%PDF-1.6 % 6 0 obj << /S /GoTo /D [7 0 R /Fit] >> endobj 8 0 obj <>] /S /P /Lang(EN-GB)>> endobj 9 0 obj <>] /S /P /Lang(EN-GB)>> endobj 11 0 obj <>] /S /Lbl /Lang(EN-GB) >> endobj 13 0 obj <> /S /Span /Lang(EN-GB) >> endobj 14 0 obj <> /S /Span /Lang(EN-GB) >> endobj 12 0 obj <> <> <> <> <> <> <>] /S /LBody /Lang(EN-GB) >> endobj 10 0 obj <> endobj 16 0 obj <>] /S /Lbl /Lang(EN-GB) >> endobj 18 0 obj <> /S /Span /Lang(EN-GB) >> endobj 19 0 obj <> /S /Span /Lang(EN-GB) >> endobj 17 0 obj <>] /S /LBody /Lang(EN-GB) >> endobj 15 0 obj <> endobj 21 0 obj <>] /S /Lbl /Lang(EN-GB) >> endobj 23 0 obj <> /S /Span /Lang(EN-GB) >> endobj 24 0 obj <> /S /Span /Lang(EN-GB) >> endobj 25 0 obj <> /S /Span /Lang(EN-GB) >> endobj 26 0 obj <> /S /Span /Lang(EN-GB) >> endobj 28 0 obj <> /S /Span /Lang(EN-GB) >> endobj 29 0 obj <> /S /Span /Lang(EN-GB) >> endobj 31 0 obj <> endobj 22 0 obj <> 25 0 R 26 0 R <> <> 28 0 R 29 0 R <> <>] /S /LBody /Lang(EN-GB) >> endobj 20 0 obj <> endobj 34 0 obj <>] /S 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-687.294 cm BT /F46 11.9552 Tf 68.165 687.294 Td [(\210)]TJ ET 1 0 0 1 77.27 687.294 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /Span <> BDC 1 0 0 1 -83.123 -687.294 cm BT /F49 11.9552 Tf 83.123 687.294 Td [(Standar)50(d)-350(disclaimer:)]TJ ET 1 0 0 1 188.607 687.294 cm EMC /LBody <> BDC 0 g 0 G 0 g 0 G 0 g 0 G 1 0 0 1 -188.607 -687.294 cm BT /F64 11.9552 Tf 97.046 668.225 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 668.225 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -668.225 cm BT /F31 11.9552 Tf 0.992 0 0 1 108.455 668.225 Tm [(This)-329(note)-330(is)-329(not)-330(suited)-329(as)-330(a)-329(complete)-330(solution)-329(or)-330(as)-329(a)-330(template)-329(for)-329(an)-330(exam)-329(pap)-28(er.)-440(It)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 0.989 0 0 1 108.455 653.779 Tm [(w)28(as)-332(written)-331(as)-331(guidance)-331(for)-331(the)-332(grading)-331(pro)-27(cess)-332(\025)-331(ho)28(w)27(ev)28(er,)-332(with)-331(additional)-331(notes)-331(and)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 639.333 Tm [(remarks)-326(for)-327(using)-326(the)-326(do)-28(c)1(umen)27(t)-327(in)-326(teac)27(hing)-326(later.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G /F64 11.9552 Tf -11.83 -19.068 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 620.265 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -620.265 cm BT /F31 11.9552 Tf 0.983 0 0 1 108.455 620.265 Tm [(The)-333(do)-28(cumen)28(t)-334(re\035ec)1(ts)-334(what)-333(w)27(as)-333(exp)-28(ecte)1(d)-334(in)-333(that)-334(particular)-333(semester,)-334(and)-333(whic)28(h)-334(ma)28(y)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 605.819 Tm [(not)-326(b)-28(e)-326(applicable)-326(to)-326(future)-327(semesters.)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 53.858 598.872 cm /Span <> BDC 0 g 0 G 1 0 0 1 10.405 -16.744 cm EMC /Lbl <> BDC 1 0 0 1 -64.263 -582.128 cm BT /F46 11.9552 Tf 68.165 582.128 Td [(\210)]TJ ET 1 0 0 1 77.27 582.128 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /Span <> BDC 1 0 0 1 -83.123 -582.128 cm BT /F49 11.9552 Tf 83.123 582.128 Td [(W)75(eighting)-350(is)-350(a)-350(suggestion,)]TJ ET 1 0 0 1 216.146 582.128 cm EMC /LBody <> BDC 1 0 0 1 -216.146 -582.128 cm BT /F31 11.9552 Tf 220.048 582.128 Td [(and)-326(the)-327(graders)-326(can)-326(deviate.)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 53.858 575.18 cm /Span <> BDC 0 g 0 G 1 0 0 1 10.405 -16.744 cm EMC /Lbl <> BDC 1 0 0 1 -64.263 -558.436 cm BT /F46 11.9552 Tf 68.165 558.436 Td [(\210)]TJ ET 1 0 0 1 77.27 558.436 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /Span <> BDC 1 0 0 1 -83.123 -558.436 cm BT /F49 11.9552 Tf 83.123 558.436 Td [(Gr)50(ade)-350(intervals:)]TJ ET 1 0 0 1 165.375 558.436 cm EMC /LBody <> BDC 0 g 0 G 0 g 0 G 1 0 0 1 -111.517 0 cm EMC /Span <> BDC 0 g 0 G 1 0 0 1 -53.858 -558.436 cm BT /F64 11.9552 Tf 97.046 539.368 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 539.368 cm EMC /Span <> BDC 1 0 0 1 -108.876 -539.368 cm BT /F49 11.9552 Tf 1.006 0 0 1 108.876 539.368 Tm [(The)-347(\023nominal\024)-347(default)]TJ ET 1 0 0 1 226.883 539.368 cm EMC /LBody <> BDC 1 0 0 1 -226.883 -539.368 cm BT /F31 11.9552 Tf 1.006 0 0 1 230.773 539.368 Tm [(p)-27(ercen)27(t)-323(score)-324(to)-323(grade)-323(con)27(v)27(ersion,)-324(is)-323(giv)27(en)-324(in)-323(the)-323(\034rst)-324(line)-323(of)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 0.98 0 0 1 108.876 524.922 Tm [(the)-308(follo)28(wing)-308(table.)-435(The)-308(second)-308(line)-308(are)]TJ 0 0 1 rg 0 0 1 RG [-308(the)-308(Mathemat)1(ics)-308(departmen)28(t's)-308(defaults,)-313(based)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F31 11.9552 Tf 1 0 0 1 108.876 510.476 Tm [(on)-326(recommendations)-327(from)-326(Norsk)-326(matematikkr\345d)]TJ 0 g 0 G [(:)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 108.876 479.403 cm EMC /LBody <> BDC 1 0 0 1 0 25.454 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 395.125 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0.199 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 70.264 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -108.876 -504.459 cm BT /F31 11.9552 Tf 185.317 494.347 Td [(F)-326(\050fail\051)]TJ ET q 1 0 0 1 228.073 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 251.078 494.347 Td [(E)]TJ ET q 1 0 0 1 282.048 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 304.565 494.347 Td [(D)]TJ ET q 1 0 0 1 336.023 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 358.784 494.347 Td [(C)]TJ ET q 1 0 0 1 389.998 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 412.841 494.347 Td [(B)]TJ ET q 1 0 0 1 443.973 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 469.5 494.347 Td [(A)]TJ ET q 1 0 0 1 503.802 490.013 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 108.876 490.013 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 395.125 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0.199 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -108.876 -489.614 cm BT /F31 11.9552 Tf 115.252 479.502 Td [(ECON4140)]TJ ET q 1 0 0 1 179.14 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 185.722 479.502 Td [(0)-326(to)-327(39)]TJ ET q 1 0 0 1 228.073 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 234.25 479.502 Td [(40)-326(to)-327(44)]TJ ET q 1 0 0 1 282.048 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 288.225 479.502 Td [(45)-326(to)-327(54)]TJ ET q 1 0 0 1 336.023 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 342.2 479.502 Td [(55)-326(to)-327(74)]TJ ET q 1 0 0 1 389.998 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 396.175 479.502 Td [(75)-326(to)-327(90)]TJ ET q 1 0 0 1 443.973 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 450.15 479.502 Td [(91)-326(to)-327(100)]TJ ET q 1 0 0 1 503.802 475.169 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 108.876 475.169 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 395.125 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0.199 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -108.876 -474.77 cm BT /F31 11.9552 Tf 116.308 464.658 Td [(Math)-326(dept.)]TJ ET q 1 0 0 1 179.14 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 185.722 464.658 Td [(0)-326(to)-327(39)]TJ ET q 1 0 0 1 228.073 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 234.25 464.658 Td [(40)-326(to)-327(45)]TJ ET q 1 0 0 1 282.048 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 288.225 464.658 Td [(46)-326(to)-327(57)]TJ ET q 1 0 0 1 336.023 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 342.2 464.658 Td [(58)-326(to)-327(76)]TJ ET q 1 0 0 1 389.998 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 396.175 464.658 Td [(77)-326(to)-327(91)]TJ ET q 1 0 0 1 443.973 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q BT /F31 11.9552 Tf 450.15 464.658 Td [(92)-326(to)-327(100)]TJ ET q 1 0 0 1 503.802 460.324 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 108.876 460.324 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 395.125 0 l S Q 1 0 0 1 0 -0.398 cm EMC 0 g 0 G 0 g 0 G 1 0 0 1 -55.018 0 cm EMC /Span <> BDC 0 g 0 G 1 0 0 1 -53.858 -459.926 cm BT /F64 11.9552 Tf 97.046 446.071 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 446.071 cm EMC /Span <> BDC 1 0 0 1 -108.876 -446.071 cm BT /F49 11.9552 Tf 0.99 0 0 1 108.876 446.071 Tm [(Pr)50(actic)51(e)-354(fr)51(om)-354(2016)-354(and)-354(forwar)50(d)]TJ ET 1 0 0 1 270.801 446.071 cm EMC /LBody <> BDC 1 0 0 1 -270.801 -446.071 cm BT /F31 11.9552 Tf 0.99 0 0 1 274.708 446.071 Tm [(has)-330(often)-330(b)-28(ecome)-330(an)-330(\023A\024)-330(threshold)-330(laxed)-330(somewhat,)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1.004 0 0 1 108.876 431.625 Tm [(to)-324(distinguish)-324(the)-324(clear)-324(b)-27(est-in-sho)27(w)-324(pap)-27(er\050s\051)-324(from)-324(other)-324(go)-27(o)-27(d)-324(ones.)-433(Graders)-324(should)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 417.18 Tm [(exercise)-326(their)-327(b)-27(est)-326(judgemen)27(t)]TJ 0.5 0 0.5 rg 0.5 0 0.5 RG /F82 7.9701 Tf 149.707 4.338 Td [(*)]TJ 0 g 0 G ET 1 0 0 1 263.314 417.18 cm /LBody <> BDC 1 0 0 1 -263.314 -417.18 cm BT /F31 11.9552 Tf 263.314 417.18 Td [(,)-326(and)-327(in)-326(particular)-326(in)-327(ligh)27(t)-326(of)-326(this)-327(y)28(ear's)-327(c)27(ha)1(nges:)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 53.858 410.232 cm /Span <> BDC 0 g 0 G 1 0 0 1 10.405 -16.744 cm EMC /Lbl <> BDC 1 0 0 1 -64.263 -393.488 cm BT /F46 11.9552 Tf 68.165 393.488 Td [(\210)]TJ ET 1 0 0 1 77.27 393.488 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /Span <> BDC 1 0 0 1 -83.123 -393.488 cm BT /F49 11.9552 Tf 83.123 393.488 Td [(New)-350(in)-350(2025)-350(\050I\051:)]TJ ET 1 0 0 1 169.523 393.488 cm EMC /LBody <> BDC 1 0 0 1 -169.523 -393.488 cm BT /F31 11.9552 Tf 173.425 393.488 Td [(4)-326(hour)-327(exam)-326(rather)-326(than)-327(3.)-435(Still)-326(op)-27(en-b)-27(o)-28(ok.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G /F64 11.9552 Tf -76.379 -19.068 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 374.42 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -374.42 cm BT /F31 11.9552 Tf 0.98 0 0 1 108.876 374.42 Tm [(It)-294(has)-293(b)-28(een)-293(comm)28(unicated)-294(that)-293(the)-294(main)-293(reason)-294(is)-293(a)-294(general)-293(preference)-293(for)-294(a)-293(4h)-294(format,)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1.02 0 0 1 108.876 359.974 Tm [(but)-330(also)-330(a)-329(hop)-27(e)-330(that)-330(the)-329(treatmen)26(t)-329(of)-330(certain)-330(time-consuming)-330(probl)1(em)-330(t)26(yp)-26(es)-330(could)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 0.98 0 0 1 108.876 345.528 Tm [(impro)28(v)28(e.)-442(Phase)-326(diagrams)-326(ha)27(v)28(e)-326(b)-28(een)-326(men)28(tioned)-326(with)-326(the)-326(disclaimer)-326(that)-326(it)-326(is)-327(neithe)1(r)-327(a)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 331.082 Tm [(promise)-326(nor)-327(a)-326(threat.)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 108.876 312.014 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -312.014 cm BT /F31 11.9552 Tf 0.98 0 0 1 108.876 312.014 Tm [(Ho)28(w)28(ev)27(er,)-329(facilitating)-328(time-consuming)-329(problem)-328(t)28(yp)-28(es)-329(w)28(ould)-328(dep)-28(end)-328(on)-329(the)-328(problem)-329(set)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1.002 0 0 1 108.876 297.568 Tm [(not)-326(b)-27(eing)-326(o)27(v)27(erall)-326(to)-27(o)-326(long)-325(\025)-326(and)-326(w)27(orkload)]TJ ET 1 0 0 1 327.462 297.568 cm EMC /Span <> BDC 1 0 0 1 -327.462 -297.568 cm BT /F49 11.9552 Tf 1.002 0 0 1 327.462 297.568 Tm [(is)]TJ ET 1 0 0 1 336.317 297.568 cm EMC /LBody <> BDC 1 0 0 1 -336.317 -297.568 cm BT /F31 11.9552 Tf 1.002 0 0 1 340.221 297.568 Tm [(supp)-27(osed)-326(to)-326(increase)-326(although)-326(not)-326(b)28(y)-326(a)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 283.122 Tm [(full)-326(one-third.)