Flags 4 +/FontBBox [-62 -251 978 758] +/FontName /CKDJFP+CMSS12 +/ItalicAngle 0 +/StemV 76 +/XHeight 474 +/StemH 60 +/CharSet (/E/K/M/I/A/Q/R/B) +/FontFile3 77 0 R +>> +endobj +77 0 obj +<< +/Filter /FlateDecode +/Length 762 +/Subtype /Type1C +>> +stream
+H,mHSaǟglڦ$5wg^iRUjeKo)XƔZQ.>((苬EhD腨γΖQϷ~JtRl_Z)0ȵftSxqOiu&NۤHd^]Qc++*^jQNUruuryhQ^Afyd!VG5?'tm?uiNO^(~w^"dLY&0ÇFiw +S,G>X*=623L~ Vf1D A7LӃ4d/*ZZ fmzɦgt$,V +`C#OJ+_`*kiikImХ$m/b`d))CtB(r y@?'ʎ<njy{P +k`DAn%(WgnhcG74nct^-IO8B{C,$7/CBJ`6X1m +Ywou<B Cr
N 㔭-.x +endstream +endobj +78 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 705 +/Descent -233 +/Flags 4 +/FontBBox [-65 -250 1062 761] +/FontName /CKDJEA+CMSS8 +/ItalicAngle 0 +/StemV 87 +/XHeight 474 +/StemH 66 +/CharSet (/T) +/FontFile3 79 0 R +>> +endobj +79 0 obj +<< +/Length 242 +/Subtype /Type1C +>> +stream
+ +ƒ
+endstream +endobj +80 0 obj +<< +/Type /FontDescriptor +/Ascent 725 +/CapHeight 699 +/Descent -233 +/Flags 68 +/FontBBox [-36 -251 1103 750] +/FontName /CKDJFA+CMTI12 +/ItalicAngle -14.04 +/StemV 63 +/XHeight 474 +/StemH 29 +/CharSet (/c/i/r/u/l/a/s/y/m/e/t/period/j/o/n/w/d/A/h/p/x/hyphen/G/v/T/f/I/comma/b/ffi/g/parenleft/one/three/parenright/fi/z/F/four) +/FontFile3 81 0 R +>> +endobj +81 0 obj +<< +/Filter /FlateDecode +/Length 4586 +/Subtype /Type1C +>> +stream
+HDT{Pw%$QiǮKTѫZez*AyV$BBHMMc+zcU<7^o9s_2:7v~A8EQMoܝkhxE{Tr4^ +z$d;\0"^@$EQ yH]FCq㠂R"J$JpWWYs/kaI,X}GU&-MZ@k%wa|C+ +fK +
Xz-7+aių+v09Ήq<k:<@;0`&[7}' +Ӫ5l(O7y09WrJWvx0{ +ڰ +.jMatchSsyɭA
n`G.ޚ5`L1}-)%"me^D76R kxw+0'(zlc_SGgKK<7B-nveHP6I͏ #t٦0^[9`W[8g"}©ۋ{oZ0;FEFEQF*{Wn܀={Om:h3jeǹLɘiRݦqX)z2_uY>D
@W-Qgde,f +OE)Z9MbSQ6)Y&svYC&:E۔.U]*C| +"y,,cN21lrIW +xe&U+xcy#G,&b9(9;tv*-sa<T7_w;#F#
F&] Dx@gI^ND!찮cNʔn&j\m}5AdnI#%IH).|cGوM|<O[K=37JrtN\Z-kjQnI$BH`p)`oc`cswrk5S! I-~(iS4N*Mlm(p>>s89|14E-@_|*4ZLQ4hc#v<
xQ9,Yvp%o`/Mjy#c/Qx2uṕ;-~Kqg-$:tEe[I_@zG൏dg,@[dfDZ7>nj1smh#DnLK ŁSpTJҤizE-2i.rzeC|G-WS^}l{5Xsd$9:o,^P97bPԶ8>alEz{QYv;B-<!}zn_?Eb'ʣ2LjdEޠ+ǭ +Xm^
Bm{x=:.tXV>0Y "ȻړU3k=`gc,:e +N TZ6摋} +K*!7ŋî%34I5Uul!4>2|^ +z?GR25N,9eL6/.o/]N()flp5b=<'D*u& J +μGa.yN1>f:]w9m`<YVhks##;j`q^+vuhamk'm~ҕv)>h6?4 +L!T:".!PCwbq6}MĨ"LH6+]Ur,|\Wї\TRt.,۷BYHˇܰk%AHmRoSb& +ƪ\]D:qcW(N~F`wYY|6KPr*Uw-s UEnk.,I" `?LMQ·SkuPG3\e6)eBVVbK3oaK ) +I'FLJw| +^3Yn0ԫ\X"Dֶ<P'!SDP\#r|(Q]pAhUX,3`0v으ݻnQd?r%LD7m2ݮ&0Jh7:͗&ԽH5Ջ-ol.ɿ*4QN8}ZK%s룉h"gԼPO݁uo|@^KklߣsNu-EԂ%s_ѝfR[;WBw3̛qxˤ'mX*_VUU),Y`~iQUtݪ3C9PBhƺ撾!dU+-~of1ƾ4^=?\5{~kڊbUo_lwrL];i_ق~/wTvΕy8Wp?G +endstream +endobj +82 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 699 +/Descent -233 +/Flags 70 +/FontBBox [10 -250 1241 750] +/FontName /CKDJKJ+CMMI6 +/ItalicAngle -14.04 +/StemV 85 +/XHeight 474 +/StemH 35 +/CharSet (/i/phi/j) +/FontFile3 83 0 R +>> +endobj +83 0 obj +<< +/Length 663 +/Subtype /Type1C +>> +stream
+ + + +endstream +endobj +84 0 obj +<< +/Type /FontDescriptor +/Ascent 0 +/CapHeight 0 +/Descent 0 +/Flags 4 +/FontBBox [-24 -2960 1454 772] +/FontName /CKDJJM+CMEX10 +/ItalicAngle 0 +/StemV 47 +/StemH 47 +/CharSet (/bracketleftbig/bracketrightbig/bracketleftbigg/bracketrightbigg/bracketlefttp/bracketleftbt/bracketrighttp/bracketrightbt/radicalbig/summationdisplay/parenleftBigg/parenrightBigg/producttext/productdi\ +splay/parenleftbig/parenrightbig) +/FontFile3 85 0 R +>> +endobj +85 0 obj +<< +/Filter /FlateDecode +/Length 1354 +/Subtype /Type1C +>> +stream
+Hl{LSWϥ+N>.+`P&*Dg[<j[(1Pd1t2▘1͂tfF0]z +2?nr;2H ڲ166n~Tܦv8U*jK#]@[ߎN%%FM@ChG,)T.wQ1sZ>dHk4}bhb1uS-}|03Sk1dgfc6w(VgHf҇{_YF81m&갨p+#2&?KI/ޙj[r7ddwN;f^7y H}$@h +T>G]9$3E=KSf/C1MMAg
xIسU)+e
c+ +GBYbM'a&oSɭxIyo'%TgjɗA$8~fƞ" 5W7`.$MۡG +