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 53.858 278.499 cm /Span <> BDC 0 g 0 G 1 0 0 1 10.405 -19.068 cm EMC /Lbl <> BDC 1 0 0 1 -64.263 -259.431 cm BT /F46 11.9552 Tf 68.165 259.431 Td [(\210)]TJ ET 1 0 0 1 77.27 259.431 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /Span <> BDC 1 0 0 1 -83.123 -259.431 cm BT /F49 11.9552 Tf 83.123 259.431 Td [(New)-350(in)-350(2025)-350(\050II\051:)]TJ ET 1 0 0 1 174.028 259.431 cm EMC /LBody <> BDC 1 0 0 1 -174.028 -259.431 cm BT /F31 11.9552 Tf 177.93 259.431 Td [(Syllabus)-326(c)27(hanges,)-326(follo)27(wing)-327(up)-326(on)-326(c)27(hanges)-326(in)-327(Mathematics)-326(2.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G /F64 11.9552 Tf -80.884 -19.069 Td [(\016)]TJ 0 g 0 G ET 1 0 0 1 108.876 240.362 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -240.362 cm BT /F31 11.9552 Tf 0.98 0 0 1 108.876 240.362 Tm [(Remo)28(v)28(ed:)-441(Dynamic)-326(programming,)-327(pro)-28(of)-326(b)28(y)-326(induction)-326(and)-326(double)-325(in)27(tegrals.)-441(Hop)-28(efully)83(,)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 225.916 Tm [(that)-326(comp)-27(ensates)-327(for)-326(the)-326(additional)-327(w)28(orkload)-327(to)-326(learn)-326(the)-327(next)-326(items:)]TJ 0 g 0 G 0 g 0 G 0 g 0 G 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[(\050a\051)-330(is)-331(not)-330(unlik)28(e)-331(exam)-330(2019)-330(problem)-331(4,)-330(assigned)-330(for)-331(a)-330(seminar)-330(\050and)-331(re-assigned)-330(as)-330(in:)]TJ/F31 11.9552 Tf 0.997 0 0 1 83.517 686.517 Tm [(if)-328(y)27(ou)-328(didn't)-328(do)-328(it,)-329(mak)27(e)-328(sure)-328(y)27(ou)-328(do)-328(it)-328(no)27(w\051)-328(\025)-328(but)-328(exp)-28(erience)-328(is)-328(that)-328(answ)27(ers)-328(could)]TJ/F31 11.9552 Tf 1.013 0 0 1 83.517 672.071 Tm [(b)-27(e)-322(a)-323(mixed)-322(bag,)-323(it)-322(isn't)-322(necessarily)-323(easy)-322(just)-323(b)-26(ecause)-323(of)-322(b)-27(eing)-322(a)-323(\023part)-322(\050a\051\024)80(.)-430(Also)-322(it)]TJ/F31 11.9552 Tf 1.02 0 0 1 83.517 657.625 Tm [(is)-339(there)-338(in)-339(order)-339(to)-338(giv)26(e)-338(a)-339(hin)27(t)-339(to)-339(part)-338(\050c\051,)-344(whic)27(h)-339(do)-26(es)-339(test)-338(a)-339(v)27(ery)-339(sp)-27(eci\034c)-338(piece)-339(of)]TJ/F31 11.9552 Tf 1 0 0 1 83.517 643.179 Tm [(theory)82(.)]TJ 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[(,)-321(lik)27(e)-321(done)-321(in)-320(the)-321(up)-27(o)-26(coming)]TJ/F31 11.9552 Tf 1.02 0 0 1 83.517 599.842 Tm [(suggested)-326(solution.)-446(Similar)-326(will)-327(also)-326(go)-326(if)-327(one)-326(c)27(ho)-27(oses)-326(to)-327(use)-326(the)-326(b)-27(ordered)-326(Hessian)]TJ/F31 11.9552 Tf 1 0 0 1 82.148 585.396 Tm [(\050whic)27(h)-326(v)54(anishes)-326(when)]TJ/F61 11.9552 Tf 114.59 0 Td [(x)]TJ/F52 11.9552 Tf 9.973 0 Td [(=)-278(0)]TJ/F31 11.9552 Tf 18.278 0 Td [(.\051)]TJ ET 1 0 0 1 83.517 570.452 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -83.517 -570.452 cm BT /F125 11.3574 Tf 83.517 558.995 Td [(Ho)15(w)-278(to)-278(solve)-278(Pr)20(ob)10(lem)-278(2:)]TJ 0 g 0 G ET 1 0 0 1 226.615 558.995 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -226.615 -558.995 cm BT /F31 11.9552 Tf 91.972 539.568 Td [(\050a\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 539.568 cm EMC /P <> BDC 1 0 0 1 -112.782 -539.568 cm BT /F61 11.9552 Tf 112.782 539.568 Td [(g)]TJ/F31 11.9552 Tf 9.937 0 Td [(is)-326(the)-327(sum)-326(of)-326(con)27(v)27(ex)-326(functions)-327(and)-326(hence)-326(con)27(v)27(ex)-326(and)-326(hence)-327(quasicon)28(v)27(ex.)]TJ ET 1 0 0 1 112.782 520.141 cm EMC /P <> BDC 1 0 0 1 -112.782 -520.141 cm BT /F52 11.9552 Tf 112.782 520.141 Td [(ln)]TJ/F61 11.9552 Tf 11.805 0 Td [(f)]TJ/F52 11.9552 Tf 0.98 0 0 1 131.634 520.141 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 136.095 520.141 Tm [(x;)-167(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 154.128 520.141 Tm [(\051)-283(=)-284(3)]TJ/F52 11.9552 Tf 1 0 0 1 181.882 520.141 Tm [(ln)]TJ/F61 11.9552 Tf 11.805 0 Td [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 202.288 520.141 Tm [(+)]TJ/F61 11.9552 Tf 1 0 0 1 213.159 520.141 Tm [(y)]TJ/F31 11.9552 Tf 0.98 0 0 1 222.851 520.141 Tm [(is)-303(conca)27(v)28(e)-303(\050qua)-304(sum)-303(of)-304(conca)28(v)28(es\051)-303(\025)-304(th)28(us)]TJ/F61 11.9552 Tf 1 0 0 1 424.552 520.141 Tm [(f)]TJ/F31 11.9552 Tf 0.98 0 0 1 435.154 520.141 Tm [(is)-303(quasiconca)27(v)28(e.)]TJ 0 g 0 G /F31 11.9552 Tf 1 0 0 1 91.321 495.732 Tm [(\050b\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 495.732 cm EMC /P <> BDC 1 0 0 1 -112.782 -495.732 cm BT /F31 11.9552 Tf 1.02 0 0 1 112.782 495.732 Tm [(Let)]TJ/F61 11.9552 Tf 1 0 0 1 134.171 495.732 Tm [(L)]TJ/F52 11.9552 Tf 1.02 0 0 1 142.135 495.732 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 146.778 495.732 Tm [(x;)-167(y)]TJ/F52 11.9552 Tf 1.02 0 0 1 164.811 495.732 Tm [(\051)-283(=)]TJ/F61 11.9552 Tf 1 0 0 1 185.642 495.732 Tm [(f)]TJ/F52 11.9552 Tf 1.02 0 0 1 192.689 495.732 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 197.332 495.732 Tm [(x;)-167(y)]TJ/F52 11.9552 Tf 1.02 0 0 1 215.365 495.732 Tm [(\051)-222(+)]TJ/F61 11.9552 Tf 1 0 0 1 234.712 495.732 Tm [(\025x)]TJ/F64 11.9552 Tf 16.189 0 Td [(\000)]TJ/F61 11.9552 Tf 12.007 0 Td [(\026)]TJ/F64 11.9552 Tf 9.752 0 Td [(\001)]TJ/F52 11.9552 Tf 1.02 0 0 1 278.689 495.732 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 283.332 495.732 Tm [(y)]TJ/F52 11.9552 Tf 1.02 0 0 1 292.178 495.732 Tm [(+)]TJ/F61 11.9552 Tf 1 0 0 1 304.173 495.732 Tm [(e)]TJ/F62 7.9701 Tf 5.425 4.339 Td [(x)]TJ/F65 7.9701 Tf 4.767 0 Td [(\000)]TJ/F55 7.9701 Tf 6.587 0 Td [(3)]TJ/F64 11.9552 Tf 7.441 -4.339 Td [(\000)]TJ/F52 11.9552 Tf 1.02 0 0 1 340.4 495.732 Tm [(2\051)]TJ/F31 11.9552 Tf 1.02 0 0 1 351.013 495.732 Tm [(.)-445(The)-327(Kuhn\025T)81(uc)26(k)27(er)-326(conditions)]TJ/F31 11.9552 Tf 1 0 0 1 112.782 481.286 Tm [(for)-326(an)-327(admissible)-326(p)-27(oin)27(t)-326(to)-327(solv)27(e,)-326(read:)]TJ ET /S/Span<0\\text\040{\)}\040\\\\\040\\mu\040\\geq\0400\040\\quad\040\\text\040{\(and:\040}\\mu\040&=0\\text\040{\040if\040}y+e^{x-3}<2\\text\040{\)})>>BDC BT /F52 11.9552 Tf 250.892 454.885 Td [(3)]TJ/F61 11.9552 Tf 5.853 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.936 Td [(2)]TJ/F61 11.9552 Tf 4.732 -4.936 Td [(e)]TJ/F62 7.9701 Tf 5.426 4.936 Td [(y)]TJ/F52 11.9552 Tf 7.626 -4.936 Td [(+)]TJ/F61 11.9552 Tf 11.762 0 Td [(\025)]TJ/F52 11.9552 Tf 10.149 0 Td [(=)]TJ/F61 11.9552 Tf 12.426 0 Td [(\026e)]TJ/F62 7.9701 Tf 12.468 4.936 Td [(x)]TJ/F65 7.9701 Tf 4.767 0 Td [(\000)]TJ/F55 7.9701 Tf 6.587 0 Td [(3)]TJ/F31 11.9552 Tf 158.83 -4.936 Td [(\0501\051)]TJ/F61 11.9552 Tf -220.178 -17.434 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.936 Td [(3)]TJ/F61 11.9552 Tf 4.732 -4.936 Td [(e)]TJ/F62 7.9701 Tf 5.426 4.936 Td [(y)]TJ/F52 11.9552 Tf 8.29 -4.936 Td [(=)]TJ/F61 11.9552 Tf 12.426 0 Td [(\026)]TJ/F31 11.9552 Tf 182.652 0 Td [(\0502\051)]TJ/F61 11.9552 Tf -277.422 -17.435 Td [(\025)]TJ/F64 11.9552 Tf 10.15 0 Td [(\025)]TJ/F52 11.9552 Tf 12.619 0 Td [(0)]TJ/F31 11.9552 Tf 17.559 0 Td [(\050and:)]TJ/F61 11.9552 Tf 31.867 0 Td [(\025)]TJ/F52 11.9552 Tf 10.149 0 Td [(=)-278(0)]TJ/F31 11.9552 Tf 22.181 0 Td [(if)]TJ/F61 11.9552 Tf 10.731 0 Td [(x)-278(>)]TJ/F52 11.9552 Tf 22.398 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(\051)-10821(\0503\051)]TJ/F61 11.9552 Tf -143.936 -17.435 Td [(\026)]TJ/F64 11.9552 Tf 10.364 0 Td [(\025)]TJ/F52 11.9552 Tf 12.62 0 Td [(0)]TJ/F31 11.9552 Tf 17.559 0 Td [(\050and:)]TJ/F61 11.9552 Tf 31.866 0 Td [(\026)]TJ/F52 11.9552 Tf 10.364 0 Td [(=)-278(0)]TJ/F31 11.9552 Tf 22.181 0 Td [(if)]TJ/F61 11.9552 Tf 10.731 0 Td [(y)]TJ/F52 11.9552 Tf 8.793 0 Td [(+)]TJ/F61 11.9552 Tf 11.761 0 Td [(e)]TJ/F62 7.9701 Tf 5.426 4.937 Td [(x)]TJ/F65 7.9701 Tf 4.767 0 Td [(\000)]TJ/F55 7.9701 Tf 6.586 0 Td [(3)]TJ/F61 11.9552 Tf 8.053 -4.937 Td [(<)]TJ/F52 11.9552 Tf 12.426 0 Td [(2)]TJ/F31 11.9552 Tf 5.853 0 Td [(\051)]TJ ET EMC BT /F31 11.9552 Tf 498.17 402.581 Td [(\0504\051)]TJ 0 g 0 G ET 1 0 0 1 119.676 376.18 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -376.18 cm BT /F46 11.9552 Tf 123.578 376.18 Td [(\210)]TJ ET 1 0 0 1 132.682 376.18 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm /LBody <> BDC 1 0 0 1 -138.535 -376.18 cm BT /F52 11.9552 Tf 1.02 0 0 1 138.535 376.18 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 143.179 376.18 Tm [(x)]TJ/F55 7.9701 Tf 6.652 -1.793 Td [(0)]TJ/F61 11.9552 Tf 4.732 1.793 Td [(;)-167(y)]TJ/F55 7.9701 Tf 10.952 -1.793 Td [(0)]TJ/F52 11.9552 Tf 1.02 0 0 1 170.247 376.18 Tm [(\051)]TJ/F31 11.9552 Tf 1.02 0 0 1 174.891 376.18 Tm [(:)]TJ/F61 11.9552 Tf 1 0 0 1 183.729 376.18 Tm [(g)]TJ/F52 11.9552 Tf 1.02 0 0 1 189.763 376.18 Tm [(\0503)]TJ/F61 11.9552 Tf 1 0 0 1 200.376 376.18 Tm [(;)]TJ/F52 11.9552 Tf 1.02 0 0 1 205.62 376.18 Tm [(1\051)-295(=)-294(1)-227(+)]TJ/F61 11.9552 Tf 1 0 0 1 253.492 376.18 Tm [(e)]TJ/F55 7.9701 Tf 5.425 4.339 Td [(3)]TJ/F65 7.9701 Tf 4.234 0 Td [(\000)]TJ/F55 7.9701 Tf 6.587 0 Td [(3)]TJ/F64 11.9552 Tf 7.497 -4.339 Td [(\000)]TJ/F52 11.9552 Tf 1.02 0 0 1 289.299 376.18 Tm [(2)-295(=)-294(0)]TJ/F31 11.9552 Tf 1.02 0 0 1 321.771 376.18 Tm [(\050equalit)27(y!\051,)-336(and)]TJ/F61 11.9552 Tf 1 0 0 1 406.557 376.18 Tm [(x)]TJ/F55 7.9701 Tf 6.652 -1.793 Td [(0)]TJ/F52 11.9552 Tf 1.02 0 0 1 421.533 376.18 Tm [(=)-295(3)]TJ/F61 11.9552 Tf 1 0 0 1 443.974 376.18 Tm [(>)]TJ/F52 11.9552 Tf 1.02 0 0 1 456.671 376.18 Tm [(0)]TJ/F31 11.9552 Tf 1.02 0 0 1 466.702 376.18 Tm [(so)]TJ/F61 11.9552 Tf 1 0 0 1 481.443 376.18 Tm [(\025)]TJ/F52 11.9552 Tf 1.02 0 0 1 491.863 376.18 Tm [(=)-295(0)]TJ/F31 11.9552 Tf 1.02 0 0 1 510.712 376.18 Tm [(.)]TJ/F31 11.9552 Tf 0.98 0 0 1 138.114 361.735 Tm [(The)-279(other)-280(conditions)-279(simplify)-280(to)-280(\0501)1('\051:)]TJ/F52 11.9552 Tf 0.98 0 0 1 327.127 361.735 Tm [(27)]TJ/F61 11.9552 Tf 1 0 0 1 338.599 361.735 Tm [(e)]TJ/F52 11.9552 Tf 0.98 0 0 1 347.346 361.735 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 359.589 361.735 Tm [(\026e)]TJ/F55 7.9701 Tf 12.469 4.338 Td [(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 376.79 361.735 Tm [(;)-297(\0502'\051:)]TJ/F52 11.9552 Tf 0.98 0 0 1 409.382 361.735 Tm [(27)]TJ/F61 11.9552 Tf 1 0 0 1 420.854 361.735 Tm [(e)]TJ/F52 11.9552 Tf 0.98 0 0 1 429.6 361.735 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 441.844 361.735 Tm [(\026)]TJ/F31 11.9552 Tf 0.98 0 0 1 448.887 361.735 Tm [(;)-297(\0504'\051:)]TJ/F61 11.9552 Tf 1 0 0 1 481.479 361.735 Tm [(\026)]TJ/F64 11.9552 Tf 10.364 0 Td [(\025)]TJ/F52 11.9552 Tf 0.98 0 0 1 504.463 361.735 Tm [(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 510.199 361.735 Tm [(;)]TJ/F31 11.9552 Tf 1 0 0 1 138.535 347.289 Tm [(all)-326(hold)-327(with)]TJ/F61 11.9552 Tf 68.937 0 Td [(\026)]TJ/F52 11.9552 Tf 10.364 0 Td [(=)-278(27)]TJ/F61 11.9552 Tf 24.132 0 Td [(e)]TJ/F31 11.9552 Tf 9.327 0 Td [(\050whic)27(h)]TJ/F64 11.9552 Tf 38.045 0 Td [(\025)]TJ/F52 11.9552 Tf 12.619 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(\051)-326(and)]TJ/F61 11.9552 Tf 31.217 0 Td [(\025)]TJ/F52 11.9552 Tf 10.149 0 Td [(=)-278(0)]TJ/F31 11.9552 Tf 18.279 0 Td [(.)]TJ 0 g 0 G ET 1 0 0 1 119.676 327.862 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -327.862 cm BT /F46 11.9552 Tf 123.578 327.862 Td [(\210)]TJ ET 1 0 0 1 132.682 327.862 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm /LBody <> BDC 1 0 0 1 -138.535 -327.862 cm BT /F61 11.9552 Tf 138.535 327.862 Td [(f)]TJ/F31 11.9552 Tf 1.02 0 0 1 149.789 327.862 Tm [(has)-345(stationary)-345(p)-27(oin)27(ts)-345(whenev)27(er)]TJ/F61 11.9552 Tf 1 0 0 1 317.07 327.862 Tm [(x)]TJ/F52 11.9552 Tf 1.02 0 0 1 327.562 327.862 Tm [(=)-315(0)]TJ/F31 11.9552 Tf 1.02 0 0 1 346.659 327.862 Tm [(.)-502(With)]TJ/F61 11.9552 Tf 1 0 0 1 387.162 327.862 Tm [(x)]TJ/F52 11.9552 Tf 1.02 0 0 1 397.654 327.862 Tm [(=)-315(0)-315(=)]TJ/F61 11.9552 Tf 1 0 0 1 433.719 327.862 Tm [(\026)]TJ/F52 11.9552 Tf 1.02 0 0 1 444.602 327.862 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 457.729 327.862 Tm [(\025)]TJ/F31 11.9552 Tf 1.02 0 0 1 464.557 327.862 Tm [(,)-351(w)26(e)-345(o)1(nly)]TJ/F31 11.9552 Tf 1.011 0 0 1 138.535 313.416 Tm [(need)-324(admissibilit)27(y)81(.)-433(One)-323(example)-324(is)-324(the)-323(origin,)-324(but)-324(an)27(y)-323(p)-27(oin)27(t)]TJ/F52 11.9552 Tf 1.011 0 0 1 454.028 313.416 Tm [(\0500)]TJ/F61 11.9552 Tf 1 0 0 1 464.548 313.416 Tm [(;)-167(y)]TJ/F55 7.9701 Tf 10.951 -1.793 Td [(0)]TJ/F52 11.9552 Tf 1.011 0 0 1 480.232 313.416 Tm [(\051)]TJ/F31 11.9552 Tf 1.011 0 0 1 488.746 313.416 Tm [(with)]TJ/F61 11.9552 Tf 1 0 0 1 138.535 298.97 Tm [(y)]TJ/F55 7.9701 Tf 5.708 -1.793 Td [(0)]TJ/F64 11.9552 Tf 8.053 1.793 Td [(\024)]TJ/F52 11.9552 Tf 12.62 0 Td [(2)]TJ/F64 11.9552 Tf 8.509 0 Td [(\000)]TJ/F61 11.9552 Tf 11.955 0 Td [(e)]TJ/F65 7.9701 Tf 5.426 4.338 Td [(\000)]TJ/F55 7.9701 Tf 6.586 0 Td [(3)]TJ/F31 11.9552 Tf 8.635 -4.338 Td [(will)-326(do.)]TJ 0 g 0 G -113.405 -24.408 Td [(\050c\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 274.561 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -274.561 cm BT /F31 11.9552 Tf 0.999 0 0 1 112.782 274.561 Tm [(F)82(rom)-327(part)-327(\050a\051)-327(w)27(e)-327(ha)27(v)27(e)-327(a)-327(quasico)1(nca)27(v)27(e)-327(program.)-436(Su\036cien)27(t)-327(conditions)-327(apply)-327(at)]TJ/F52 11.9552 Tf 1 0 0 1 111.413 260.116 Tm [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 -1.794 Td [(0)]TJ/F61 11.9552 Tf 4.732 1.794 Td [(;)-167(y)]TJ/F55 7.9701 Tf 10.952 -1.794 Td [(0)]TJ/F52 11.9552 Tf 4.732 1.794 Td [(\051)]TJ ET 1 0 0 1 151.488 260.116 cm EMC /Span <> BDC 1 0 0 1 -151.488 -260.116 cm BT /F49 11.9552 Tf 151.488 260.116 Td [(b)50(e)50(c)50(ause)-350(that)-350(is)-350(not)-350(a)-350(stationary)-350(p)50(oint)-350(for)]TJ/F61 11.9552 Tf 211.905 0 Td [(f)]TJ/F49 11.9552 Tf 7.046 0 Td [(.)]TJ ET 1 0 0 1 374.026 260.116 cm EMC /LBody <> BDC 1 0 0 1 -261.665 -19.427 cm EMC /LBody <> BDC 1 0 0 1 -112.361 -240.689 cm BT /F31 11.9552 Tf 0.98 0 0 1 112.361 240.689 Tm [(That)-294(latter)-293(condition)-294(fails)-294(when)]TJ/F61 11.9552 Tf 1 0 0 1 274.629 240.689 Tm [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 284.602 240.689 Tm [(=)-283(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 302.582 240.689 Tm [(,)-302(b)-27(ecause)]TJ/F61 11.9552 Tf 1 0 0 1 351.374 240.689 Tm [(f)]TJ/F65 7.9701 Tf 7.046 4.338 Td [(0)]TJ/F62 7.9701 Tf -1.276 -7.294 Td [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 362.409 240.689 Tm [(\0500)]TJ/F61 11.9552 Tf 1 0 0 1 372.606 240.689 Tm [(;)-167(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 383.987 240.689 Tm [(\051)-283(=)-284(3)]TJ/F64 11.9552 Tf 1 0 0 1 411.466 240.689 Tm [(\001)]TJ/F52 11.9552 Tf 0.98 0 0 1 416.504 240.689 Tm [(0)]TJ/F55 7.9701 Tf 1 0 0 1 422.24 245.027 Tm [(2)]TJ/F61 11.9552 Tf 4.733 -4.338 Td [(e)]TJ/F62 7.9701 Tf 5.425 4.338 Td [(y)]TJ/F31 11.9552 Tf 0.98 0 0 1 440.81 240.689 Tm [(and)]TJ/F61 11.9552 Tf 1 0 0 1 462.736 240.689 Tm [(f)]TJ/F65 7.9701 Tf 7.046 4.338 Td [(0)]TJ/F62 7.9701 Tf -1.276 -7.294 Td [(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 473.475 240.689 Tm [(\0500)]TJ/F61 11.9552 Tf 1 0 0 1 483.673 240.689 Tm [(;)-167(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 495.053 240.689 Tm [(\051)-283(=)]TJ/F52 11.9552 Tf 1 0 0 1 112.782 226.243 Tm [(0)]TJ/F55 7.9701 Tf 5.853 4.338 Td [(3)]TJ/F61 11.9552 Tf 4.733 -4.338 Td [(e)]TJ/F62 7.9701 Tf 5.425 4.338 Td [(y)]TJ/F31 11.9552 Tf 8.872 -4.338 Td [(b)-27(oth)-327(v)55(anish.)]TJ 0 g 0 G ET 1 0 0 1 65.564 748.306 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 464.148 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0.199 -539.418 cm []0 d 0 J 0.398 w 0 0 m 0 539.618 l S Q q 1 0 0 1 463.948 -539.418 cm []0 d 0 J 0.398 w 0 0 m 0 539.618 l S Q 1 0 0 1 0 -539.219 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 464.148 0 l S Q 1 0 0 1 0 -0.399 cm EMC 0 g 0 G 1 0 0 1 -11.706 267.02 cm EMC 0 g 0 G 0 g 0 G 1 0 0 1 0 -421.451 cm /Artifact <> BDC 0 g 0 G 1 0 0 1 -53.858 -53.858 cm BT /F31 11.9552 Tf 294.711 53.858 Td [(3)]TJ 0 g 0 G ET 1 0 0 1 541.417 53.858 cm EMC 0 g 0 G endstream endobj 73 0 obj << /Type /Page /Contents 99 0 R /Resources 98 0 R /MediaBox [0 0 595.276 841.89] /Parent 60 0 R >> endobj 100 0 obj << /D [73 0 R /XYZ 52.858 789.032 null] >> endobj 101 0 obj << /D [73 0 R /XYZ 83.517 735.832 null] >> endobj 102 0 obj << /D [73 0 R /XYZ 83.517 573.441 null] >> endobj 103 0 obj << /D [73 0 R /XYZ 83.517 558.853 null] >> endobj 104 0 obj << /D [73 0 R /XYZ 83.517 512.17 null] >> endobj 105 0 obj << /D [73 0 R /XYZ 499.54 472.32 null] >> endobj 106 0 obj << /D [73 0 R /XYZ 499.54 454.885 null] >> endobj 107 0 obj << /D [73 0 R /XYZ 499.54 437.451 null] >> endobj 108 0 obj << /D [73 0 R /XYZ 499.54 420.016 null] 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12.426 29.49 Td [(0)]TJ 0 -17.535 Td [(B)]TJ 0 -5.977 Td [(B)]TJ 0 -5.978 Td [(B)]TJ 0 -6.376 Td [(@)]TJ/F52 11.9552 Tf 8.717 28.145 Td [(3)-833(2)-834(0)-833(0)]TJ 0 -14.446 Td [(1)-833(2)-834(0)-833(0)]TJ 0 -14.446 Td [(0)-833(0)-834(2)-833(3)]TJ 0 -14.446 Td [(0)-833(0)-834(2)-833(1)]TJ/F67 9.9626 Tf 53.3 51.059 Td [(1)]TJ 0 -17.534 Td [(C)]TJ 0 -5.978 Td [(C)]TJ 0 -5.978 Td [(C)]TJ 0 -6.376 Td [(A)]TJ/F31 11.9552 Tf 20.423 6.376 Td [(and)]TJ/F157 11.9552 Tf 34.469 0 Td [(W)]TJ/F52 11.9552 Tf 17.269 0 Td [(=)]TJ/F67 9.9626 Tf 12.426 29.49 Td [(0)]TJ 0 -17.534 Td [(B)]TJ 0 -5.978 Td [(B)]TJ 0 -5.978 Td [(B)]TJ 0 -6.376 Td [(@)]TJ/F52 11.9552 Tf 8.717 28.145 Td [(2)-833(0)-834(4)]TJ 0 -14.446 Td [(1)-833(0)-834(2)]TJ 0 -14.446 Td [(0)-833(3)-834(6)]TJ 0 -14.446 Td [(0)-833(2)-834(4)]TJ/F67 9.9626 Tf 37.485 51.059 Td [(1)]TJ 0 -17.534 Td [(C)]TJ 0 -5.978 Td [(C)]TJ 0 -5.978 Td [(C)]TJ 0 -6.376 Td [(A)]TJ/F31 11.9552 Tf 8.717 6.376 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -317.926 -40.905 Td [(\050a\051)]TJ 0 g 0 G ET 1 0 0 1 83.123 675.52 cm EMC /P <> BDC 1 0 0 1 -83.123 -675.52 cm BT /F31 11.9552 Tf 83.123 675.52 Td [(Find)-326(the)-327(rank)-326(of)]TJ/F157 11.9552 Tf 88.282 0 Td [(W)]TJ/F31 11.9552 Tf 13.949 0 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -123.692 -22.768 Td [(\050b\051)]TJ 0 g 0 G ET 1 0 0 1 83.123 652.752 cm EMC /P <> BDC 1 0 0 1 -83.123 -652.752 cm BT /F31 11.9552 Tf 1.002 0 0 1 83.123 652.752 Tm [(Sho)27(w)-326(that)-325(eac)27(h)-326(of)-326(the)-326(columns)]TJ/F157 11.9552 Tf 1.002 0 0 1 245.083 652.752 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 254.816 650.959 Tm [(1)]TJ/F31 11.9552 Tf 1.002 0 0 1 259.548 652.752 Tm [(,)]TJ/F157 11.9552 Tf 1.002 0 0 1 266.71 652.752 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 276.443 650.959 Tm [(2)]TJ/F31 11.9552 Tf 1.002 0 0 1 281.175 652.752 Tm [(,)]TJ/F157 11.9552 Tf 1.002 0 0 1 288.337 652.752 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 298.07 650.959 Tm [(3)]TJ/F31 11.9552 Tf 1.002 0 0 1 306.706 652.752 Tm [(of)]TJ/F157 11.9552 Tf 1.002 0 0 1 320.058 652.752 Tm [(W)]TJ/F31 11.9552 Tf 1.002 0 0 1 334.035 652.752 Tm [(,)-326(is)-326(an)-326(e)1(igen)27(v)27(ector)-326(of)]TJ/F157 11.9552 Tf 1.002 0 0 1 443.544 652.752 Tm [(A)]TJ/F31 11.9552 Tf 1.002 0 0 1 453.72 652.752 Tm [(,)]TJ ET 1 0 0 1 460.882 652.752 cm EMC /Span <> BDC 1 0 0 1 -460.882 -652.752 cm BT /F49 11.9552 Tf 1.002 0 0 1 460.882 652.752 Tm [(and)-349(al)-75(l)-350(with)-349(the)]TJ 0 g 0 G 0 g 0 G /F49 11.9552 Tf 1 0 0 1 82.501 638.306 Tm [(same)-350(\050r)50(e)50(al!\051)-450(eigenvalue)]TJ ET 1 0 0 1 201.721 638.306 cm EMC /P <> BDC 1 0 0 1 -201.721 -638.306 cm BT /F31 11.9552 Tf 201.721 638.306 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -138.758 -22.768 Td [(\050c\051)]TJ 0 g 0 G ET 1 0 0 1 83.123 615.538 cm EMC /P <> BDC 1 0 0 1 -83.123 -615.538 cm BT /F61 11.9552 Tf 83.123 615.538 Td [(\026)]TJ/F52 11.9552 Tf 10.364 0 Td [(=)]TJ/F64 11.9552 Tf 12.426 0 Td [(\000)]TJ/F52 11.9552 Tf 9.298 0 Td [(1)]TJ/F31 11.9552 Tf 9.755 0 Td [(is)-326(an)-327(eigen)28(v)54(alue)-326(of)]TJ/F157 11.9552 Tf 97.291 0 Td [(A)]TJ/F31 11.9552 Tf 10.156 0 Td [(.)-435(Find)-327(a)1(n)-327(asso)-27(ciated)-326(eigen)27(v)27(ector.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -170.751 -22.767 Td [(\050d\051)]TJ 0 g 0 G ET 1 0 0 1 83.123 592.771 cm EMC /P <> BDC 1 0 0 1 -83.123 -592.771 cm BT /F31 11.9552 Tf 1.02 0 0 1 83.123 592.771 Tm [(Do)-337(parts)-337(\050a\051\025\050c\051)-337(pro)27(vide)-337(enough)-337(information)-336(to)-337(decide)-337(the)-337(de\034niteness)-337(of)-337(the)-337(quadratic)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 83.123 578.325 Tm [(form)]TJ/F61 11.9552 Tf 27.64 0 Td [(Q)]TJ/F52 11.9552 Tf 9.271 0 Td [(\050)]TJ/F157 11.9552 Tf 4.552 0 Td [(z)]TJ/F52 11.9552 Tf 5.978 0 Td [(\051)-278(=)]TJ/F157 11.9552 Tf 20.298 0 Td [(z)]TJ/F65 7.9701 Tf 5.978 4.338 Td [(0)]TJ/F157 11.9552 Tf 2.795 -4.338 Td [(Az)]TJ/F31 11.9552 Tf 16.134 0 Td [(?)-1958(\050)]TJ ET 1 0 0 1 209.261 578.325 cm EMC /Span <> BDC 1 0 0 1 -209.261 -578.325 cm BT /F49 11.9552 Tf 209.261 578.325 Td [(Caution:)-450(b)50(e)-350(pr)50(e)50(cise!)]TJ ET 1 0 0 1 312.144 578.325 cm EMC /P <> BDC 1 0 0 1 -312.144 -578.325 cm BT /F31 11.9552 Tf 312.144 578.325 Td [(\051)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 65.564 330.881 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 29.659 220.465 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -95.223 -551.346 cm BT /F125 11.3574 Tf 1.02 0 0 1 95.223 543.061 Tm [(\050A)-405(quite)-404(standar)19(d)-404(pr)19(ob)10(lem)-405(\226)-404(compare)-405(\050b\051\050c\051\050d\051)-405(to)-404(e)14(xam)-404(2022#1)-405(assigned)-405(f)20(or)]TJ/F125 11.3574 Tf 1 0 0 1 95.223 528.615 Tm [(seminar)-278(10,)-278(and)-278(to)-278(2019#1\050a\051\050b\051\050c\051)-278(f)20(or)-278(seminar)-278(5.\051)-2344(Ho)15(w)-278(to)-278(solve:)]TJ 0 g 0 G ET 1 0 0 1 471.439 528.615 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -471.439 -528.615 cm BT /F31 11.9552 Tf 103.678 509.188 Td [(\050a\051)]TJ 0 g 0 G ET 1 0 0 1 124.488 509.188 cm EMC /P <> BDC 1 0 0 1 -124.488 -509.188 cm BT /F31 11.9552 Tf 1.02 0 0 1 124.488 509.188 Tm [(Elemen)27(tary)]TJ ET 1 0 0 1 188.452 509.188 cm EMC /Span <> BDC 1 0 0 1 -188.452 -509.188 cm BT /F49 11.9552 Tf 1.02 0 0 1 188.452 509.188 Tm [(c)49(olumn)]TJ ET 1 0 0 1 225.953 509.188 cm EMC /P <> BDC 1 0 0 1 -225.953 -509.188 cm BT /F31 11.9552 Tf 1.02 0 0 1 230.045 509.188 Tm [(op)-27(erations)-335(\050t)27(w)26(o)-335(of)-336(columns)-335(1)-336(and)-336(2)-335(subtracted)-336(fr)1(om)-336(the)]TJ 1.02 0 0 1 124.488 494.742 Tm [(third\051)-378(w)27(ould)-378(yield)-377(the)-378(answ)27(er)-378(faster,)-392(but)-378(in)-378(\023Math)-378(2)-377(t)26(yp)-26(e)-378(ro)27(w)-378(op)-27(eratio)1(ns)-1(\024:)]TJ/F31 11.9552 Tf 1.018 0 0 1 124.488 480.296 Tm [(scale)-320(the)-321(\034rst)-320(ro)27(w)-321(b)27(y)]TJ/F55 8.3686 Tf 1 0 0 1 237.147 482.986 Tm [(1)]TJ/F61 11.9552 Tf 3.782 -2.69 Td [(=)]TJ/F55 8.3686 Tf 4.524 0 Td [(2)]TJ/F31 11.9552 Tf 1.018 0 0 1 253.799 480.296 Tm [(and)-320(subtract)-321(it)-320(from)-320(the)-321(second)-320(ro)27(w;)-321(scale)-320(the)-321(t)1(hird)]TJ/F31 11.9552 Tf 1.02 0 0 1 124.488 465.851 Tm [(ro)27(w)-366(b)26(y)]TJ/F55 8.3686 Tf 1 0 0 1 164.939 468.541 Tm [(1)]TJ/F61 11.9552 Tf 3.782 -2.69 Td [(=)]TJ/F55 8.3686 Tf 4.525 0 Td [(3)]TJ/F31 11.9552 Tf 1.02 0 0 1 182.156 465.851 Tm [(and)-366(subtract)-366(t)27(w)26(o)-366(of)-366(it)-366(from)-366(the)-366(fourth.)-565(Those)-366(op)-27(erations)-366(do)-366(not)]TJ 1.02 0 0 1 124.488 429.985 Tm [(c)27(hange)-325(the)-325(rank,)-326(whic)27(h)-325(is)-325(then)-325(the)-325(same)-325(as)-325(of)]TJ/F67 9.9626 Tf 1 0 0 1 367.325 459.475 Tm [(0)]TJ 0 -17.535 Td [(B)]TJ 0 -5.977 Td [(B)]TJ 0 -5.978 Td [(B)]TJ 0 -6.376 Td [(@)]TJ/F52 11.9552 Tf 8.717 28.145 Td [(1)-833(0)-834(2)]TJ 0 -14.446 Td [(0)-833(0)-834(0)]TJ 0 -14.446 Td [(0)-833(1)-834(2)]TJ 0 -14.446 Td [(0)-833(0)-834(0)]TJ/F67 9.9626 Tf 37.484 51.059 Td [(1)]TJ 0 -17.535 Td [(C)]TJ 0 -5.977 Td [(C)]TJ 0 -5.978 Td [(C)]TJ 0 -6.376 Td [(A)]TJ/F31 11.9552 Tf 1.02 0 0 1 422.244 429.985 Tm [(,)-326(i.e.)