u8F_}:T =]:DNShx0ѸXLz&o$^=CWؓp)2=TVZ/Q
K_\e?Lrݬd !rDV^t䜂OrWڬtxKF9 K2LRar9oP+|#bM݆emaxH<2v2'dzWߪ<Oa߆9Qӛ; smڣLrT6RWZp'; 6Y`GS&Ԡ>K".Ī,;.>5"X?8B +endstream +endobj +86 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 698 +/Descent -233 +/Flags 6 +/FontBBox [-27 -250 1122 750] +/FontName /CKDKEF+CMR7 +/ItalicAngle 0 +/StemV 79 +/XHeight 474 +/StemH 36 +/CharSet (/one/two/three/four/five) +/FontFile3 87 0 R +>> +endobj +87 0 obj +<< +/Length 769 +/Subtype /Type1C +>> +stream
+ +ڛ
VDDoI_ +endstream +endobj +88 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 715 +/Descent -233 +/Flags 70 +/FontBBox [36 -250 1349 750] +/FontName /CKDKFG+CMMI5 +/ItalicAngle -14.04 +/StemV 90 +/XHeight 474 +/StemH 36 +/CharSet (/i/phi) +/FontFile3 89 0 R +>> +endobj +89 0 obj +<< +/Length 527 +/Subtype /Type1C +>> +stream
+ + +endstream +endobj +90 0 obj +<< +/Type /FontDescriptor +/Ascent 713 +/CapHeight 698 +/Descent -233 +/Flags 70 +/FontBBox [0 -250 1171 750] +/FontName /CKDKFB+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/XHeight 474 +/StemH 32 +/CharSet (/e/n/j/i/phi) +/FontFile3 91 0 R +>> +endobj +91 0 obj +<< +/Filter /FlateDecode +/Length 939 +/Subtype /Type1C +>> +stream
+HdmL[e{{
:әLf6g@5ٚdƖHGihY_h-hV1ɜe5FdždѸhg9??YĒIkRCu +->&aNUCvNDnOOSswoG0e~TQzS/#+ݿ^p[S)TTvE-8UzcZ-hL4+(u=ʓiD u!*E"j`(-d0w0}|w*u+=pFȅu5P@%3GCY##ѤXL +TK +/"[A[]/>sx*phΟOD?2*
*Wֈ־&M벛S5Yq%S%*6ϵrUM~=x4Nj2t| Er"4}Aڝ/i(KQ+'on7mCȏ[=γ#NlF|!C_o +endstream +endobj +92 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 706 +/Descent -233 +/Flags 4 +/FontBBox [-61 -250 999 759] +/FontName /CKDKEN+CMSS10 +/ItalicAngle 0 +/StemV 78 +/XHeight 474 +/StemH 61 +/CharSet (/M/I/K) +/FontFile3 93 0 R +>> +endobj +93 0 obj +<< +/Length 375 +/Subtype /Type1C +>> +stream
+ +Ȏٖ
+endstream +endobj +94 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 707 +/Descent -233 +/Flags 68 +/FontBBox [-98 -251 1052 758] +/FontName /CKDKBL+CMSSI12 +/ItalicAngle -12 +/StemV 78 +/XHeight 474 +/StemH 60 +/CharSet (/M/K/A) +/FontFile3 95 0 R +>> +endobj +95 0 obj +<< +/Length 439 +/Subtype /Type1C +>> +stream
+ +Ï +endstream +endobj +96 0 obj +<< +/Type /FontDescriptor +/Ascent 715 +/CapHeight 698 +/Descent -233 +/Flags 70 +/FontBBox [-32 -250 1048 750] +/FontName /CKDKCF+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/XHeight 474 +/StemH 31 +/CharSet (/e/phi/v/c/Z) +/FontFile3 97 0 R +>> +endobj +97 0 obj +<< +/Length 843 +/Subtype /Type1C +>> +stream
+ +07}Gqv_[C>?N㳡n {}}}{|zs\D#!1<#(<LpǴĪ¶~pѠ +5#*u?aCy + +endstream +endobj +98 0 obj +<< +/Type /FontDescriptor +/Ascent 0 +/CapHeight 715 +/Descent 0 +/Flags 4 +/FontBBox [-55 -420 2343 920] +/FontName /CKDKHJ+MSBM10 +/ItalicAngle 0 +/StemV 40 +/StemH 40 +/CharSet (/C/R) +/FontFile3 99 0 R +>> +endobj +99 0 obj +<< +/Length 633 +/Subtype /Type1C +>> +stream
+ +y{yzĐYYRxzyzRUkl&JmX$xU}h +lx2~{w|pys +
r*""?+ +endstream +endobj +100 0 obj +<< +/Type /FontDescriptor +/Ascent 0 +/CapHeight 749 +/Descent 0 +/Flags 68 +/FontBBox [-15 -951 1252 782] +/FontName /CKDKOF+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/StemH 49 +/CharSet (/minus) +/FontFile3 101 0 R +>> +endobj +101 0 obj +<< +/Length 226 +/Subtype /Type1C +>> +stream