-325(the)-325(same)-325(as)-325(of)]TJ/F67 9.9626 Tf 1 0 0 1 124.488 402.688 Tm [(\040)]TJ/F52 11.9552 Tf 7.887 -10.212 Td [(1)-833(0)-834(2)]TJ 0 -14.446 Td [(0)-833(1)-834(2)]TJ/F67 9.9626 Tf 37.485 24.658 Td [(!)]TJ/F31 11.9552 Tf 7.887 -17.535 Td [(,)-326(and)-327(that)-326(is)]TJ/F52 11.9552 Tf 67.05 0 Td [(2)]TJ ET q 1 0 0 1 244.797 383.759 cm []0 d 0 J 0.398 w 0 0 m 5.853 0 l S Q q 1 0 0 1 244.797 381.766 cm []0 d 0 J 0.398 w 0 0 m 5.853 0 l S Q BT /F31 11.9552 Tf 250.65 385.153 Td [(,)-326(as)-327(the)-326(righ)27(tmost)-326(square)-327(blo)-27(c)28(k)]TJ/F52 11.9552 Tf 162.455 0 Td [(=)]TJ/F157 11.9552 Tf 12.425 0 Td [(I)]TJ/F31 11.9552 Tf 8.912 0 Td [(has)-326(full)-327(rank.)]TJ 0 g 0 G -331.415 -31.88 Td [(\050b\051)]TJ 0 g 0 G ET 1 0 0 1 124.488 353.273 cm EMC /P <> BDC 1 0 0 1 -124.488 -353.273 cm BT /F31 11.9552 Tf 0.98 0 0 1 124.488 353.273 Tm [(HO)28(W)-332(TO:)-332(Multiply)-332(out)-332(all)-332(three:)]TJ/F157 11.9552 Tf 1 0 0 1 299.21 353.273 Tm [(A)94(w)]TJ/F62 7.9701 Tf 18.788 -1.794 Td [(i)]TJ/F31 11.9552 Tf 0.98 0 0 1 325.27 353.273 Tm [(to)-332(get)]TJ/F52 11.9552 Tf 0.98 0 0 1 358.543 353.273 Tm [(4)]TJ/F157 11.9552 Tf 0.98 0 0 1 364.279 353.273 Tm [(w)]TJ/F62 7.9701 Tf 1 0 0 1 373.799 351.479 Tm [(i)]TJ/F31 11.9552 Tf 0.98 0 0 1 377.18 353.273 Tm [(,)-332(con\034rming)-332(the)-332(claim)-332(with)-332(a)]TJ/F31 11.9552 Tf 1 0 0 1 124.488 338.827 Tm [(common)-326(eigen)27(v)54(alue)-326(\050whic)27(h)-326(is)]TJ/F52 11.9552 Tf 152.57 0 Td [(=)-278(4)]TJ/F31 11.9552 Tf 18.279 0 Td [(\051.)]TJ ET 1 0 0 1 123.119 317.905 cm EMC /P <> BDC 1 0 0 1 -123.119 -317.905 cm BT /F31 11.9552 Tf 0.98 0 0 1 123.119 317.905 Tm [(\050Y)83(es)-299(sure,)]TJ/F157 11.9552 Tf 0.98 0 0 1 175.564 317.905 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 185.083 316.112 Tm [(3)]TJ/F52 11.9552 Tf 0.98 0 0 1 193.136 317.905 Tm [(=)-283(2\050)]TJ/F157 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[(\051)]TJ/F67 9.9626 Tf 1 0 0 1 427.698 329.462 Tm [(i)]TJ/F52 11.9552 Tf 0.98 0 0 1 435.723 317.905 Tm [(=)-283(2)]TJ/F157 11.9552 Tf 0.98 0 0 1 453.703 317.905 Tm [(A)]TJ/F52 11.9552 Tf 0.98 0 0 1 463.656 317.905 Tm [([)]TJ/F157 11.9552 Tf 0.98 0 0 1 466.912 317.905 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 476.431 316.112 Tm [(1)]TJ/F52 11.9552 Tf 0.98 0 0 1 483.011 317.905 Tm [(+)]TJ/F157 11.9552 Tf 0.98 0 0 1 493.782 317.905 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 503.302 316.112 Tm [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 508.034 317.905 Tm [(])-283(=)]TJ/F52 11.9552 Tf 1.02 0 0 1 124.196 301.965 Tm [(2)]TJ/F64 11.9552 Tf 1 0 0 1 133.015 301.965 Tm [(\001)]TJ/F52 11.9552 Tf 1.02 0 0 1 139.186 301.965 Tm [(4[)]TJ/F157 11.9552 Tf 1.02 0 0 1 148.542 301.965 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 158.45 300.172 Tm [(1)]TJ/F52 11.9552 Tf 1.02 0 0 1 166.032 301.965 Tm [(+)]TJ/F157 11.9552 Tf 1.02 0 0 1 178.168 301.965 Tm [(w)]TJ/F55 7.9701 Tf 1 0 0 1 188.076 300.172 Tm [(2)]TJ/F52 11.9552 Tf 1.02 0 0 1 192.808 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[(of)-339(that\051)-339(did)-340(re\035e)1(ct)-340(the)-339(view)-339(that)-339(there)-339(is)-340(a)-339(job)-339(to)-339(do)-339(understanding)-339(what)-340(a)-339(phase)]TJ/F31 11.9552 Tf 1 0 0 1 83.517 620.265 Tm [(diagram)-326(is.)]TJ ET 1 0 0 1 83.517 605.819 cm EMC /P <> BDC 1 0 0 1 -83.517 -605.819 cm BT /F31 11.9552 Tf 0.982 0 0 1 83.517 605.819 Tm [(P)28(arts)-334(\050b\051\050c\051)-333(resem)27(ble)-333(2016#2)-334(\050assigned)-333(for)-334(seminar)-334(9\051,)-334(part)1(s)-334(\050c\051\050d\051)-334(resem)28(ble)-334(2)1(019#1)]TJ/F31 11.9552 Tf 1.02 0 0 1 82.148 591.373 Tm [(\050d\051\050e\051)-380(\050assigned)-381(for)-381(seminar)-380(8;)-411(had)-381(a)-380(similar)-381(plot)-381(as)-380(hin)26(t\051)-380(and)-381(\050c\051\050d\051\050e\051)-380(resem)27(ble)]TJ/F31 11.9552 Tf 1 0 0 1 83.225 576.928 Tm [(2017#1)-326(\050for)-327(seminar)-326(9;)-326(also)-327(assigned:)-435(more)-326(phase)-326(diagrams\051.)]TJ ET 1 0 0 1 83.517 561.984 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -83.517 -561.984 cm BT /F125 11.3574 Tf 83.517 550.527 Td [(Ho)15(w)-278(to)-278(solve)-278(Pr)20(ob)10(lem)-278(3:)]TJ 0 g 0 G ET 1 0 0 1 226.615 550.527 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -226.615 -550.527 cm BT /F31 11.9552 Tf 91.972 531.099 Td [(\050a\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 531.099 cm EMC /P <> BDC 1 0 0 1 -112.782 -531.099 cm BT /F61 11.9552 Tf 112.782 531.099 Td [(r)]TJ/F52 11.9552 Tf 0.982 0 0 1 121.715 531.099 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 133.989 531.099 Tm [(\000)]TJ/F52 11.9552 Tf 0.982 0 0 1 143.287 531.099 Tm [(2)]TJ/F61 11.9552 Tf 1 0 0 1 149.035 531.099 Tm [(k)]TJ/F64 11.9552 Tf 9.151 0 Td [(\006)]TJ 11.96 10.378 Td [(p)]TJ ET q 1 0 0 1 180.108 541.717 cm []0 d 0 J 0.478 w 0 0 m 44.029 0 l S Q BT /F52 11.9552 Tf 180.108 531.099 Td [(4)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ/F55 7.9701 Tf 6.49 3.454 Td [(2)]TJ/F64 11.9552 Tf 7.389 -3.454 Td [(\000)]TJ/F52 11.9552 Tf 11.955 0 Td [(3)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ/F31 11.9552 Tf 0.982 0 0 1 224.137 531.099 Tm [(,)-333(and)-333(w)28(e)-333(need)-333(to)-333(distinguish)-333(b)-28(et)28(w)28(een)-333(the)-333(situation)-333(where)]TJ/F61 11.9552 Tf 1 0 0 1 112.782 516.654 Tm [(k)]TJ/F64 11.9552 Tf 9.15 0 Td [(\001)]TJ/F52 11.9552 Tf 0.989 0 0 1 127.912 516.654 Tm [(\0504)]TJ/F61 11.9552 Tf 1 0 0 1 138.203 516.654 Tm [(k)]TJ/F64 11.9552 Tf 9.15 0 Td [(\000)]TJ/F52 11.9552 Tf 0.989 0 0 1 159.311 516.654 Tm [(3\051)]TJ/F31 11.9552 Tf 0.989 0 0 1 173.508 516.654 Tm [(is)]TJ/F61 11.9552 Tf 1 0 0 1 185.198 516.654 Tm [(<)]TJ/F52 11.9552 Tf 0.989 0 0 1 197.631 516.654 Tm [(0)]TJ/F31 11.9552 Tf 0.989 0 0 1 207.326 516.654 Tm [(\050that)-330(is,)]TJ/F61 11.9552 Tf 1 0 0 1 251.867 516.654 Tm [(k)]TJ/F64 11.9552 Tf 9.818 0 Td [(2)]TJ/F52 11.9552 Tf 0.989 0 0 1 272.984 516.654 Tm [(\0500)]TJ/F61 11.9552 Tf 1 0 0 1 283.275 516.654 Tm [(;)]TJ/F52 11.9552 Tf 0.989 0 0 1 288.519 516.654 Tm [(3)]TJ/F61 11.9552 Tf 1 0 0 1 294.308 516.654 Tm [(=)]TJ/F52 11.9552 Tf 0.989 0 0 1 300.161 516.654 Tm [(4\051)]TJ/F31 11.9552 Tf 0.989 0 0 1 310.451 516.654 Tm [(\051)-330(and)-331(the)-330(situation)-330(where)]TJ/F61 11.9552 Tf 1 0 0 1 443.25 516.654 Tm [(k)]TJ/F64 11.9552 Tf 9.149 0 Td [(\001)]TJ/F52 11.9552 Tf 0.989 0 0 1 458.38 516.654 Tm [(\0504)]TJ/F61 11.9552 Tf 1 0 0 1 468.67 516.654 Tm [(k)]TJ/F64 11.9552 Tf 9.15 0 Td [(\000)]TJ/F52 11.9552 Tf 0.989 0 0 1 489.778 516.654 Tm [(3\051)]TJ/F31 11.9552 Tf 0.989 0 0 1 503.976 516.654 Tm [(is)]TJ/F64 11.9552 Tf 1 0 0 1 112.782 502.208 Tm [(\025)]TJ/F52 11.9552 Tf 12.62 0 Td [(0)]TJ/F31 11.9552 Tf 9.755 0 Td [(\050that)-326(is,)-327(elsewhere)1(\051:)]TJ 0 g 0 G ET 1 0 0 1 119.676 482.781 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -482.781 cm BT /F46 11.9552 Tf 123.578 482.781 Td [(\210)]TJ ET 1 0 0 1 132.682 482.781 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -482.781 cm BT /F31 11.9552 Tf 138.535 482.781 Td [(If)]TJ/F61 11.9552 Tf 11.702 0 Td [(k)]TJ/F64 11.9552 Tf 9.811 0 Td [(2)]TJ/F52 11.9552 Tf 11.291 0 Td [(\0500)]TJ/F61 11.9552 Tf 10.405 0 Td [(;)]TJ/F52 11.9552 Tf 5.244 0 Td [(3)]TJ/F61 11.9552 Tf 5.853 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(4\051)]TJ/F31 11.9552 Tf 10.405 0 Td [(,)-326(the)-327(real)-326(part)-326(is)]TJ/F64 11.9552 Tf 87.21 0 Td [(\000)]TJ/F52 11.9552 Tf 9.299 0 Td [(2)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ/F31 11.9552 Tf 10.391 0 Td [(\050for)-326(b)-28(ot)1(h)-327(ro)-27(ots\051)]TJ 0 g 0 G ET 1 0 0 1 119.676 463.354 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -463.354 cm BT /F46 11.9552 Tf 123.578 463.354 Td [(\210)]TJ ET 1 0 0 1 132.682 463.354 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -463.354 cm BT /F31 11.9552 Tf 138.535 463.354 Td [(If)]TJ/F61 11.9552 Tf 11.702 0 Td [(k)]TJ/F64 11.9552 Tf 9.811 0 Td [(62)]TJ/F52 11.9552 Tf 11.291 0 Td [(\0500)]TJ/F61 11.9552 Tf 10.405 0 Td [(;)]TJ/F52 11.9552 Tf 5.244 0 Td [(3)]TJ/F61 11.9552 Tf 5.853 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(4\051)]TJ/F31 11.9552 Tf 10.405 0 Td [(,)-326(the)-327(real)-326(part)-326(is)]TJ/F61 11.9552 Tf 87.21 0 Td [(r)]TJ/F31 11.9552 Tf 9.503 0 Td [(itself,)-326(namely)]TJ/F64 11.9552 Tf 72.253 0 Td [(\000)]TJ/F52 11.9552 Tf 9.298 0 Td [(2)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ/F64 11.9552 Tf 9.146 0 Td [(\006)]TJ 11.956 9.784 Td [(p)]TJ ET q 1 0 0 1 424.28 473.377 cm []0 d 0 J 0.478 w 0 0 m 44.029 0 l S Q BT /F52 11.9552 Tf 424.28 463.354 Td [(4)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ/F55 7.9701 Tf 6.49 3.453 Td [(2)]TJ/F64 11.9552 Tf 7.389 -3.453 Td [(\000)]TJ/F52 11.9552 Tf 11.955 0 Td [(3)]TJ/F61 11.9552 Tf 5.853 0 Td [(k)]TJ 0 g 0 G /F31 11.9552 Tf -370.499 -24.409 Td [(\050b\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 438.945 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -438.945 cm BT /F31 11.9552 Tf 1.02 0 0 1 112.361 438.945 Tm [(The)-337(c)26(haracteristic)-337(equation)-338(is)-337(the)-338(instance)]TJ/F61 11.9552 Tf 1 0 0 1 338.919 438.945 Tm [(k)]TJ/F52 11.9552 Tf 1.02 0 0 1 349.094 438.945 Tm [(=)]TJ/F55 7.9701 Tf 1 0 0 1 363.262 443.652 Tm [(1)]TJ ET q 1 0 0 1 363.262 441.934 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 363.262 434.822 Td [(2)]TJ/F31 11.9552 Tf 1.02 0 0 1 372.808 438.945 Tm [(of)-338(t)1(he)-338(equation)-337(in)-338(\050a\051;)]TJ/F52 11.9552 Tf 1.02 0 0 1 492.998 438.945 Tm [(0)]TJ/F61 11.9552 Tf 1 0 0 1 502.654 438.945 Tm [(<)]TJ/F52 11.9552 Tf 0.98 0 0 1 112.197 424.499 Tm [(1)]TJ/F61 11.9552 Tf 1 0 0 1 117.933 424.499 Tm [(=)]TJ/F52 11.9552 Tf 0.98 0 0 1 123.786 424.499 Tm [(2)]TJ/F61 11.9552 Tf 1 0 0 1 132.843 424.499 Tm [(<)]TJ/F52 11.9552 Tf 0.98 0 0 1 145.268 424.499 Tm [(3)]TJ/F61 11.9552 Tf 1 0 0 1 151.004 424.499 Tm [(=)]TJ/F52 11.9552 Tf 0.98 0 0 1 156.857 424.499 Tm [(4)]TJ/F31 11.9552 Tf 0.98 0 0 1 165.428 424.499 Tm [(so)-242(ro)-28(ots)-242(are)-242(non-re)1(al.)-414(Then)-242(w)28(e)-242(need)-242(\023)]TJ/F61 11.9552 Tf 1 0 0 1 350.57 424.499 Tm [(b)]TJ/F31 11.9552 Tf 0.98 0 0 1 355.547 424.499 Tm [(\024)-242(=)-242(the)]TJ/F61 11.9552 Tf 1 0 0 1 395.282 424.499 Tm [(x)]TJ/F62 7.9701 Tf 6.652 -1.793 Td [(t)]TJ/F31 11.9552 Tf 0.98 0 0 1 408.325 424.499 Tm [(co)-28(e\036cien)28(t)]TJ/F52 11.9552 Tf 0.98 0 0 1 460.872 424.499 Tm [(=)-283(3)]TJ/F61 11.9552 Tf 1 0 0 1 478.851 424.499 Tm [(=)]TJ/F52 11.9552 Tf 0.98 0 0 1 484.704 424.499 Tm [(2)]TJ/F31 11.9552 Tf 0.98 0 0 1 493.275 424.499 Tm [(and)]TJ/F31 11.9552 Tf 1.006 0 0 1 110.827 407.712 Tm [(\023)]TJ/F65 7.9701 Tf 1 0 0 1 120.48 412.419 Tm [(\000)]TJ/F62 7.9701 Tf 6.587 0 Td [(a)]TJ ET q 1 0 0 1 118.566 410.701 cm []0 d 0 J 0.398 w 0 0 m 14.914 0 l S Q BT /F55 7.9701 Tf 118.566 402.564 Td [(2)]TJ/F65 7.9701 Tf 4.234 6.822 Td [(p)]TJ ET q 1 0 0 1 129.857 409.565 cm []0 d 0 J 0.359 w 0 0 m 3.623 0 l S Q BT /F62 7.9701 Tf 129.857 402.564 Td [(b)]TJ/F31 11.9552 Tf 1.006 0 0 1 134.675 407.712 Tm [(\024)-324(where)]TJ/F61 11.9552 Tf 1 0 0 1 179.112 407.712 Tm [(a)]TJ/F31 11.9552 Tf 1.006 0 0 1 189.157 407.712 Tm [(is)-324(the)]TJ/F61 11.9552 Tf 1 0 0 1 221.23 407.712 Tm [(x)]TJ/F62 7.9701 Tf 6.652 -1.793 Td [(t)]TJ/F55 7.9701 Tf 3.058 0 Td [(+1)]TJ/F31 11.9552 Tf 1.006 0 0 1 246.158 407.712 Tm [(co)-27(e\036cien)27(t,)-324(namely)]TJ/F52 11.9552 Tf 1.006 0 0 1 345.226 407.712 Tm [(2)]TJ/F31 11.9552 Tf 1.006 0 0 1 351.114 407.712 Tm [(;)-324(th)27(us,)]TJ/F65 7.9701 Tf 1 0 0 1 390.552 412.419 Tm [(\000)]TJ/F62 7.9701 Tf 6.587 0 Td [(a)]TJ ET q 1 0 0 1 388.638 410.701 cm []0 d 0 J 0.398 w 0 0 m 14.914 0 l S Q BT /F55 7.9701 Tf 388.638 402.564 Td [(2)]TJ/F65 7.9701 Tf 4.234 6.822 Td [(p)]TJ ET q 1 0 0 1 399.929 409.565 cm []0 d 0 J 0.359 w 0 0 m 3.623 0 l S Q BT /F62 7.9701 Tf 399.929 402.564 Td [(b)]TJ/F52 11.9552 Tf 1.006 0 0 1 408.068 407.712 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 420.548 407.712 Tm [(\000)]TJ/F55 7.9701 Tf 21.827 4.707 Td [(2)]TJ ET q 1 0 0 1 431.042 410.701 cm []0 d 0 J 0.398 w 0 0 m 26.899 0 l S Q BT /F55 7.9701 Tf 431.042 401.167 Td [(2)]TJ/F64 11.9552 Tf 4.234 7.98 Td [(p)]TJ ET q 1 0 0 1 445.239 409.386 cm []0 d 0 J 0.478 w 0 0 m 12.702 0 l S Q BT /F55 7.9701 Tf 445.239 401.167 Td [(3)]TJ/F62 7.9701 Tf 4.234 0 Td [(=)]TJ/F55 7.9701 Tf 4.234 0 Td [(2)]TJ/F52 11.9552 Tf 1.006 0 0 1 462.458 407.712 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 474.938 407.712 Tm [(\000)]TJ/F67 9.9626 Tf 9.298 12.005 Td [(q)]TJ ET q 1 0 0 1 494.199 419.916 cm []0 d 0 J 0.398 w 0 0 m 17.559 0 l S Q BT /F52 11.9552 Tf 494.199 407.712 Td [(2)]TJ/F61 11.9552 Tf 5.853 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(3)]TJ/F31 11.9552 Tf -394.492 -21.747 Td [(\050or)-326(if)-327(y)28(ou)-327(lik)27(e,)]TJ/F52 11.9552 Tf 76.415 0 Td [(=)]TJ/F64 11.9552 Tf 12.425 0 Td [(\000)]TJ/F55 7.9701 Tf 10.494 4.708 Td [(1)]TJ ET q 1 0 0 1 210.747 388.954 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 210.747 381.843 Td [(3)]TJ/F64 11.9552 Tf 5.43 13.874 Td [(p)]TJ ET q 1 0 0 1 226.14 395.956 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 226.14 385.965 Td [(6)]TJ/F31 11.9552 Tf 5.853 0 Td [(\051.)]TJ ET 1 0 0 1 112.782 366.538 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -366.538 cm BT /F31 11.9552 Tf 1.02 0 0 1 112.782 366.538 Tm [(Using)-1340(the)-1339(form)26(ula,)-1594(w)27(e)-1340(get)-1340(fo)1(r)-1340(the)-1340(homogeneous)-1339(equation:)]TJ/F52 11.9552 Tf 1.02 0 0 1 111.413 350.415 Tm [(\0503)]TJ/F61 11.9552 Tf 1 0 0 1 122.026 350.415 Tm [(=)]TJ/F52 11.9552 Tf 1.02 0 0 1 127.879 350.415 Tm [(2\051)]TJ/F62 7.9701 Tf 1 0 0 1 138.493 354.754 Tm [(t=)]TJ/F55 7.9701 Tf 7.292 0 Td [(2)]TJ/F52 11.9552 Tf 6.725 -4.339 Td [([)]TJ/F61 11.9552 Tf 3.32 0 Td [(C)]TJ/F52 11.9552 Tf 11.226 0 Td [(cos\050)]TJ/F61 11.9552 Tf 20.226 0 Td [(\022)-27(t)]TJ/F52 11.9552 Tf 10.007 0 Td [(\051)-222(+)]TJ/F61 11.9552 Tf 18.971 0 Td [(D)]TJ/F52 11.9552 Tf 12.037 0 Td [(sin)-5(\050)]TJ/F61 11.9552 Tf 18.982 0 Td [(\022)-27(t)]TJ/F52 11.9552 Tf 10.007 0 Td [(\051])]TJ/F31 11.9552 Tf 1.02 0 0 1 272.483 350.415 Tm [(with)]TJ/F61 11.9552 Tf 1 0 0 1 303.093 350.415 Tm [(\022)]TJ/F31 11.9552 Tf 1.02 0 0 1 316.266 350.415 Tm [(suc)27(h)-607(that)]TJ/F52 11.9552 Tf 1 0 0 1 375.9 350.415 Tm [(cos)]TJ/F52 11.9552 Tf 1.02 0 0 1 391.573 350.415 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 396.216 350.415 Tm [(\022)]TJ/F52 11.9552 Tf 1.02 0 0 1 401.997 350.415 Tm [(\051)-760(=)]TJ/F67 9.9626 Tf 1 0 0 1 434.452 362.42 Tm [(q)]TJ ET q 1 0 0 1 444.415 362.62 cm []0 d 0 J 0.398 w 0 0 m 17.559 0 l S Q BT /F52 11.9552 Tf 444.415 350.415 Td [(2)]TJ/F61 11.9552 Tf 5.853 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(3)]TJ/F31 11.9552 Tf 1.02 0 0 1 461.974 350.415 Tm [(.)-1285(F)80(or)-607(a)]TJ/F31 11.9552 Tf 1 0 0 1 112.782 334.649 Tm [(particular)-326(solution,)-327(try)]TJ/F61 11.9552 Tf 120.704 0 Td [(K)-72(e)]TJ/F62 7.9701 Tf 16.243 4.338 Td [(\031)-36(t)]TJ/F31 11.9552 Tf 8.705 -4.338 Td [(:)]TJ ET /S/Span<>BDC BT /F61 11.9552 Tf 136.336 303.757 Td [(K)]TJ/F67 9.9626 Tf 12.81 11.557 Td [(h)]TJ/F61 11.9552 Tf 4.705 -11.557 Td [(e)]TJ/F62 7.9701 Tf 5.425 4.936 Td [(\031)-36(t)]TJ/F55 7.9701 Tf 8.207 0 Td [(+2)]TJ/F62 7.9701 Tf 10.821 0 Td [(\031)]TJ/F52 11.9552 Tf 8.303 -4.936 Td [(+)-222(2)]TJ/F61 11.9552 Tf 17.615 0 Td [(e)]TJ/F62 7.9701 Tf 5.425 4.936 Td [(\031)-36(t)]TJ/F55 7.9701 Tf 8.207 0 Td [(+)]TJ/F62 7.9701 Tf 6.586 0 Td [(\031)]TJ/F52 11.9552 Tf 8.304 -4.936 Td [(+)]TJ/F55 7.9701 Tf 12.957 4.707 Td [(3)]TJ ET q 1 0 0 1 245.701 306.746 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 245.701 299.634 Td [(2)]TJ/F61 11.9552 Tf 5.43 4.123 Td [(e)]TJ/F62 7.9701 Tf 5.425 4.936 Td [(\031)-36(t)]TJ/F67 9.9626 Tf 8.705 6.621 Td [(i)]TJ/F52 11.9552 Tf 8.026 -11.557 Td [(=)]TJ/F61 11.9552 Tf 12.425 0 Td [(e)]TJ/F62 7.9701 Tf 5.426 4.936 Td [(\031)-36(t)]TJ/F31 11.9552 Tf 32.117 -4.936 Td [(so:)]TJ/F61 11.9552 Tf 37.134 0 Td [(K)]TJ/F52 11.9552 Tf 34.371 0 Td [(=)]TJ 50.009 8.088 Td [(1)]TJ ET q 1 0 0 1 408.381 306.746 cm []0 d 0 J 0.398 w 0 0 m 78.627 0 l S Q BT /F61 11.9552 Tf 408.381 295.556 Td [(e)]TJ/F55 7.9701 Tf 5.426 3.454 Td [(2)]TJ/F62 7.9701 Tf 4.234 0 Td [(\031)]TJ/F52 11.9552 Tf 8.304 -3.454 Td [(+)-222(2)]TJ/F61 11.9552 Tf 17.614 0 Td [(e)]TJ/F62 7.9701 Tf 5.426 3.454 Td [(\031)]TJ/F52 11.9552 Tf 8.303 -3.454 Td [(+)-222(3)]TJ/F61 11.9552 Tf 17.615 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(2)]TJ ET EMC BT /F31 11.9552 Tf 112.782 271.38 Td [(and)-326(so)-327(the)-326(general)-326(solution)-327(is:)]TJ ET /S/Span<>BDC BT /F52 11.9552 Tf 117.508 238.776 Td [(\0503)]TJ/F61 11.9552 Tf 10.405 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(2\051)]TJ/F62 7.9701 Tf 10.406 4.936 Td [(t=)]TJ/F55 7.9701 Tf 7.292 0 Td [(2)]TJ/F52 11.9552 Tf 6.725 -4.936 Td [([)]TJ/F61 11.9552 Tf 3.32 0 Td [(C)]TJ/F52 11.9552 Tf 11.227 0 Td [(cos\050)]TJ/F61 11.9552 Tf 20.225 0 Td [(\022)-27(t)]TJ/F52 11.9552 Tf 10.007 0 Td [(\051)-222(+)]TJ/F61 11.9552 Tf 18.971 0 Td [(D)]TJ/F52 11.9552 Tf 12.037 0 Td [(sin)-5(\050)]TJ/F61 11.9552 Tf 18.982 0 Td [(\022)-27(t)]TJ/F52 11.9552 Tf 10.007 0 Td [(\051])-222(+)]TJ/F61 11.9552 Tf 55.666 8.088 Td [(e)]TJ/F62 7.9701 Tf 5.426 4.338 Td [(\031)-36(t)]TJ ET q 1 0 0 1 286.383 241.765 cm []0 d 0 J 0.398 w 0 0 m 78.627 0 l S Q BT /F61 11.9552 Tf 286.383 230.575 Td [(e)]TJ/F55 7.9701 Tf 5.425 3.454 Td [(2)]TJ/F62 7.9701 Tf 4.235 0 Td [(\031)]TJ/F52 11.9552 Tf 8.303 -3.454 Td [(+)-222(2)]TJ/F61 11.9552 Tf 17.615 0 Td [(e)]TJ/F62 7.9701 Tf 5.425 3.454 Td [(\031)]TJ/F52 11.9552 Tf 8.304 -3.454 Td [(+)-222(3)]TJ/F61 11.9552 Tf 17.614 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(2)]TJ/F31 11.9552 Tf 18.755 8.201 Td [(where)]TJ/F52 11.9552 Tf 35.809 0 Td [(cos\050)]TJ/F61 11.9552 Tf 20.226 0 Td [(\022)]TJ/F52 11.9552 Tf 5.78 0 Td [(\051)-278(=)]TJ/F64 11.9552 Tf 20.299 0 Td [(\000)]TJ/F67 9.9626 Tf 9.298 12.598 Td [(q)]TJ ET q 1 0 0 1 479.287 251.574 cm []0 d 0 J 0.398 w 0 0 m 19.552 0 l S Q BT /F52 11.9552 Tf 479.287 238.776 Td [(2)]TJ/F61 11.9552 Tf 5.853 0 Td [(=)]TJ/F52 11.9552 Tf 5.853 0 Td [(3)]TJ ET EMC 0 g 0 G BT /F31 11.9552 Tf 92.622 200.687 Td [(\050c\051)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 119.676 200.687 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -200.687 cm BT /F46 11.9552 Tf 123.578 200.687 Td [(\210)]TJ ET 1 0 0 1 132.682 200.687 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -200.687 cm BT /F31 11.9552 Tf 138.535 200.687 Td [(Saddle)-326(p)-28(oin)28(t,)-327(as)-326(the)-326(determinan)27(t)-326(of)-327(the)-326(co)-27(e\036cien)27(t)-326(matrix)-327(is)]TJ/F61 11.9552 Tf 310.017 0 Td [(<)]TJ/F52 11.9552 Tf 12.426 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(.)]TJ 0 g 0 G ET 1 0 0 1 119.676 181.26 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -181.26 cm BT /F46 11.9552 Tf 123.578 181.26 Td [(\210)]TJ ET 1 0 0 1 132.682 181.26 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -181.26 cm BT /F31 11.9552 Tf 0.98 0 0 1 137.938 181.26 Tm [(W)83(e)-259(need)-260(the)-259(negativ)28(e)-260(eigen)28(v)56(alue,)-275(call)-259(it)]TJ/F61 11.9552 Tf 1 0 0 1 334.611 181.26 Tm [(\015)]TJ/F31 11.9552 Tf 0.98 0 0 1 341.333 181.26 Tm [(.)-420(F)84(rom)-260(that)-259(w)28(e)-260(\034nd)-259(an)-260(eigen)28(v)28(ector)]TJ/F52 11.9552 Tf 0.98 0 0 1 137.166 166.814 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 141.627 166.814 Tm [(v)]TJ/F55 7.9701 Tf 5.659 -1.793 Td [(1)]TJ/F61 11.9552 Tf 4.733 1.793 Td [(;)-167(v)]TJ/F55 7.9701 Tf 10.903 -1.793 Td [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 167.654 166.814 Tm [(\051)]TJ/F31 11.9552 Tf 0.98 0 0 1 175.495 166.814 Tm [(suc)28(h)-289(that)]TJ/F52 11.9552 Tf 0.98 0 0 1 225.331 166.814 Tm [(\0501)]TJ/F64 11.9552 Tf 1 0 0 1 237.118 166.814 Tm [(\000)]TJ/F61 11.9552 Tf 10.888 0 Td [(\015)]TJ/F52 11.9552 Tf 0.98 0 0 1 254.728 166.814 Tm [(\051)]TJ/F61 11.9552 Tf 1 0 0 1 259.189 166.814 Tm [(v)]TJ/F55 7.9701 Tf 5.659 -1.793 Td [(1)]TJ/F52 11.9552 Tf 0.98 0 0 1 271.17 166.814 Tm [(+)-136(1)]TJ/F64 11.9552 Tf 1 0 0 1 289.007 166.814 Tm [(\001)]TJ/F61 11.9552 Tf 4.911 0 Td [(v)]TJ/F55 7.9701 Tf 5.659 -1.793 Td [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 307.63 166.814 Tm [(=)-283(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 325.61 166.814 Tm [(;)]TJ/F157 11.9552 Tf 0.98 0 0 1 332.35 166.814 Tm [(v)]TJ/F52 11.9552 Tf 0.98 0 0 1 342.663 166.814 Tm [(=)-283(\0501)]TJ/F61 11.9552 Tf 1 0 0 1 365.104 166.814 Tm [(;)]TJ/F64 11.9552 Tf 5.244 0 Td [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 379.647 166.814 Tm [(\0501)]TJ/F64 11.9552 Tf 1 0 0 1 391.434 166.814 Tm [(\000)]TJ/F61 11.9552 Tf 10.887 0 Td [(\015)]TJ/F52 11.9552 Tf 0.98 0 0 1 409.044 166.814 Tm [(\051\051)]TJ/F65 7.9701 Tf 1 0 0 1 417.966 171.153 Tm [(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 424.141 166.814 Tm [(will)-288(do,)-298(and)-288(has)-289(a)]TJ 0.98 0 0 1 138.535 152.368 Tm [(slop)-28(e)-288(of)]TJ/F64 11.9552 Tf 1 0 0 1 179.772 152.368 Tm [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 189.07 152.368 Tm [(\0501)]TJ/F64 11.9552 Tf 1 0 0 1 200.848 152.368 Tm [(\000)]TJ/F61 11.9552 Tf 10.879 0 Td [(\015)]TJ/F52 11.9552 Tf 0.98 0 0 1 218.449 152.368 Tm [(\051)]TJ/F31 11.9552 Tf 0.98 0 0 1 222.91 152.368 Tm [(.)-429(W)83(e)-288(need)]TJ/F61 11.9552 Tf 1 0 0 1 276.727 152.368 Tm [(\015)]TJ/F31 11.9552 Tf 0.98 0 0 1 283.45 152.368 Tm [(;)-303(since)-288(the)-288(trace)-288(is)-288(zero,)]TJ/F61 11.9552 Tf 1 0 0 1 403.531 152.368 Tm [(\015)]TJ/F52 11.9552 Tf 0.98 0 0 1 413.574 152.368 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 425.818 152.368 Tm [(\000)]TJ 9.298 9.536 Td [(p)]TJ ET q 1 0 0 1 445.079 162.143 cm []0 d 0 J 0.478 w 0 0 m 25.085 0 l S Q BT /F64 11.9552 Tf 445.079 152.368 Td [(\000)]TJ/F280 11.3574 Tf 9.298 0 Td [(det)]TJ/F52 11.9552 Tf 0.98 0 0 1 473.485 152.368 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 485.728 152.368 Tm [(\000)]TJ 9.299 9.752 Td [(p)]TJ ET q 1 0 0 1 504.989 162.359 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 504.989 152.368 Td [(3)]TJ/F31 11.9552 Tf 0.98 0 0 1 510.842 152.368 Tm [(.)]TJ/F31 11.9552 Tf 1 0 0 1 138.114 137.923 Tm [(The)-326(answ)27(er)-326(is)]TJ/F64 11.9552 Tf 74.593 0 Td [(\000)]TJ/F52 11.9552 Tf 9.299 0 Td [(\0501)-222(+)]TJ/F64 11.9552 Tf 24.823 9.751 Td [(p)]TJ ET q 1 0 0 1 256.792 147.913 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 256.792 137.923 Td [(3\051)]TJ/F31 11.9552 Tf 10.405 0 Td [(.)]TJ ET 1 0 0 1 83.517 110.525 cm EMC /LBody <> BDC 1 0 0 1 -83.517 -110.525 cm BT /F31 11.9552 Tf 83.517 110.525 Td [(con)27(tin)27(ued)-326(next)-326(page)]TJ 0 g 0 G ET 1 0 0 1 65.564 748.306 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 464.148 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0.199 -657.46 cm []0 d 0 J 0.398 w 0 0 m 0 657.66 l S Q q 1 0 0 1 463.948 -657.46 cm []0 d 0 J 0.398 w 0 0 m 0 657.66 l S Q 1 0 0 1 0 -657.261 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 464.148 0 l S Q 1 0 0 1 0 -0.399 cm EMC 0 g 0 G 1 0 0 1 -11.706 326.041 cm EMC 0 g 0 G 0 g 0 G 1 0 0 1 0 -362.43 cm /Artifact <> BDC 0 g 0 G 1 0 0 1 -53.858 -53.858 cm BT /F31 11.9552 Tf 294.711 53.858 Td [(6)]TJ 0 g 0 G ET 1 0 0 1 541.417 53.858 cm EMC 0 g 0 G endstream endobj 155 0 obj << /Type /Page /Contents 194 0 R /Resources 193 0 R /MediaBox [0 0 595.276 841.89] /Parent 60 0 R >> endobj 195 0 obj << /D [155 0 R /XYZ 52.858 789.032 null] >> endobj 196 0 obj << /D [155 0 R /XYZ 83.517 735.832 null] >> endobj 197 0 obj << /D [155 0 R /XYZ 83.517 564.972 null] >> endobj 198 0 obj << /D [155 0 R /XYZ 83.517 550.385 null] >> endobj 199 0 obj << /D [155 0 R /XYZ 83.517 455.383 null] >> endobj 200 0 obj << /D [155 0 R /XYZ 83.517 215.631 null] >> endobj 193 0 obj << /ColorSpace 3 0 R /Pattern 2 0 R /ExtGState 1 0 R /Font << /F125 50 0 R /F31 54 0 R /F61 89 0 R /F52 90 0 R /F64 53 0 R /F55 91 0 R /F46 51 0 R /F62 92 0 R /F65 93 0 R /F67 123 0 R /F157 122 0 R /F280 201 0 R >> /ProcSet [ /PDF /Text ] >> endobj 192 0 obj <>] /S /P /Lang(EN-GB)>> endobj 204 0 obj << /Length 12479 >> stream 0 g 0 G 0 g 0 G 1 0 0 1 65.564 450.409 cm EMC /P <> BDC 0 g 0 G 0 g 0 G 1 0 0 1 -65.564 -450.409 cm BT /F31 11.9552 Tf 91.321 716.405 Td [(\050d\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 716.405 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -716.405 cm BT /F31 11.9552 Tf 112.185 716.405 Td [(W)82(e)-327(need)-326(the)-326(Jacobian)-327(of)-326(the)-326(transformation:)]TJ ET /S/Span<>BDC BT /F157 11.9552 Tf 249.184 682.531 Td [(J)]TJ/F62 7.9701 Tf 6.946 -1.793 Td [(x;y)]TJ/F52 11.9552 Tf 15.41 1.793 Td [(=)]TJ/F67 9.9626 Tf 12.425 17.535 Td [(\040)]TJ/F61 11.9552 Tf 13.856 -10.212 Td [(x)]TJ/F64 11.9552 Tf 9.308 0 Td [(\000)]TJ/F52 11.9552 Tf 11.955 0 Td [(1)]TJ/F61 11.9552 Tf 21.784 0 Td [(y)]TJ/F64 11.9552 Tf 8.793 0 Td [(\000)]TJ/F52 11.9552 Tf 11.955 0 Td [(1)]TJ/F55 7.9701 Tf -68.568 -9.739 Td [(3)]TJ ET q 1 0 0 1 293.048 678.397 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 293.048 671.286 Td [(8)]TJ/F61 11.9552 Tf 5.43 4.122 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.339 Td [(2)]TJ/F52 11.9552 Tf 7.389 -4.339 Td [(+)]TJ/F55 7.9701 Tf 12.957 4.707 Td [(1)]TJ ET q 1 0 0 1 325.476 678.397 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 325.476 671.286 Td [(2)]TJ/F64 11.9552 Tf 21.117 4.122 Td [(\000)]TJ/F52 11.9552 Tf 9.299 0 Td [(1)]TJ/F67 9.9626 Tf 11.578 24.658 Td [(!)]TJ ET EMC 0 g 0 G 1 0 0 1 119.676 647.781 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -647.781 cm BT /F46 11.9552 Tf 123.578 647.781 Td [(\210)]TJ ET 1 0 0 1 132.682 647.781 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -647.781 cm BT /F31 11.9552 Tf 0.98 0 0 1 138.535 647.781 Tm [(Let)]TJ/F61 11.9552 Tf 1 0 0 1 157.947 647.781 Tm [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 167.92 647.781 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 180.163 647.781 Tm [(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 189.621 647.781 Tm [(=)-283(2)]TJ/F31 11.9552 Tf 0.98 0 0 1 207.6 647.781 Tm [(;)-264(then)]TJ/F52 11.9552 Tf 1 0 0 1 240.893 647.781 Tm [(_)]TJ/F61 11.9552 Tf -2.025 0 Td [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 248.84 647.781 Tm [(=)]TJ/F55 7.9701 Tf 1 0 0 1 262.28 652.488 Tm [(1)]TJ ET q 1 0 0 1 262.28 650.77 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 262.28 643.659 Td [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 267.709 647.781 Tm [(1)]TJ/F55 7.9701 Tf 1 0 0 1 273.445 652.12 Tm [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 278.346 647.781 Tm [(+)]TJ/F55 7.9701 Tf 1 0 0 1 288.633 652.488 Tm [(1)]TJ ET q 1 0 0 1 288.633 650.77 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 288.633 643.659 Td [(2)]TJ/F52 11.9552 Tf 0.98 0 0 1 294.063 647.781 Tm [(1)]TJ/F55 7.9701 Tf 1 0 0 1 299.799 652.12 Tm [(2)]TJ/F64 11.9552 Tf 4.9 -4.339 Td [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 314.167 647.781 Tm [(1)-283(=)-284(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 343.887 647.781 Tm [(and)]TJ/F52 11.9552 Tf 1 0 0 1 367.146 647.781 Tm [(_)]TJ/F61 11.9552 Tf -2.092 0 Td [(y)]TJ/F52 11.9552 Tf 0.98 0 0 1 374.511 647.781 Tm [(=)]TJ/F55 7.9701 Tf 1 0 0 1 387.95 652.488 Tm [(1)]TJ ET q 1 0 0 1 387.95 650.77 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 387.95 643.659 Td [(4)]TJ/F64 11.9552 Tf 5.598 4.122 Td [(\001)]TJ/F52 11.9552 Tf 0.98 0 0 1 397.038 647.781 Tm [(2)]TJ/F55 7.9701 Tf 1 0 0 1 402.774 652.12 Tm [(3)]TJ/F52 11.9552 Tf 0.98 0 0 1 407.675 647.781 Tm [(+)-14(2)]TJ/F64 11.9552 Tf 1 0 0 1 422.671 647.781 Tm [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 432.138 647.781 Tm [(4)-283(=)-284(2)-14(+)-15(2)]TJ/F64 11.9552 Tf 1 0 0 1 474.339 647.781 Tm [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 483.806 647.781 Tm [(4)-283(=)-284(0)]TJ/F31 11.9552 Tf 0.98 0 0 1 510.842 647.781 Tm [(.)]TJ/F31 11.9552 Tf 1.013 0 0 1 138.535 630.707 Tm [(So)-322(an)-323(equilibrium)-322(p)-27(oin)27(t.)-430(Then)]TJ/F157 11.9552 Tf 1.013 0 0 1 300.672 630.707 Tm [(J)]TJ/F55 7.9701 Tf 1 0 0 1 307.708 628.914 Tm [(2)]TJ/F62 7.9701 Tf 4.235 0 Td [(;)]TJ/F55 7.9701 Tf 2.352 0 Td [(2)]TJ/F52 11.9552 Tf 1.013 0 0 1 322.351 630.707 Tm [(=)]TJ/F67 9.9626 Tf 1 0 0 1 334.898 642.264 Tm [(\020)]TJ/F55 7.9701 Tf 21.821 -6.318 Td [(1)-2562(1)]TJ -13.878 -7.644 Td [(3)]TJ/F62 7.9701 Tf 4.234 0 Td [(=)]TJ/F55 7.9701 Tf 4.234 0 Td [(2+1)]TJ/F62 7.9701 Tf 15.055 0 Td [(=)]TJ/F55 7.9701 Tf 4.234 0 Td [(2)]TJ/F65 7.9701 Tf 7.485 0 Td [(\000)]TJ/F55 7.9701 Tf 6.586 0 Td [(1)]TJ/F67 9.9626 Tf 6.227 13.962 Td [(\021)]TJ/F31 11.9552 Tf 1.013 0 0 1 400.749 630.707 Tm [(is)-322(the)-323(same)-322(matrix)-322(as)]TJ/F31 11.9552 Tf 1 0 0 1 138.535 614.767 Tm [(for)-326(\050L\051,)-327(th)28(us)-327(saddle.)]TJ 0 g 0 G ET 1 0 0 1 119.676 595.34 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -595.34 cm BT /F46 11.9552 Tf 123.578 595.34 Td [(\210)]TJ ET 1 0 0 1 132.682 595.34 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -595.34 cm BT /F31 11.9552 Tf 0.989 0 0 1 138.114 595.34 Tm [(The)]TJ/F61 11.9552 Tf 1 0 0 1 161.944 595.34 Tm [(x)]TJ/F31 11.9552 Tf 0.989 0 0 1 168.596 595.34 Tm [(-n)27(ullc)1(line)-330(is)-329(a)-329(circle)-329(cen)28(tered)-329(at)]TJ/F52 11.9552 Tf 0.989 0 0 1 330.287 595.34 Tm [(\0501)]TJ/F61 11.9552 Tf 1 0 0 1 340.578 595.34 Tm [(;)]TJ/F52 11.9552 Tf 0.989 0 0 1 345.822 595.34 Tm [(1\051)]TJ/F31 11.9552 Tf 0.989 0 0 1 360.004 595.34 Tm [(and)-329(with)-329(radius)]TJ/F64 11.9552 Tf 1 0 0 1 443.781 605.092 Tm [(p)]TJ ET q 1 0 0 1 453.743 605.331 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 453.743 595.34 Td [(2)]TJ/F31 11.9552 Tf 0.989 0 0 1 459.596 595.34 Tm [(,)-329(and)-329(ev)27(en)]TJ/F31 11.9552 Tf 0.98 0 0 1 138.535 580.894 Tm [(the)]TJ ET 1 0 0 1 158.212 580.894 cm EMC /Span <> BDC 1 0 0 1 -158.212 -580.894 cm BT /F49 11.9552 Tf 0.98 0 0 1 158.212 580.894 Tm [(disk)]TJ ET 1 0 0 1 178.409 580.894 cm EMC /LBody <> BDC 1 0 0 1 -178.409 -580.894 cm BT /F31 11.9552 Tf 0.98 0 0 1 182.152 580.894 Tm [(inside)-319(it)-320(w)28(on't)-320(co)28(v)28(er)-319(to)-28(o)-320(man)28(y)-319(p)-28(oin)28(ts)-320(of)-319(in)27(teg)1(er)-320(co)-28(ordinates;)]TJ/F52 11.9552 Tf 0.98 0 0 1 487.489 580.894 Tm [(\0502)]TJ/F61 11.9552 Tf 1 0 0 1 497.686 580.894 Tm [(;)]TJ/F52 11.9552 Tf 0.98 0 0 1 502.931 580.894 Tm [(2\051)]TJ/F31 11.9552 Tf 0.994 0 0 1 138.535 566.448 Tm [(is)-329(alre)1(ady)-329(tak)27(e)1(n,)-329(and)-328(if)-329(one)-328(of)-329(the)-328(co)-28(ordinat)1(es)-329(is)]TJ/F52 11.9552 Tf 0.994 0 0 1 387.858 566.448 Tm [(1)]TJ/F31 11.9552 Tf 0.994 0 0 1 393.676 566.448 Tm [(,)-329(the)1(n)-329(the)-328(other)-329(cannot)]TJ/F31 11.9552 Tf 1.02 0 0 1 138.535 552.002 Tm [(b)-27(e)-353(in)26(tege)1(r)-354(to)-354(end)-353(up)-354(on)-353(the)-354(circle.)-527(That)-354(lea)27(v)26(e)1(s)]TJ/F52 11.9552 Tf 1.02 0 0 1 389.824 552.002 Tm [(\0500)]TJ/F61 11.9552 Tf 1 0 0 1 400.438 552.002 Tm [(;)]TJ/F52 11.9552 Tf 1.02 0 0 1 405.682 552.002 Tm [(0\051)]TJ/F31 11.9552 Tf 1.02 0 0 1 420.607 552.002 Tm [(to)-354(try;)-370(insert)-354(and)]TJ 1.02 0 0 1 138.231 536.062 Tm [(v)27(erify)-374(it)-374(zero)-27(es)-374(out)-374(b)-27(oth)]TJ/F52 11.9552 Tf 1 0 0 1 273.238 536.062 Tm [(_)]TJ/F61 11.9552 Tf -2.026 0 Td [(x)]TJ/F31 11.9552 Tf 1.02 0 0 1 282.426 536.062 Tm [(and)]TJ/F52 11.9552 Tf 1 0 0 1 308.317 536.062 Tm [(_)]TJ/F61 11.9552 Tf -2.093 0 Td [(y)]TJ/F31 11.9552 Tf 1.02 0 0 1 312.361 536.062 Tm [(.)]TJ/F157 11.9552 Tf 1.02 0 0 1 322.858 536.062 Tm [(J)]TJ/F55 7.9701 Tf 1 0 0 1 329.943 534.269 Tm [(0)]TJ/F62 7.9701 Tf 4.234 0 Td [(;)]TJ/F55 7.9701 Tf 2.353 0 Td [(0)]TJ/F52 11.9552 Tf 1.02 0 0 1 345.705 536.062 Tm [(=)]TJ/F67 9.9626 Tf 1 0 0 1 359.435 547.619 Tm [(\020)]TJ/F65 7.9701 Tf 8.883 -5.903 Td [(\000)]TJ/F55 7.9701 Tf 6.587 0 Td [(1)]TJ/F65 7.9701 Tf 8.426 0 Td [(\000)]TJ/F55 7.9701 Tf 6.586 0 Td [(1)]TJ -22.539 -8.474 Td [(1)]TJ/F62 7.9701 Tf 4.234 0 Td [(=)]TJ/F55 7.9701 Tf 4.234 0 Td [(2)]TJ/F65 7.9701 Tf 7.485 0 Td [(\000)]TJ/F55 7.9701 Tf 6.586 0 Td [(1)]TJ/F67 9.9626 Tf 6.227 14.377 Td [(\021)]TJ/F31 11.9552 Tf 1.02 0 0 1 406.655 536.062 Tm [(has)-374(trace)]TJ/F52 11.9552 Tf 1.02 0 0 1 458.961 536.062 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 472.691 536.062 Tm [(\000)]TJ/F52 11.9552 Tf 1.02 0 0 1 481.989 536.062 Tm [(2)]TJ/F31 11.9552 Tf 1.02 0 0 1 492.521 536.062 Tm [(and)]TJ 1.02 0 0 1 138.535 520.122 Tm [(determinan)27(t)]TJ/F52 11.9552 Tf 1.02 0 0 1 206.812 520.122 Tm [(=)-414(3)]TJ/F61 11.9552 Tf 1 0 0 1 227.122 520.122 Tm [(=)]TJ/F52 11.9552 Tf 1.02 0 0 1 232.975 520.122 Tm [(2)]TJ/F31 11.9552 Tf 1.02 0 0 1 238.945 520.122 Tm [(,)-424(i.e.)-404(the)-403(same)-404(\023)]TJ/F61 11.9552 Tf 1 0 0 1 326.607 520.122 Tm [(k)]TJ/F52 11.9552 Tf 1.02 0 0 1 338.15 520.122 Tm [(=)-414(1)]TJ/F61 11.9552 Tf 1 0 0 1 358.461 520.122 Tm [(=)]TJ/F52 11.9552 Tf 1.02 0 0 1 364.314 520.122 Tm [(2)]TJ/F31 11.9552 Tf 1.02 0 0 1 370.284 520.122 Tm [(\024)-403(instance)-404(of)-403(the)-404(\050a\051)-403(ro)-27(ots)]TJ 1.02 0 0 1 138.535 505.676 Tm [(as)-366(w)26(e)-366(had)-366(in)-366(\050b\051.)-566(Non-real)-366(ro)-27(ots)-366(with)-366(negativ)26(e)-366(real)-366(part)]TJ/F64 11.9552 Tf 1 0 0 1 441.311 505.676 Tm [(\000)]TJ/F52 11.9552 Tf 1.02 0 0 1 450.61 505.676 Tm [(2)]TJ/F61 11.9552 Tf 1 0 0 1 456.58 505.676 Tm [(k)]TJ/F52 11.9552 Tf 1.02 0 0 1 467.351 505.676 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 480.921 505.676 Tm [(\000)]TJ/F52 11.9552 Tf 1.02 0 0 1 490.219 505.676 Tm [(1)]TJ/F31 11.9552 Tf 1.02 0 0 1 496.189 505.676 Tm [(,)-378(it)]TJ 1.02 0 0 1 138.535 491.23 Tm [(is)]TJ/F31 11.9552 Tf 1 0 0 1 150.966 491.23 Tm [(asymptotically)-326(stable)]TJ ET q 1 0 0 1 150.966 487.511 cm []0 d 0 J 0.398 w 0 0 m 108.737 0 l S Q q 1 0 0 1 150.966 485.518 cm []0 d 0 J 0.398 w 0 0 m 108.737 0 l S Q BT /F31 11.9552 Tf 1.02 0 0 1 259.703 491.23 Tm [(.)-550(\050And)-361(spiralling)-361(in)26(w)27(ards,)-371(but)-361(that)-361(need)-361(not)-362(b)-26(e)]TJ/F31 11.9552 Tf 1 0 0 1 138.535 474.958 Tm [(p)-27(oin)27(ted)-326(out)-327(explicitly)-326(giv)27(en)-326(the)-326(question.\051)]TJ 0 g 0 G -45.913 -24.409 Td [(\050e\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 450.549 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -450.549 cm BT /F31 11.9552 Tf 0.98 0 0 1 112.782 450.549 Tm [(Left:)-439(a)-324(sk)28(etc)27(h)-323(that)-324(should)-324(b)-28(e)-323(go)-28(o)-28(d)-324(e)1(nough)-324(for)-324(the)-324(graders)-323(to)-324(recognize)-324(that)-323(the)]TJ 0.98 0 0 1 112.782 436.104 Tm [(crucial)-323(prop)-27(erties)-323(are)-323(captured:)-439(directions)-323(\050including)-322(n)27(ullclines)-323(no)1(t-unlik)27(e)-323(th)1(os)-1(e)]TJ 0.98 0 0 1 112.782 421.658 Tm [(in)-298(the)-297(problem)-298(set)1(\051)-298(and)-298(solutio)1(n)-298(curv)28(es)-298(in)-297(all)-298(regions.)-432(It)-298(is)-297(not)-298(required)-297(that)-298(the)]TJ 0.98 0 0 1 112.782 407.212 Tm [(saddle)-296(path)-295(is)-296(one)-296(of)-295(the)-296(solution)-295(curv)27(es;)-308(it)-295(is)-296(decreasing)-296(at)-295(slop)-28(e)-296(asymptotic)1(ally)]TJ/F64 11.9552 Tf 1 0 0 1 112.782 392.766 Tm [(!)-278(\000)]TJ/F52 11.9552 Tf 24.575 0 Td [(\0501)-222(+)]TJ/F64 11.9552 Tf 24.823 9.752 Td [(p)]TJ ET q 1 0 0 1 172.143 402.757 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 172.143 392.766 Td [(3\051)]TJ/F31 11.9552 Tf 14.307 0 Td [(lik)27(e)-326(system)-327(\050)1(L\051.)