+ + +endstream +endobj +4 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 1 +/LastChar 147 +/Widths [816 680 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 326 326 326 326 326 326 381 381 326 762 272 326 272 490 490 +490 490 490 490 490 490 490 490 490 272 272 326 762 326 462 326 +734 693 707 748 666 639 768 734 353 503 326 612 897 734 762 666 +326 721 544 707 734 326 1006 326 326 326 272 326 272 326 326 326 +490 544 435 544 435 299 490 544 272 299 517 272 816 544 490 544 +517 381 386 381 544 517 707 517 517 435 326 326 326 326 326 326 +326 326 326 326 490 326 326 326 326 326 326 326 326 326 326 272 +326 326 544 ] +/Encoding 102 0 R +/BaseFont /CKDJAN+CMR12 +/FontDescriptor 54 0 R +/ToUnicode 103 0 R +>> +endobj +5 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 121 +/Widths [302 302 302 302 302 302 302 302 302 302 302 302 302 302 302 302 +302 302 302 302 302 302 302 302 302 302 302 302 302 302 302 302 +302 302 302 668 302 302 302 726 302 302 302 302 302 302 302 302 +302 302 302 511 302 302 302 302 302 302 302 302 302 302 302 302 +302 459 302 406 511 406 302 302 302 250 302 302 250 772 511 459 +302 302 354 359 354 511 485 302 302 485 ] +/Encoding 104 0 R +/BaseFont /CKDJAA+CMR17 +/FontDescriptor 56 0 R +/ToUnicode 105 0 R +>> +endobj +6 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 147 +/Widths [333 333 333 333 333 333 333 333 389 389 333 778 278 333 278 333 +500 500 500 333 333 333 500 500 500 333 333 333 333 778 333 333 +333 750 333 722 764 681 333 785 333 361 333 333 333 333 750 778 +681 333 736 556 722 333 333 1028 333 333 333 333 333 333 333 333 +333 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 +556 528 392 394 389 556 528 722 528 528 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 500 500 333 +333 333 333 556 ] +/Encoding 106 0 R +/BaseFont /CKDJBI+CMR10 +/FontDescriptor 58 0 R +/ToUnicode 107 0 R +>> +endobj +7 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 116 +/Widths [383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 +383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 +383 869 383 383 383 383 383 383 383 383 383 383 383 383 383 383 +383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 383 +383 559 639 511 383 383 383 383 383 383 383 383 383 383 383 383 +383 383 474 454 447 ] +/Encoding 108 0 R +/BaseFont /CKDJBD+CMBX10 +/FontDescriptor 60 0 R +/ToUnicode 109 0 R +>> +endobj +8 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 121 +/Widths [375 375 375 375 375 375 375 375 375 375 375 375 375 375 313 375 +375 563 563 563 563 563 563 375 375 375 313 375 375 375 375 375 +375 375 375 375 375 738 375 884 375 375 375 375 676 375 375 375 +769 375 375 625 782 375 375 375 375 375 375 375 375 375 375 375 +375 547 625 500 625 513 344 563 625 313 375 375 313 938 625 563 +625 375 459 444 438 625 594 375 594 594 ] +/Encoding 110 0 R +/BaseFont /CKDJCG+CMBX12 +/FontDescriptor 62 0 R +/ToUnicode 111 0 R +>> +endobj +9 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 61 +/Widths [354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 +531 531 531 531 531 531 354 354 354 354 354 354 354 826 ] +/Encoding 112 0 R +/BaseFont /CKDJDF+CMR8 +/FontDescriptor 64 0 R +/ToUnicode 113 0 R +>> +endobj +10 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 113 +/Widths [333 580 458 571 434 555 395 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 272 333 272 490 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 432 333 333 333 333 333 333 +333 333 333 333 333 665 333 924 333 568 670 333 333 333 333 333 +333 333 416 333 333 454 483 333 333 334 405 509 333 856 584 333 +333 434 ] +/Encoding 114 0 R +/BaseFont /CKDJDB+CMMI12 +/FontDescriptor 66 0 R +/ToUnicode 115 0 R +>> +endobj +11 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 110 +/Widths [333 632 620 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 295 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 493 333 333 333 362 430 553 333 940 645 ] +/Encoding 116 0 R +/BaseFont /CKDJDK+CMMI8 +/FontDescriptor 68 0 R +/ToUnicode 117 0 R +>> +endobj +12 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 1 +/LastChar 177 +/Widths [722 722 778 778 778 833 389 389 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 527 0 0 0 0 0 0 0 0 0 0 820 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 500 278 500 0 0 500 +0 0 0 0 0 0 0 0 0 778 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +778 ] +/Encoding 118 0 R +/BaseFont /CKDJEF+CMSY10 +/FontDescriptor 70 0 R +/ToUnicode 119 0 R +>> +endobj +13 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 1 +/LastChar 138 +/Widths [531 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +472 0 0 0 0 0 0 0 0 826 ] +/Encoding 120 0 R +/BaseFont /CKDJGJ+CMSY8 +/FontDescriptor 72 0 R +/ToUnicode 121 0 R +>> +endobj +14 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 122 +/Widths [414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 +414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 +414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 414 +414 414 414 414 414 414 866 1160 414 866 709 414 414 414 414 414 +414 414 532 414 414 414 414 414 414 414 414 414 414 944 414 414 +414 532 502 414 414 414 532 414 414 414 491 ] +/Encoding 122 0 R +/BaseFont /CKDJCM+CMBXTI10 +/FontDescriptor 74 0 R +/ToUnicode 123 0 R +>> +endobj +15 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 82 +/Widths [326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 647 650 326 326 583 326 326 326 266 326 674 326 850 326 326 +326 722 630 ] +/Encoding 124 0 R +/BaseFont /CKDJFP+CMSS12 +/FontDescriptor 76 0 R +/ToUnicode 125 0 R +>> +endobj +16 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 84 +/Widths [354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 +354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 +354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 354 +354 354 354 354 726 ] +/Encoding 126 0 R +/BaseFont /CKDJEA+CMSS8 +/FontDescriptor 78 0 R +/ToUnicode 127 0 R +>> +endobj +17 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 1 +/LastChar 147 +/Widths [863 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 +350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 +350 350 350 350 350 350 350 400 400 350 350 300 350 300 350 350 +500 350 500 500 350 350 350 350 350 350 350 350 350 350 350 350 +727 350 350 350 350 638 757 350 377 350 350 350 350 350 350 350 +350 350 350 700 350 350 350 350 350 350 350 350 350 350 350 350 +500 450 450 500 450 300 450 500 300 300 350 250 800 550 500 500 +350 413 400 325 525 450 650 450 475 400 350 350 350 350 350 350 +350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 +350 350 550 ] +/Encoding 128 0 R +/BaseFont /CKDJFA+CMTI12 +/FontDescriptor 80 0 R +/ToUnicode 129 0 R +>> +endobj +23 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 106 +/Widths [333 742 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 446 512 ] +/Encoding 130 0 R +/BaseFont /CKDJKJ+CMMI6 +/FontDescriptor 82 0 R +/ToUnicode 131 0 R +>> +endobj +24 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 1 +/LastChar 32 +/Widths [417 417 528 528 667 667 667 667 1000 1444 792 792 944 1278 458 458 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +] +/Encoding 132 0 R +/BaseFont /CKDJJM+CMEX10 +/FontDescriptor 84 0 R +/ToUnicode 133 0 R +>> +endobj +28 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 53 +/Widths [385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 +385 569 569 569 569 569 ] +/Encoding 134 0 R +/BaseFont /CKDKEF+CMR7 +/FontDescriptor 86 0 R +/ToUnicode 135 0 R +>> +endobj +29 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 105 +/Widths [333 842 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 534 ] +/Encoding 136 0 R +/BaseFont /CKDKFG+CMMI5 +/FontDescriptor 88 0 R +/ToUnicode 137 0 R +>> +endobj +30 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 110 +/Widths [333 687 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 542 333 333 333 404 473 333 333 333 706 ] +/Encoding 138 0 R +/BaseFont /CKDKFB+CMMI7 +/FontDescriptor 90 0 R +/ToUnicode 139 0 R +>> +endobj +31 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 77 +/Widths [333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 278 333 694 333 875 ] +/Encoding 140 0 R +/BaseFont /CKDKEN+CMSS10 +/FontDescriptor 92 0 R +/ToUnicode 141 0 R +>> +endobj +32 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 32 +/LastChar 77 +/Widths [326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 326 +326 647 326 326 326 326 326 326 326 326 326 674 326 850 ] +/Encoding 142 0 R +/BaseFont /CKDKBL+CMSSI12 +/FontDescriptor 94 0 R +/ToUnicode 143 0 R +>> +endobj +33 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 118 +/Widths [333 596 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 333 333 333 333 683 333 333 333 333 333 +333 333 333 433 333 466 333 333 333 333 333 333 333 333 333 333 +333 333 333 333 333 333 485 ] +/Encoding 144 0 R +/BaseFont /CKDKCF+CMMI10 +/FontDescriptor 96 0 R +/ToUnicode 145 0 R +>> +endobj +37 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 0 +/LastChar 82 +/Widths [300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 +300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 +300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 +300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 +300 300 300 722 300 300 300 300 300 300 300 300 300 300 300 300 +300 300 722 ] +/Encoding 146 0 R +/BaseFont /CKDKHJ+MSBM10 +/FontDescriptor 98 0 R +/ToUnicode 147 0 R +>> +endobj +41 0 obj +<< +/Type /Font +/Subtype /Type1 +/FirstChar 138 +/LastChar 138 +/Widths [893 ] +/Encoding 148 0 R +/BaseFont /CKDKOF+CMSY7 +/FontDescriptor 100 0 R +/ToUnicode 149 0 R +>> +endobj +102 0 obj +<< +/Type /Encoding +/Differences [ 1/ffi/Lambda 32/space 40/parenleft/parenright 43/plus/comma/hyphen +/period/slash/zero/one/two/three/four/five +/six/seven/eight/nine/colon/semicolon 61/equal 63/question + 65/A/B/C/D/E/F/G/H +/I/J 76/L/M/N/O/P 82/R +/S/T/U 87/W 91/bracketleft 93/bracketright 97/a/b +/c/d/e/f/g/h/i/j +/k/l/m/n/o/p/q/r +/s/t/u/v/w/x/y/z + 133/endash 144/quoteright 147/fi +] +>> +endobj +104 0 obj +<< +/Type /Encoding +/Differences [ 32/space 45/hyphen 67/C 71/G 83/S 97/a 99/c/d +/e 105/i 108/l/m/n/o 114/r/s +/t/u/v 121/y +] +>> +endobj +106 0 obj +<< +/Type /Encoding +/Differences [ 32/space 40/parenleft/parenright 43/plus/comma/hyphen/period 48/zero +/one/two 54/six/seven/eight 61/equal 65/A 67/C +/D/E 71/G 73/I 78/N/O/P 82/R +/S/T 87/W 97/a/b/c/d/e +/f/g/h/i/j/k/l/m +/n/o/p/q/r/s/t/u +/v/w/x/y 141/quotedblleft/quotedblright 147/fi +] +>> +endobj +108 0 obj +<< +/Type /Encoding +/Differences [ 32/space 65/A 97/a/b/c 114/r/s/t +] +>> +endobj +110 0 obj +<< +/Type /Encoding +/Differences [ 32/space 45/hyphen/period 49/one/two/three/four/five +/six 58/colon 69/E 71/G 76/L 80/P 83/S/T + 97/a/b/c/d/e/f/g/h +/i 108/l/m/n/o/p 114/r/s +/t/u/v 120/x/y +] +>> +endobj +112 0 obj +<< +/Type /Encoding +/Differences [ 32/space 48/zero/one/two/three/four/five 61/equal +] +>> +endobj +114 0 obj +<< +/Type /Encoding +/Differences [ 1/phi/epsilon/lambda/delta/pi/epsilon1 44/comma 46/period +/slash 73/I 85/U 87/W 89/Y/Z 98/b 101/e +/f 105/i/j/k 109/m/n 113/q +] +>> +endobj +116 0 obj +<< +/Type /Encoding +/Differences [ 1/phi/lambda 44/comma 101/e 105/i/j/k 109/m +/n +] +>> +endobj +118 0 obj +<< +/Type /Encoding +/Differences [ 1/Rfractur/Ifractur/lessequal/similar/approxequal/radical/angbracketleft/angbracketright + 67/C 78/N 123/braceleft/bar/braceright 128/bullet 138/minus 177/plusminus +] +>> +endobj +120 0 obj +<< +/Type /Encoding +/Differences [ 1/asteriskmath 129/dagger 138/minus +] +>> +endobj +122 0 obj +<< +/Type /Encoding +/Differences [ 32/space 86/V/W 89/Y/Z 98/b 109/m 113/q +/r 118/v 122/z +] +>> +endobj +124 0 obj +<< +/Type /Encoding +/Differences [ 32/space 65/A/B 69/E 73/I 75/K 77/M 81/Q +/R +] +>> +endobj +126 0 obj +<< +/Type /Encoding +/Differences [ 32/space 84/T +] +>> +endobj +128 0 obj +<< +/Type /Encoding +/Differences [ 1/ffi 32/space 40/parenleft/parenright 44/comma/hyphen/period 49/one + 51/three/four 65/A 70/F/G 73/I 84/T 97/a +/b/c/d/e/f/g/h/i +/j 108/l/m/n/o/p 114/r/s +/t/u/v/w/x/y/z 147/fi +] +>> +endobj +130 0 obj +<< +/Type /Encoding +/Differences [ 1/phi 105/i/j +] +>> +endobj +132 0 obj +<< +/Type /Encoding +/Differences [ 1/bracketleftbig/bracketrightbig/bracketleftbigg/bracketrightbigg/bracketlefttp/bracketleftbt/bracketrighttp/bracketrightbt +/radicalbig/summationdisplay/parenleftBigg/parenrightBigg/producttext/productdisplay/parenleftbig/parenrightbig + 32/space +] +>> +endobj +134 0 obj +<< +/Type /Encoding +/Differences [ 32/space 49/one/two/three/four/five +] +>> +endobj +136 0 obj +<< +/Type /Encoding +/Differences [ 1/phi 105/i +] +>> +endobj +138 0 obj +<< +/Type /Encoding +/Differences [ 1/phi 101/e 105/i/j 110/n +] +>> +endobj +140 0 obj +<< +/Type /Encoding +/Differences [ 32/space 73/I 75/K 77/M +] +>> +endobj +142 0 obj +<< +/Type /Encoding +/Differences [ 32/space 65/A 75/K 77/M +] +>> +endobj +144 0 obj +<< +/Type /Encoding +/Differences [ 1/phi 90/Z 99/c 101/e 118/v +] +>> +endobj +146 0 obj +<< +/Type /Encoding +/Differences [ 67/C 82/R +] +>> +endobj +148 0 obj +<< +/Type /Encoding +/Differences [ 138/minus +] +>> +endobj +103 0 obj +<< +/Filter /FlateDecode +/Length 332 +>> +stream
+HTn0E|,Su! bDCM=!E*2dMRu>r/ch w?Nv8Wojt3<oWRnѶE~8,Y<A,?p:= %4&rUv9r6]eWPYB69K|W>[[KbE,t%VYА mqLqYܟMF"rά, +9YݳŬڰ I6]tRl*`~0SY)*X>r7WPAs;M'` +endstream +endobj +105 0 obj +<< +/Filter /FlateDecode +/Length 285 +>> +stream
+HTOo |9nv&Ƌ&'u;5H~`A7#VeQ+˼ZpaԐfFUxId~b6g78<eWЎz%$[ 7¼ {۟vB>xV! += TYRCU5Vct\{%,_& bLpL\~zB\F.T'ߨr(?EW&Gm2<^峾%$Wk)p!!#Ψvgf6> +endstream +endobj +107 0 obj +<< +/Filter /FlateDecode +/Length 331 +>> +stream
+HTRn0St-Ctj%E7E[;wQovjO@?<]me*vYwߎOy p^
61x +*(3/ojIdQp'B81.Y<l'WKKS0BlۉpR&r!R6Bq"."&8=2'I,)גl\hy*wc
){^Qs`&m` +endstream +endobj +109 0 obj +<< +/Filter /FlateDecode +/Length 247 +>> +stream
+HTPn0t"xIPCDbI_=$;Gz鮝臷 +b 3DEOtz̈ ?mV,D\F}$~Zg]9=+ +endstream +endobj +111 0 obj +<< +/Filter /FlateDecode +/Length 309 +>> +stream
+HTQMo +|h*EVz؇nw +Ni!ِux~,3ȷ0K0'<low3hiaFwpSu݁|
Cΰ:D.n,vBn?xE<hq`YMi'T8uK2hJqHx]ELpp$%\Z +to$ +L*;V *Iܦ$\Sj E뤦X.H=|=l榹@FE?m~l/# +endstream +endobj +113 0 obj +<< +/Filter /FlateDecode +/Length 239 +>> +stream
+HTPn -l+͝"%/9X;H1 }x8;30ԟ{k"зԀFcuŭA!p2Qqʮf&-ގ8'=Kkpm>>ScXmBƑӋ9#,]7Ж; +o +endstream +endobj +115 0 obj +<< +/Filter /FlateDecode +/Length 320 +>> +stream