-327(Righ)27(t:)-435(a)-326(plot)-326(\050with)-327(the)-326(n)27(ullclines)-326(in)-327(gree)1(n\051.)]TJ ET 1 0 0 1 112.782 198.86 cm EMC /Figure <> BDC q 1 0 0 1 -96.377 -651.967 cm /Im1 Do Q 1 0 0 1 385.512 0 cm EMC 1 0 0 1 -386.881 -19.427 cm /P <> BDC 1 0 0 1 -111.413 -179.433 cm BT 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7.9701 Tf 5.645 0 Td [(R)]TJ/F67 9.9626 Tf 10.405 21.696 Td [(Z)]TJ/F62 7.9701 Tf 9.963 -3.155 Td [(T)]TJ/F55 7.9701 Tf -4.428 -19.483 Td [(0)]TJ/F67 9.9626 Tf 13.025 23.125 Td [(\022)]TJ/F52 11.9552 Tf 7.334 -14.545 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(x)]TJ/F52 11.9552 Tf 9.309 0 Td [(+)-222(1\051)]TJ/F64 11.9552 Tf 24.823 0 Td [(\001)]TJ/F61 11.9552 Tf 5.978 0 Td [(u)]TJ/F64 11.9552 Tf 9.319 0 Td [(\000)]TJ/F52 11.9552 Tf 13.151 8.087 Td [(1)]TJ ET q 1 0 0 1 208.942 707.713 cm []0 d 0 J 0.398 w 0 0 m 5.853 0 l S Q BT /F52 11.9552 Tf 208.942 696.524 Td [(2)]TJ 7.048 8.201 Td [(\0503)]TJ/F61 11.9552 Tf 10.405 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.936 Td [(2)]TJ/F52 11.9552 Tf 7.389 -4.936 Td [(+)]TJ/F61 11.9552 Tf 11.762 0 Td [(u)]TJ/F55 7.9701 Tf 6.662 4.936 Td [(2)]TJ/F52 11.9552 Tf 4.733 -4.936 Td [(\051)]TJ/F67 9.9626 Tf 4.552 14.545 Td [(\023)]TJ/F61 11.9552 Tf 11.983 -14.545 Td [(dt)]TJ/F31 11.9552 Tf 33.721 0 Td [(when)]TJ/F52 11.9552 Tf 40.396 0 Td [(_)]TJ/F61 11.9552 Tf -2.026 0 Td [(x)]TJ/F52 11.9552 Tf 9.973 0 Td [(=)]TJ/F61 11.9552 Tf 12.426 0 Td [(u;)-1146(x)]TJ/F52 11.9552 Tf 30.265 0 Td [(\0500\051)-278(=)]TJ/F61 11.9552 Tf 30.704 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 -1.794 Td [(0)]TJ/F61 11.9552 Tf 4.732 1.794 Td [(;)-1146(x)]TJ/F52 11.9552 Tf 23.602 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)]TJ/F64 11.9552 Tf 7.873 0 Td [(\025)]TJ/F52 11.9552 Tf 12.62 0 Td [(0)]TJ ET EMC 0 g 0 G BT /F31 11.9552 Tf 62.312 672.18 Td [(\050a\051)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 90.016 672.18 cm EMC /Lbl <> BDC 1 0 0 1 -90.016 -672.18 cm BT /F46 11.9552 Tf 93.918 672.18 Td [(\210)]TJ ET 1 0 0 1 103.023 672.18 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -672.18 cm BT /F31 11.9552 Tf 108.279 672.18 Td [(W)82(rite)-327(out)-326(the)-326(conditions)-327(from)-326(the)-326(maxim)27(um)-326(principle.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET 1 0 0 1 90.016 652.753 cm EMC /Lbl <> BDC 1 0 0 1 -90.016 -652.753 cm BT /F46 11.9552 Tf 93.918 652.753 Td [(\210)]TJ ET 1 0 0 1 103.023 652.753 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -652.753 cm BT /F31 11.9552 Tf 1.006 0 0 1 108.876 652.753 Tm [(Supp)-27(ose)-324(an)-324(admissible)-324(pair)]TJ/F52 11.9552 Tf 1.006 0 0 1 252.566 652.753 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 257.146 652.753 Tm [(x;)-167(u)]TJ/F52 11.9552 Tf 1.006 0 0 1 275.704 652.753 Tm [(\051)]TJ/F31 11.9552 Tf 1.006 0 0 1 284.181 652.753 Tm [(satis\034es)-324(these)-324(conditions;)-324(do)-324(w)27(e)-324(then)-324(kno)27(w)-324(that)-324(it)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.455 638.307 Tm [(will)-326(solv)27(e)-326(the)-327(problem?)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 53.858 613.898 cm EMC /LBody <> BDC 1 0 0 1 -53.858 -613.898 cm BT /F31 11.9552 Tf 0.985 0 0 1 53.858 613.898 Tm [(Let)]TJ/F52 11.9552 Tf 0.985 0 0 1 74.575 613.898 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 79.059 613.898 Tm [(x;)-167(u)]TJ/F52 11.9552 Tf 0.985 0 0 1 97.618 613.898 Tm [(\051)]TJ/F31 11.9552 Tf 0.985 0 0 1 106.006 613.898 Tm [(b)-28(e)-331(an)-332(admissible)-331(pair)-332(satisfying)-331(the)-332(necessary)-331(conditions)-332(from)-331(the)-332(maxim)28(um)-332(principle)1(,)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 53.437 599.453 Tm [(with)-326(adjoin)27(t)-326(\050costate\051)]TJ/F61 11.9552 Tf 115.174 0 Td [(p)]TJ/F31 11.9552 Tf 5.875 0 Td [(.)-435(Y)81(ou)-326(can)-326(tak)27(e)-326(for)-327(gran)28(ted)-327(that)]TJ/F61 11.9552 Tf 165.181 0 Td [(u)]TJ/F52 11.9552 Tf 6.662 0 Td [(\050)]TJ/F61 11.9552 Tf 4.553 0 Td [(t)]TJ/F52 11.9552 Tf 4.227 0 Td [(\051)]TJ/F31 11.9552 Tf 8.454 0 Td [(is)-326(a)-327(con)27(tin)28(uous)-327(function)-326(of)]TJ/F61 11.9552 Tf 139.303 0 Td [(t)]TJ/F31 11.9552 Tf 4.227 0 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -445.431 -24.409 Td [(\050b\051)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 90.016 575.044 cm EMC /Lbl <> BDC 1 0 0 1 -90.016 -575.044 cm BT /F46 11.9552 Tf 93.918 575.044 Td [(\210)]TJ ET 1 0 0 1 103.023 575.044 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -575.044 cm BT /F31 11.9552 Tf 108.876 575.044 Td [(Deduce)-326(a)-327(di\033eren)28(tial)-327(equation)-326(system)-326(for)]TJ/F52 11.9552 Tf 214.252 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(x;)-167(p)]TJ/F52 11.9552 Tf 17.772 0 Td [(\051)]TJ/F31 11.9552 Tf 4.552 0 Td [(.)-435(\050That)-326(is,)-327(with)-326(no)-327(\023)]TJ/F61 11.9552 Tf 106.721 0 Td [(u)]TJ/F31 11.9552 Tf 6.662 0 Td [(\024)-326(letter.\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET 1 0 0 1 90.016 555.617 cm EMC /Lbl <> BDC 1 0 0 1 -90.016 -555.617 cm BT /F46 11.9552 Tf 93.918 555.617 Td [(\210)]TJ ET 1 0 0 1 103.023 555.617 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -108.876 -555.617 cm BT /F31 11.9552 Tf 1.02 0 0 1 108.876 555.617 Tm [(Explain)-338(\050in)-339(w)27(ords,)-343(if)-339(y)27(ou)-338(lik)26(e\051)-338(ho)27(w)-339(the)-338(in)27(tegration)-339(constan)27(ts)-338(will)-339(b)-26(e)-339(determined)-338(in)]TJ 0 g 0 G 0 g 0 G /F31 11.9552 Tf 1 0 0 1 108.876 541.171 Tm [(eac)27(h)-326(of)-326(the)-327(t)27(w)28(o)-327(cases)]TJ/F61 11.9552 Tf 111.337 0 Td [(x)]TJ/F52 11.9552 Tf 6.652 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)-278(=)-277(0)]TJ/F31 11.9552 Tf 30.054 0 Td [(and)]TJ/F61 11.9552 Tf 22.762 0 Td [(x)]TJ/F52 11.9552 Tf 6.652 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)]TJ/F64 11.9552 Tf 7.873 0 Td [(6)]TJ/F52 11.9552 Tf 0 0 Td [(=)-278(0)]TJ/F31 11.9552 Tf 18.279 0 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -275.6 -24.408 Td [(\050c\051)]TJ 0 g 0 G ET 1 0 0 1 83.123 516.763 cm EMC /LBody <> BDC 1 0 0 1 -83.123 -516.763 cm BT /F31 11.9552 Tf 83.123 516.763 Td [(Sho)27(w)-326(that)]TJ/F61 11.9552 Tf 56.254 0 Td [(u)]TJ/F52 11.9552 Tf 6.663 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)]TJ/F61 11.9552 Tf 7.873 0 Td [(>)]TJ/F52 11.9552 Tf 12.426 0 Td [(0)]TJ/F31 11.9552 Tf 9.755 0 Td [(\050i.e.)-326(at)-327(\034nal)-326(time)]TJ/F61 11.9552 Tf 90.397 0 Td [(T)]TJ/F31 11.9552 Tf 8.487 0 Td [(\051.)]TJ 0 g 0 G 0 g 0 G ET 1 0 0 1 65.564 313.845 cm EMC /LBody <> BDC 0 g 0 G 1 0 0 1 17.953 171.017 cm EMC /P <> BDC 0 g 0 G 1 0 0 1 -83.517 -484.862 cm BT /F125 11.3574 Tf 83.517 476.577 Td [(Quite)-278(common)-278(pr)20(ob)10(lem)-278(type)-278(\050e)-20(.g.)-278(2022#3)-278(f)20(or)-278(seminar)-278(10.\051)-2344(Ho)15(w)-278(to)-278(solve:)]TJ 0 g 0 G ET 1 0 0 1 504.435 476.577 cm EMC /P <> BDC 1 0 0 1 -504.435 -476.577 cm BT /F31 11.9552 Tf 82.92 462.131 Td [(W)82(e)-327(are)-326(going)-326(to)-327(need)]TJ/F61 11.9552 Tf 112.504 0 Td [(H)]TJ/F52 11.9552 Tf 10.622 0 Td [(\050)]TJ/F61 11.9552 Tf 4.553 0 Td [(x;)-167(u;)-166(p)]TJ/F52 11.9552 Tf 29.678 0 Td [(\051)-278(=)-277(\050)]TJ/F61 11.9552 Tf 24.851 0 Td [(x)]TJ/F52 11.9552 Tf 9.309 0 Td [(+)-222(1\051)]TJ/F64 11.9552 Tf 24.823 0 Td [(\001)]TJ/F61 11.9552 Tf 5.978 0 Td [(u)]TJ/F64 11.9552 Tf 9.319 0 Td [(\000)]TJ/F55 7.9701 Tf 13.15 4.707 Td [(1)]TJ ET q 1 0 0 1 327.707 465.119 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 327.707 458.008 Td [(2)]TJ/F52 11.9552 Tf 5.43 4.123 Td [(\0503)]TJ/F61 11.9552 Tf 10.405 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F52 11.9552 Tf 7.389 -4.338 Td [(+)]TJ/F61 11.9552 Tf 11.762 0 Td [(u)]TJ/F55 7.9701 Tf 6.662 4.338 Td [(2)]TJ/F52 11.9552 Tf 4.732 -4.338 Td [(\051)-222(+)]TJ/F61 11.9552 Tf 18.971 0 Td [(pu)]TJ/F31 11.9552 Tf 12.537 0 Td [(.)]TJ 0 g 0 G -320.275 -19.427 Td [(\050a\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 442.704 cm EMC /P <> BDC 1 0 0 1 -112.782 -442.704 cm BT /F31 11.9552 Tf 1.009 0 0 1 112.782 442.704 Tm [(First)-324(note)-324(that)-324(the)-324(conditions)-324(are)-324(su\036cien)27(t,)-324(as)]TJ/F61 11.9552 Tf 1 0 0 1 357.09 442.704 Tm [(H)]TJ/F31 11.9552 Tf 1.009 0 0 1 371.621 442.704 Tm [(is)-324(conca)27(v)27(e)-324(in)]TJ/F52 11.9552 Tf 1.009 0 0 1 440.837 442.704 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 445.43 442.704 Tm [(x;)-167(u)]TJ/F52 11.9552 Tf 1.009 0 0 1 463.989 442.704 Tm [(\051)]TJ/F31 11.9552 Tf 1.009 0 0 1 468.582 442.704 Tm [(:)-432(On)]TJ/F72 11.9552 Tf 1 0 0 1 496.738 442.704 Tm [(R)]TJ/F55 7.9701 Tf 8.634 4.338 Td [(2)]TJ/F31 11.9552 Tf 1.009 0 0 1 510.104 442.704 Tm [(,)]TJ/F61 11.9552 Tf 1 0 0 1 112.782 428.258 Tm [(H)]TJ/F65 7.9701 Tf 10.623 4.338 Td [(00)]TJ/F62 7.9701 Tf -0.924 -7.294 Td [(xx)]TJ/F61 11.9552 Tf 10.032 2.956 Td [(H)]TJ/F65 7.9701 Tf 10.623 4.338 Td [(00)]TJ/F62 7.9701 Tf -0.924 -7.294 Td [(uu)]TJ/F64 11.9552 Tf 12.961 2.956 Td [(\000)]TJ/F52 11.9552 Tf 11.955 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(H)]TJ/F65 7.9701 Tf 10.623 4.338 Td [(00)]TJ/F62 7.9701 Tf -0.924 -7.294 Td [(xu)]TJ/F52 11.9552 Tf 10.168 2.956 Td [(\051)]TJ/F55 7.9701 Tf 4.553 4.338 Td [(2)]TJ/F52 11.9552 Tf 8.053 -4.338 Td [(=)-278(\050)]TJ/F64 11.9552 Tf 16.978 0 Td [(\000)]TJ/F52 11.9552 Tf 9.298 0 Td [(3\051)]TJ/F64 11.9552 Tf 13.062 0 Td [(\001)]TJ/F52 11.9552 Tf 5.978 0 Td [(\050)]TJ/F64 11.9552 Tf 4.552 0 Td [(\000)]TJ/F52 11.9552 Tf 9.298 0 Td [(1\051)]TJ/F64 11.9552 Tf 13.062 0 Td [(\000)]TJ/F52 11.9552 Tf 11.956 0 Td [(1)]TJ/F55 7.9701 Tf 5.853 4.338 Td [(2)]TJ/F61 11.9552 Tf 8.053 -4.338 Td [(>)]TJ/F52 11.9552 Tf 12.425 0 Td [(0)]TJ/F31 11.9552 Tf 9.755 0 Td [(with)]TJ/F61 11.9552 Tf 26.664 0 Td [(H)]TJ/F65 7.9701 Tf 10.623 4.338 Td [(00)]TJ/F62 7.9701 Tf -0.924 -7.294 Td [(uu)]TJ/F61 11.9552 Tf 13.625 2.956 Td [(<)]TJ/F52 11.9552 Tf 12.425 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(.)]TJ ET 1 0 0 1 112.361 408.831 cm EMC /P <> BDC 1 0 0 1 -112.361 -408.831 cm BT /F31 11.9552 Tf 112.361 408.831 Td [(Then)-326(on)-327(to)-326(the)-326(conditions:)]TJ 0 g 0 G ET 1 0 0 1 119.676 389.403 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -389.403 cm BT /F46 11.9552 Tf 123.578 389.403 Td [(\210)]TJ ET 1 0 0 1 132.682 389.403 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm EMC /LBody <> BDC 1 0 0 1 -138.535 -389.403 cm BT /F31 11.9552 Tf 138.114 389.403 Td [(The)-326(optimal)]TJ/F61 11.9552 Tf 66.985 0 Td [(u)]TJ/F65 7.9701 Tf 6.663 4.339 Td [(\003)]TJ/F31 11.9552 Tf 8.634 -4.339 Td [(maximizes)]TJ/F52 11.9552 Tf 56.97 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(x)]TJ/F52 11.9552 Tf 9.309 0 Td [(+)-222(1\051)]TJ/F64 11.9552 Tf 24.824 0 Td [(\001)]TJ/F61 11.9552 Tf 5.977 0 Td [(u)]TJ/F64 11.9552 Tf 9.319 0 Td [(\000)]TJ/F55 7.9701 Tf 13.151 4.708 Td [(1)]TJ ET q 1 0 0 1 344.498 392.392 cm []0 d 0 J 0.398 w 0 0 m 4.234 0 l S Q BT /F55 7.9701 Tf 344.498 385.281 Td [(2)]TJ/F52 11.9552 Tf 5.43 4.122 Td [(\0503)]TJ/F61 11.9552 Tf 10.405 0 Td [(x)]TJ/F55 7.9701 Tf 6.652 4.339 Td [(2)]TJ/F52 11.9552 Tf 7.389 -4.339 Td [(+)]TJ/F61 11.9552 Tf 11.761 0 Td [(u)]TJ/F55 7.9701 Tf 6.663 4.339 Td [(2)]TJ/F52 11.9552 Tf 4.732 -4.339 Td [(\051)-222(+)]TJ/F61 11.9552 Tf 18.971 0 Td [(pu)]TJ/F31 11.9552 Tf 16.439 0 Td [(o)27(v)27(er)-326(all)-326(real)]TJ/F61 11.9552 Tf 64.058 0 Td [(u)]TJ/F31 11.9552 Tf 6.663 0 Td [(;)]TJ 0 g 0 G ET 1 0 0 1 119.676 369.976 cm EMC /Lbl <> BDC 1 0 0 1 -119.676 -369.976 cm BT /F46 11.9552 Tf 123.578 369.976 Td [(\210)]TJ ET 1 0 0 1 132.682 369.976 cm EMC 0 g 0 G 1 0 0 1 5.853 0 cm /LBody <> BDC 1 0 0 1 -138.535 -369.976 cm BT /F61 11.9552 Tf 138.535 369.976 Td [(p)]TJ/F31 11.9552 Tf 9.778 0 Td [(satis\034es)]TJ/F52 11.9552 Tf 45.404 0 Td [(_)]TJ/F61 11.9552 Tf -2.287 0 Td [(p)]TJ/F52 11.9552 Tf 9.196 0 Td [(=)]TJ/F64 11.9552 Tf 12.425 0 Td [(\000)]TJ/F61 11.9552 Tf 9.299 0 Td [(u)]TJ/F65 7.9701 Tf 6.662 4.339 Td [(\003)]TJ/F52 11.9552 Tf 7.389 -4.339 Td [(+)-222(3)]TJ/F61 11.9552 Tf 17.615 0 Td [(x)]TJ/F65 7.9701 Tf 6.652 4.339 Td [(\003)]TJ/F31 11.9552 Tf 8.634 -4.339 Td [(with)]TJ/F61 11.9552 Tf 26.664 0 Td [(p)]TJ/F52 11.9552 Tf 5.875 0 Td [(\050)]TJ/F61 11.9552 Tf 4.553 0 Td [(T)]TJ/F52 11.9552 Tf 8.486 0 Td [(\051)]TJ/F64 11.9552 Tf 7.874 0 Td [(\025)]TJ/F52 11.9552 Tf 12.619 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(,)-326(and)]TJ/F61 11.9552 Tf 29.916 0 Td [(p)]TJ/F52 11.9552 Tf 5.875 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)-278(=)-278(0)]TJ/F31 11.9552 Tf 30.054 0 Td [(if)]TJ/F61 11.9552 Tf 10.731 0 Td [(x)]TJ/F52 11.9552 Tf 6.652 0 Td [(\050)]TJ/F61 11.9552 Tf 4.552 0 Td [(T)]TJ/F52 11.9552 Tf 8.487 0 Td [(\051)]TJ/F61 11.9552 Tf 7.873 0 Td [(>)]TJ/F52 11.9552 Tf 12.425 0 Td [(0)]TJ/F31 11.9552 Tf 5.853 0 Td [(.)]TJ ET 1 0 0 1 111.413 350.549 cm EMC /LBody <> BDC 1 0 0 1 -111.413 -350.549 cm BT /F31 11.9552 Tf 0.98 0 0 1 111.413 350.549 Tm [(\050In)-269(addition,)-282(the)-268(di\033eren)27(tia)1(l)-269(equation)-269(for)]TJ/F61 11.9552 Tf 1 0 0 1 316.239 350.549 Tm [(x)]TJ/F31 11.9552 Tf 0.98 0 0 1 326.042 350.549 Tm [(m)28(ust)-269(hold,)-282(with)-269(the)-269(initia)1(l)-269(condition.