+HTMO0>qh-ցb{M;c'eC'ײfۻ~-3tkN%X{ymoo;%ӌu#TsVO彼5zw1$7fPb'3 d;^=B"<8yc1wFd^CU҅'%/D +FEb^'2ooUąeECyLFT*HuT$ֱ$#bwd5t~{KVRP%G*ʤ,YJT4GSrĈE-nhqq<m~<S>G +endstream +endobj +117 0 obj +<< +/Filter /FlateDecode +/Length 262 +>> +stream
+HTPMO +-j&MۍI~Į)L+B^Û73oh;<7gDFŬN 8)
%^bh qh }Ż
O
W')=R~|@Z3j4
H m}3e,el$.t\OuQ6PW +\=$>e&c9Ȓy8g^ +sA{g)ד[cȏ +endstream +endobj +119 0 obj +<< +/Filter /FlateDecode +/Length 285 +>> +stream
+HTMO09Жe7!$.j꽴Hi +v +;[V&`onPNtF;)AwjnaW|qiȲ8vO[~itiaw>P~cfyҾQ_X8qRE>9si%]*䞓.pr$>sϸ#'
cbꉩ 9<l֖Tezޔk W^9oS>A>tcKcӊ~ +endstream +endobj +121 0 obj +<< +/Filter /FlateDecode +/Length 232 +>> +stream
+HT=o w~;uCo@,WUpm\sH
B +,/: 6ߟx]#h9ߟ
&Gɸy +59n։lB'ELM{wV?y'3KJmU(be +0 +endstream +endobj +123 0 obj +<< +/Filter /FlateDecode +/Length 274 +>> +stream
+HTQMo +|!SM"U&i!Cdv +n5Ju8vi9vOBw_Fo +h[3~|E<![IB/ДEM-[@*3̢ Ú}0:z0D#>7_\"SfYcd*a\prm|xOINɍۏAa? +endstream +endobj +125 0 obj +<< +/Filter /FlateDecode +/Length 264 +>> +stream
+HTQn )7JAvr]ErC&=c/Rƅ>F)`=uΚ +endstream +endobj +127 0 obj +<< +/Filter /FlateDecode +/Length 224 +>> +stream
+HT=o w~ō:t$m ]@g<ý<tǎ\yboz08_ \qtU
֙E6 ܯsĩCyN9 +Y=dhݥN~ ' +,Bu,_6[6ȚFV-4u0?ŽSdDH֑_ȋ=Ԙ9 -9Y#||P!G +endstream +endobj +129 0 obj +<< +/Filter /FlateDecode +/Length 316 +>> +stream
+HTQn0St +y<[E1Ri)[Nuxvȟ` +endstream +endobj +131 0 obj +<< +/Filter /FlateDecode +/Length 233 +>> +stream
+HTPN pML.|^saZI,J{<3Cs6}^`D5G뀟XzRh6pAB39߲`nӅ|f_B ]RY5!/k@8ךﭽ9(QA0.A4J:u\"ٔm$=4E4wޔWz1QSӖ᱿CU` +endstream +endobj +133 0 obj +<< +/Filter /FlateDecode +/Length 245 +>> +stream
+HTMo +; +endstream +endobj +135 0 obj +<< +/Filter /FlateDecode +/Length 233 +>> +stream
+HTPn +w@ȩꂲܩR^ڝ'Ej +endstream +endobj +137 0 obj +<< +/Filter /FlateDecode +/Length 228 +>> +stream
+HT=o w~ǫ: +endstream +endobj +139 0 obj +<< +/Filter /FlateDecode +/Length 249 +>> +stream
+HTPn )7JU,YB4DrC&=c)gs7ǣmw @z0=.GcA([5I4m 8uvsBcq ~k;^7vÅ}|D: +: ~H~?$[ZIcdA6;zˢ+MW7nzG +endstream +endobj +141 0 obj +<< +/Filter /FlateDecode +/Length 235 +>> +stream
+HTP=o +"h[082~~UM- %%(܄ kтlLkv0""&SHxsfǗy3OU(-PRdfp'` +endstream +endobj +143 0 obj +<< +/Filter /FlateDecode +/Length 234 +>> +stream
+HTPn +w +@3ߖsFBK^@ߢh;ʅ~
gt H GB/*Ԍ@+xBSs~|
.AiMaDk$3{èU$Kr ͎yL.?T5Ƽ@JYZbW +endstream +endobj +145 0 obj +<< +/Filter /FlateDecode +/Length 245 +>> +stream
+HT=o w~ǫ:DDT2C͵;N +BS-4uh{uT2eq5B&.#q}LX,SSb2z]Ҕb@ʒXcD|Җ` +endstream +endobj +147 0 obj +<< +/Filter /FlateDecode +/Length 224 +>> +stream
+HT=o w~ō:`vmT ]@g<*ý<toapdgAj֙E6 ܯsĩCsvj\=bhݩ9DR +,B>t,Uz-AdM#BoyU- ǚP72_YUɈ$?#1sZ/rGxC +0 +endstream +endobj +149 0 obj +<< +/Filter /FlateDecode +/Length 216 +>> +stream
+HTP1n0 +)2(:d0!ivԔ@˃IqSt<pGC֒ ?؛#,g67A:u +endstream +endobj +1 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 3 0 R +/Contents 2 0 R +>> +endobj +20 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 22 0 R +/Contents 21 0 R +>> +endobj +25 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 27 0 R +/Contents 26 0 R +>> +endobj +34 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 36 0 R +/Contents 35 0 R +>> +endobj +38 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 40 0 R +/Contents 39 0 R +>> +endobj +42 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 44 0 R +/Contents 43 0 R +>> +endobj +45 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 47 0 R +/Contents 46 0 R +>> +endobj +48 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 50 0 R +/Contents 49 0 R +>> +endobj +51 0 obj +<< +/Type /Page +/Parent 19 0 R +/Resources 53 0 R +/Contents 52 0 R +>> +endobj +150 0 obj +<< +/S /D +>> +endobj +151 0 obj +<< +/Nums [0 150 0 R ] +>> +endobj +19 0 obj +<< +/Type /Pages +/Kids [1 0 R 20 0 R 25 0 R 34 0 R 38 0 R 42 0 R 45 0 R 48 0 R 51 0 R] +/Count 9 +/MediaBox [0 0 612 792] +>> +endobj +152 0 obj +<< +/CreationDate (D:20080101160309-05'00') +/ModDate (D:20080101160309-05'00') +/Producer (PSNormalizer.framework) +>> +endobj +153 0 obj +<< +/Type /Catalog +/Pages 19 0 R +/PageLabels 151 0 R +>> +endobj +xref +0 154 +0000000000 65535 f +0000212995 00000 n +0000000016 00000 n +0000009818 00000 n +0000189474 00000 n +0000190243 00000 n +0000190780 00000 n +0000191424 00000 n +0000191942 00000 n +0000192480 00000 n +0000192771 00000 n +0000193407 00000 n +0000194029 00000 n +0000194599 00000 n +0000195061 00000 n +0000195607 00000 n +0000195987 00000 n +0000196374 00000 n +0000139234 00000 n +0000213819 00000 n +0000213076 00000 n +0000010056 00000 n +0000029855 00000 n +0000197144 00000 n +0000197750 00000 n +0000213160 00000 n +0000030088 00000 n +0000044850 00000 n +0000198055 00000 n +0000198315 00000 n +0000198917 00000 n +0000199539 00000 n +0000199898 00000 n +0000200258 00000 n +0000213244 00000 n +0000045153 00000 n +0000056000 00000 n +0000200914 00000 n +0000213328 00000 n +0000056255 00000 n +0000075668 00000 n +0000201423 00000 n +0000213412 00000 n +0000075937 00000 n +0000097930 00000 n +0000213496 00000 n +0000098209 00000 n +0000114266 00000 n +0000213580 00000 n +0000114499 00000 n +0000132176 00000 n +0000213664 00000 n +0000132385 00000 n +0000139003 00000 n +0000139375 00000 n +0000139884 00000 n +0000146877 00000 n +0000147145 00000 n +0000149210 00000 n +0000149624 00000 n +0000155352 00000 n +0000155600 00000 n +0000156707 00000 n +0000157042 00000 n +0000160552 00000 n +0000160812 00000 n +0000161838 00000 n +0000162155 00000 n +0000165551 00000 n +0000165812 00000 n +0000167338 00000 n +0000167693 00000 n +0000169887 00000 n +0000170128 00000 n +0000170776 00000 n +0000171036 00000 n +0000172748 00000 n +0000172990 00000 n +0000173842 00000 n +0000174070 00000 n +0000174381 00000 n +0000174735 00000 n +0000179412 00000 n +0000179651 00000 n +0000180383 00000 n +0000180826 00000 n +0000182271 00000 n +0000182520 00000 n +0000183358 00000 n +0000183595 00000 n +0000184191 00000 n +0000184433 00000 n +0000185462 00000 n +0000185694 00000 n +0000186138 00000 n +0000186375 00000 n +0000186883 00000 n +0000187128 00000 n +0000188040 00000 n +0000188253 00000 n +0000188955 00000 n +0000189178 00000 n +0000201602 00000 n +0000204957 00000 n +0000202005 00000 n +0000205363 00000 n +0000202149 00000 n +0000205722 00000 n +0000202454 00000 n +0000206127 00000 n +0000202543 00000 n +0000206448 00000 n +0000202753 00000 n +0000206831 00000 n +0000202859 00000 n +0000207144 00000 n +0000203040 00000 n +0000207538 00000 n +0000203143 00000 n +0000207874 00000 n +0000203363 00000 n +0000208233 00000 n +0000203455 00000 n +0000208539 00000 n +0000203566 00000 n +0000208887 00000 n +0000203666 00000 n +0000209225 00000 n +0000203736 00000 n +0000209523 00000 n +0000203967 00000 n +0000209913 00000 n +0000204037 00000 n +0000210220 00000 n +0000204339 00000 n +0000210539 00000 n +0000204431 00000 n +0000210846 00000 n +0000204499 00000 n +0000211148 00000 n +0000204581 00000 n +0000211471 00000 n +0000204661 00000 n +0000211780 00000 n +0000204741 00000 n +0000212088 00000 n +0000204825 00000 n +0000212407 00000 n +0000204891 00000 n +0000212705 00000 n +0000213748 00000 n +0000213777 00000 n +0000213957 00000 n +0000214090 00000 n +trailer +<< +/Size 154 +/Root 153 0 R +/Info 152 0 R +/ID [<4c53a8626bd9fa40644cbecaffe36125><4c53a8626bd9fa40644cbecaffe36125>] +>> +startxref +214162 +%%EOF |