\051)]TJ 0 g 0 G /F31 11.9552 Tf 1 0 0 1 91.321 326.141 Tm [(\050b\051)]TJ 0 g 0 G ET 1 0 0 1 112.782 326.141 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -326.141 cm BT /F31 11.9552 Tf 1.02 0 0 1 112.361 326.141 Tm [(The)-334(co)1(nca)26(v)27(e)-334(quadratic)-333(is)-334(maximized)-333(for)-334(the)-333(stationary)-334(p)-27(oin)27(t)]TJ/F61 11.9552 Tf 1 0 0 1 434.028 326.141 Tm [(u)]TJ/F65 7.9701 Tf 6.663 4.338 Td [(\003)]TJ/F52 11.9552 Tf 1.02 0 0 1 449.027 326.141 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 461.918 326.141 Tm [(x)]TJ/F52 11.9552 Tf 1.02 0 0 1 471.34 326.141 Tm [(+)]TJ/F61 11.9552 Tf 1 0 0 1 483.397 326.141 Tm [(p)]TJ/F52 11.9552 Tf 1.02 0 0 1 492.042 326.141 Tm [(+)-227(1)]TJ/F31 11.9552 Tf 1.02 0 0 1 510.068 326.141 Tm [(,)]TJ/F31 11.9552 Tf 0.98 0 0 1 112.782 311.695 Tm [(and)-328(so)]TJ/F52 11.9552 Tf 1 0 0 1 151.241 311.695 Tm [(_)]TJ/F61 11.9552 Tf -2.025 0 Td [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 159.189 311.695 Tm [(=)]TJ/F61 11.9552 Tf 1 0 0 1 171.433 311.695 Tm [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 180.625 311.695 Tm [(+)-217(1)-217(+)]TJ/F61 11.9552 Tf 1 0 0 1 211.826 311.695 Tm [(p)]TJ/F31 11.9552 Tf 0.98 0 0 1 217.701 311.695 Tm [(.)-442(Then)]TJ/F52 11.9552 Tf 1 0 0 1 258.334 311.695 Tm [(_)]TJ/F61 11.9552 Tf -2.287 0 Td [(p)]TJ/F52 11.9552 Tf 0.98 0 0 1 265.243 311.695 Tm [(=)]TJ/F64 11.9552 Tf 1 0 0 1 277.487 311.695 Tm [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 286.785 311.695 Tm [(\050)]TJ/F61 11.9552 Tf 1 0 0 1 291.247 311.695 Tm [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 300.439 311.695 Tm [(+)-217(1)-217(+)]TJ/F61 11.9552 Tf 1 0 0 1 331.64 311.695 Tm [(p)]TJ/F52 11.9552 Tf 0.98 0 0 1 337.515 311.695 Tm [(\051)-217(+)-217(3)]TJ/F61 11.9552 Tf 1 0 0 1 361.715 311.695 Tm [(x)]TJ/F52 11.9552 Tf 0.98 0 0 1 371.688 311.695 Tm [(=)-283(2)]TJ/F61 11.9552 Tf 1 0 0 1 389.668 311.695 Tm [(x)]TJ/F64 11.9552 Tf 9.192 0 Td [(\000)]TJ/F61 11.9552 Tf 11.838 0 Td [(p)]TJ/F64 11.9552 Tf 8.416 0 Td [(\000)]TJ/F52 11.9552 Tf 0.98 0 0 1 430.952 311.695 Tm [(1)]TJ/F31 11.9552 Tf 0.98 0 0 1 436.688 311.695 Tm [(.)-442(That)-329(w)28(as)-328(the)]TJ/F31 11.9552 Tf 1 0 0 1 112.782 297.249 Tm [(system.)]TJ ET 1 0 0 1 112.782 277.822 cm EMC /LBody <> BDC 1 0 0 1 -112.782 -277.822 cm BT /F31 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Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMRoman8-Bold)readonly def /FamilyName(LMRoman8)readonly def /Weight(Bold)readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -117 def /UnderlineThickness 54 def end readonly def /FontName /DFNYGL+LMRoman8-Bold def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 51 /three put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-519 -307 1704 1136}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp_3/h)C-UrHLz$v\m3Xb ϫKjӬ[ :fGp6@%R Z:#o3ܕjLbKaNT.DםK Awge=xq &û[KVW7lGbG#}+mb9&v˾Hqګ$LQH[HT)i5)HvDUf}KqBt~-S&δeaq7˫[AflYsW{ S+54<>=M+`:S((Qj _nAIcRn+t`{&kmH9j4&! \T+f27_\XxEb,ϧ"&j})e^H~dB8ꄉp׊NΠ͊+,z6@TԢV>-&3̉K6کǑGݸ'[=AEɿRm@!L2m0etzWՅ%`ĕ!\;_y~Sit6 /]>6@8oDxg3&5\79'LR)/cwbc+@VA|`LŧXV970VZ21oU$@$j!%{kpLRE퇴׸WqӓIb9yQo4Kf藖rjFq.Ƃv#[_|*GC 0 [+KмY:QK?4&?y㵿 + "# ZM6R#4'A>h5v=χPZVWq9WYlA \v 8Q1 ϳ&L8؄54o&GLj~Cft ;79"8HBVJ q>:yI6q4,9bsU F$V9=)5}<:dg]ƞax 7Hg(Lb^ri:/G,#]%t5v<+aҰ)PY&xNVYeI.ùK0  j_'Xn5P3FR@oY41C>0<.‰jdҢtsj WZ}EVp"A^@$Y2'}ZivPhoy#QN"AAk7 S BfYDTɁ%QkQCTBs6G_!JModk| *VLxTDOz0 !Uh4?fOT;tAҡ1{}5OvS1[ܯu~x䏟]ӆ: l@BtmccP9  Q8w'%SyKN_сGYKp P1>]Md|PA{@+AU [ؓ4:'WJ"sޯ\]P7їU>+!}&rhegXZk- 53)\:Ms 2ҁ_ie.)td.IOSp? fOuWװ_$lZ (cSIJz?Yƽݕ)SC&xK]břy*oG9a^&شDqv'G2K0`OX.=相0OEh#^9DsbG˪ոV׽n^j˼pL">b} sw%ɦežd'!:aq1z#X8O(uVsS؉iFE.QEDA|df[ 8 媰J;0!\%2R:4}0=3~a! 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ONzj(e윛Hmm]yRAn ]ㄐwWxL7ЏK* &16z_ҁН%85&Snt-)s⍉qKːCp&ýDfp*R7;|kq۔Ik)@q&ӗ?,ӬOo ׹mFЅ4_~n} f AGVao5V` >Ck4nM gC.G Au0!9NーVڊԌ3IbTsdbUG1,ucѻgIׂqW"x3Wm6QEaӬ=ʌÓ6reعUH˧+424w V$Wo^CV+`;X~(JﻠDqBW@Iܥ khJ]AW=ϐoͭEf =)w >1rG/~n/We*o99f6T>'`/L7 &(byAc2fRM( d:4rٽ1S 쬶31&mFV0Ѭ$J/z"P fN=v]VUcܲd(0g8ZiW&x_MSq ڏUX 4"bэGm۔Ewڥ qpX>rp2ဖ'T >'31icw%4{W鯇{məLD[RZ weRe)51p2dK=Hv+ !g}LvPoݭ$HL-Ec] a0UC,)vZc\*ټB>V`;ϵa헓 ן'_P\Zӕƴ$ӝg )ˮ=!$o !G=pLgސ=cކusP>"kqzLtTx9,E9X_mqtN(0'Ǽ\z)GKֿ".*ќ0qe5!Ytbs>9q T3I^؇WP:n;yX uڐGhw&+}(+zՓ=] w0l''ġ;J37_1w9 U+ Q`UY]y*.pcU!`g̋—ש-Gg1ҳ4QN9uXf7b8ӆ,RC6)*;]H_XNBM./7ӻ,3&v|Q@3z s9X6ٝ%}и2B JXA|Oڷ*(Ɋ|Y?h@f-x8z 6(5u eCAB} A_ b_{;8;1+7F6ی eKC1|G#lTBHSv)›/pHBltUmЧUr/si#rֲV!8)g4zɋs%i&9 mP~(/JV..[d`gWC Zqi,O5pv9P <az0]'!~ꥀzGR<V?|%!fJr02O5i#B O:*K7'/BopHx`I]ذa%0דFڷ6)X M[d2;5b rÇD.HH{ ހX ^6sv5BgY1{\@FWCSE{v`LgsgG\@XHl;ӥ#sUL0, /gGpa >uW\ @ۂCmG#ʊ1RoɌ ?xsd x`%*ed&{Fд%M_{ s[u􇃲/><qN|n֤E$Ö据Sˈ?OT_ɓHٮ۫4&D3?%)?2Zwk3ΰk$0Bu0P&yĔ$y7(X1Uu@g)_4Y9xcS!mȈw7gT x vԮ:j{f!wDƭ ԗn3 ]5jI.c=sqΥ0eTNUT-brq&6ǐ]&uL;tC}ak+qJ6-(\? ׂ۠逷͑".f Ek@T2RrZȅ393v4dxR 'k׆k-JA(rT@Iiɨݐjqae>9<_8NA)],ٚ"yq('aU+Z8'!nk4xQtuTwϒ| 9˱籫5x䰭ʵ4=h"Գ(4ݦhjm(}eOS mJ.iĴ[Zц m􏄧<̤˞:=7s"M#W"Gu.h6"n<- TΫEFv"ÔóD%5gb7,Qۓ0q#qX\ #"]]-@u}o@TV>?#4ҸӴy ޘ$bN`*f&464^O|!71[IZk?`ߙ켙qm#y(Ra7JDl](0h4cPG!>A'}ՔjɁD.4NQK5tW28QS3r Go ʿ0x]DUwTH1G#_VŲ p~bc.)]:Om޶H^y!5Z[ZvE>2#`[V9ugl>#|@+:7ChDPc"p+c >+W/gjPwlXEbXRGth ^*hbmtKJTp4~,nJp:Ёrt|N endstream endobj 287 0 obj << /Type /FontDescriptor /FontName /DFNYGL+LMRoman8-Bold /Flags 4 /FontBBox [-519 -307 1704 1136] /Ascent 705 /CapHeight 676 /Descent -194 /ItalicAngle 0 /StemV 122 /XHeight 444 /CharSet (/three) /FontFile 286 0 R >> endobj 288 0 obj << /Length1 2092 /Length2 3674 /Length3 0 /Length 5766 >> stream %!PS-AdobeFont-1.0: LMMathExtension10-Regular 1.200 %%CreationDate: 16th September 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 694 194 0 %%EndComments FontDirectory/LMMathExtension10-Regular known{/LMMathExtension10-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.003)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMMathExtension10-Regular)readonly def /FamilyName(LMMathExtension10)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -146 def /UnderlineThickness 40 def end readonly def /FontName /HROVNS+LMMathExtension10-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 232 /bracketleftBig put dup 233 /bracketrightBig put dup 218 /integraldisplay put dup 49 /parenleftBig put dup 65 /parenleftBigg put dup 51 /parenleftbigg put dup 97 /parenleftbt put dup 99 /parenleftex put dup 81 /parenlefttp put dup 50 /parenrightBig put dup 66 /parenrightBigg put dup 52 /parenrightbigg put dup 98 /parenrightbt put dup 100 /parenrightex put dup 82 /parenrighttp put dup 241 /radicalBig put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp[K{}sG6s+߯ ~hzDUF7Mr3MkL46#fZߪY@fc^"b`;,#KcWh+z}_j?6U鄵 k~"Xb5(;k~jGSlKk٪*WHҌ9AAāc&8]_5 R SY<./`1[s{y!(-v~av]{&stf2q#g]G$9> ,MY M)`V+%}t :$:*f 5We3G*"] A`>f|ڍc>EVcƕ-(I7]B8>lf{QXG^\M=? ҍ=߳BH GV9\69FׯHnqS ?yEwzk8j-Tx]PMD;aNzKfNo%슸% %g|rmLԡ[멋ѭEb310܉# ype|6`>i&x uq΋)_$Nz ޽62~Ff8n%p|*/}qh63$&l.m'xM,:ЌSS-K #Վ],1څq Br,5%q! u75Cth4 x3Eut=# HuP_?o8+mj c)Cz;.A+eӻ7C$ "HX|yЄ><`-JC\8hm%ȇ ,Ԁ^ԶV*p˲#)]xYT1v(jKkmP2\ؘǼ4Q:< 2ҦLXUqL=ȝx_23]d>rԳ>eˌS$6i)%}Gґ%Ը<%3$H{^e jg I޷3Oep5:XyY_Bo9nbXTߝ=J+3" ZV IW $]Û '맼̊}-X#e.T)Hǀ&|p!8ut~N|ԧӃkyJi6UyWIH#,.bZo~ pӡ!DSyTb$n.mz$}/#S[NI) m#'Z)c~`vL$ hE Ɔe3"*ǦeSHcÈB`3߮x#'ChTH4Hίsz*Ocsuj\Vxu"<^oނ&_;.łl)?D;dڽ!;| ?Jlchc{ q`C`Hr@ZEvz[E)! q5u?`7pyLR!PldbJ!s>HС=}j.3Fq X J^9>6m#(-(g [hF[“mP!^#Ⱥri5Su7⠁lJyύ0\~vwt{o[;0E6.@u7^EAfj[fO;5[qnGmNЄx=*]7lvx;-Ofk7\'g;q]YM*,_x;4. =i15e~Wy-"yĚH0OPR4hǩ! lG5W-D\\3%UXݍŬ\Rܚ|WQ|n`ٛ;\ΗZ[.2~[v.yEY"KĿu) 2nza4+_?|w1߫j~cKe>gs3 @hyvݴC;\[or<|HѴ)]0t] :nXƝƸPkܛr|?w6.^4'ߡƺ`7J?XTYEd_rOm܆4ܓ0BdPPկ|0jJfe$QsV|_xB,8fض`0 -N™pɡ[ AH旖 R-}jq/okeƢA}~`(xZ(jҬAHÀ̓L2ғSC ڷ*dCkI7to KxT]Ed@YݡL` k*bk곖"unaM VҞfApN0^AA$Y2:{}#= C65fDqiv߀E$ӟ *m/|QɃ0miܧkq+R/IkWfgRƓ*@ Om8/nZd-¢ѧ%f|PP[mC$6:X:z˥|^wh/(Rd'p 5@ڐv9p=p0$b/y. D.V6l u@]Yu] \ZM-;K1`w4E <*A{hds3616ŦzjtE~gCx=#vcGVxc>OEsU|,>OMfYZ8Q45lg6-'.xǡp#AQҲqf7w!#B-5kݧߩORח&E>ȅI"fTNBzr}Q} R *9k\ѐHNiy#n(reB`s^bveV%y1SbgIV  endstream endobj 289 0 obj << /Type /FontDescriptor /FontName /HROVNS+LMMathExtension10-Regular /Flags 4 /FontBBox [-24 -2960 1454 772] /Ascent 40 /CapHeight 0 /Descent -600 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/bracketleftBig/bracketrightBig/integraldisplay/parenleftBig/parenleftBigg/parenleftbigg/parenleftbt/parenleftex/parenlefttp/parenrightBig/parenrightBigg/parenrightbigg/parenrightbt/parenrightex/parenrighttp/radicalBig) /FontFile 288 0 R >> endobj 290 0 obj << /Length1 2118 /Length2 7439 /Length3 0 /Length 9557 >> stream %!PS-AdobeFont-1.0: LMMathItalic12-Regular 1.200 %%CreationDate: 16th September 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 833 233 0 %%EndComments FontDirectory/LMMathItalic12-Regular known{/LMMathItalic12-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.003)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMMathItalic12-Regular)readonly def /FamilyName(LMMathItalic12)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle -14.0362 def /UnderlinePosition -175 def /UnderlineThickness 44 def end readonly def /FontName /WONXQY+LMMathItalic12-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 68 /D put dup 72 /H put dup 75 /K put dup 76 /L put dup 81 /Q put dup 84 /T put dup 97 /a put dup 98 /b put dup 44 /comma put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 210 /gamma put dup 62 /greater put dup 107 /k put dup 218 /lambda put dup 60 /less put dup 219 /mu put dup 112 /p put dup 114 /r put dup 47 /slash put dup 116 /t put dup 215 /theta put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-31 -250 1026 750}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp^h?qFg :*ۆ.ۈ`e&6{҇ J+9SC?+310r5,;2ۉ3OxW4' O}0=5 u,rA;%JBFĬk \VsΨb/ yc/Lf@8R ="Т.h@e,j:f+OWr:pv=lD2y{8o.fxavM @^].z~ ERy!R]wv )&1I"?[]BLmpIw A޼O;(Cq5p|:M!Omc +3]hsSf  w~/[{YSwΆ".ԽQݹ<1؆POБO'}*B;Qs|$ىc[(^1V~Lfקywp3wAJH֍m=@n'RI-b5qlfN(STt/dV1}DF}yT]cHr (⫎h`6섣q SS&-<κΠjeMڼ)b#IS(llP[vrIZvza8Vw: _ 60Q*a?{W^59;֣Ib0#%Ӝ5Hw"AtƆQg \N4=&r#pGHô,Rɱ'o;b]ОyQ0cv]b֥zj/o#)5,ݣl Dt`2Puԅy-N_[j{kȲncvME׉l5DME~ dd DнuuУdz+:^eu& o|^{`Ax cCp3re"aV[L ڧYW0M/RO(r%=O\ ]j|8an Q1.87!NzGeɒ#xK,ڢF+97Cn1<kdQQIG.L4w6ކzkk k:\ae3-:պ1KZ Hu;[pD[b̦fV߇+4QOW,?ctJe.DidNKޮ!;GP;;֢K]2[}`…<29rU}z*eZqlBuhmqe mCɾ PWS^-6y +С{lZVio)(,2|1h~虼 JȻ.@߿(A :FʸI?k"{LgQ{:B0pbl*^+FLXX]bрcݓ !Q1`Muϸ @_C[UPq4ŲCBR/9xr(&qRf|'Pܴɕ]TҺǦ׈Y63K6X/)Ep忆n4 Ux=wx܄V2T.y#2o~eɼ|SOt'äYB%tY-ן#GПUdXpBz/bۇۭ0Ş`%dzWֺ^ T>U%eQ_}@xaVA2 Sݦ;\gP ny<6xbT+0s=V)|req>)\|$ 6s~`j<_}Fm)^?ۄ8xjDgހh1?d*`v6B3ᅱKM|+T3\PP]ж6À-p/,?%D{14CQ IqdabKᢑ]=yӢ!;#v؍U'sԑb%o]%b:6G/A[ UxleH9 a )TV8 A:ұ4$ٔey#y)2o IIDxZʴ%m\\t")Vy>< rRd^*O.' mi5ODؔ"_VNscVၐeP=uZȂ t.-dU=ڪ !Ww1tDLb6wq[Km% 螒kR٠v âT:sk\ϝ$Sń$>[ͭ?jRf{&ZG6&G877fL/j;߀ ,ὸud&{rBkKoD-p PLXuv909ώo53"vlGס#"=٠I'q`DQ)@vDz;GVioj AKP"ٌ茢&y) }&d==*ZfBSpܞy68MOdK'g~ o E-Jkfd-#6L{˓/BM4|!%,L,%VMX `&F!9uIJuEoU$d8e]:|_Q[STVID4/y\$g0u|~^8QAg=| y! `I%h/S܎:˳̡ X'*{l7@!$0е[//ڰ1 $0ч,Z`oYc2 ?Y0^Ex-e$h/̀O-lbi=xU0 ykzj) >kn6g70tg2 1D 7sנּ0A-Y )` vkMcuƗ}tW#G>/rPfv5Y!J 'eB]?]eEπ ĺvߴYym|ybo@k YZ}- b[7XL QO[2me`KH"AQR[íG xu|$CNsbNrL^kv_B9Ϲs 8Bp@Ke lJng $kxbՈ}{>T_Qrmu z?pO+%m( ##"" WS粬&1`[uPǭs2st&-&Z\ */ݤ">xlRgK ]7cY),%ע9qPTcl B((ym}ϝ<O)Tk'8u0ac2J6W7{8p#^Y{~m]ڙq1ְYc6yy кȷĎ6^6k8zxuI y{׎ZR5.)|lbݑ"4$9>bZRIz„"{W ~!Q.H+KNe|Δyh&uhrrm1'?H@7V0*%f*˄0T)FA5iܔ]$7em+͈ppW\~TX&;pzr ` r7H73mw%kFvpz{S|`X,îO#Վh~!#E23S/k͔#@"B$["w`p1ծp2B)r怞>kZ=-ɷoqT deeIɚ~jj#bZYAg#gqz +"3G4ue8S[͌Vΐ xe*[ Ơtv͢27RHh>ӗpDL~;=hRH603,bg+b_if,mtt )*^+宑(6jQQ"ѿg};LhVR=-G +и\Ю@UjC,7mU=! Tמ̱-Vg"#^paܦ_-Z ]z J'|vF&($?اXM"&Ag2nC,|{Rh\,ָ툤=>f)yi`nsc79bxgΓ&{:.i ^Ϋ?+ԛG۰oѰ}Y3`: .E d7If)m ZG<̌e{엉tS6<=_w^f6d8p;%kutmf6ZvANh/aDXUjMetR0-Ʈ pN:RDF'A6Bh-JI] #xNz${f 3谞m'9OFhy54t#Vd7*g 5>P60(E'm{I/tG{?#֤`-Tb?,YN)_K+hɲ[EwcUrǥ ZJ6&.Aij_CIo Nj.;]gCIWP{lw頣 y th&#DoewՙT!r=\̂rUEbihʐjUfj2r)-m>6e5Dq/ p$8~h3^ ӄi?vraX%eT_9H٠Vz;P=ePwCAooaH{8sPsi' Kڋt2<"b;CoQeP(R(QDW4`Tq7VDLM3A^5lX{69ӼxD= znD#o72kG}`ox[~9QJ8Dy-lfA-4!l3~=v%? d#q-1s!+sA'<#m^Wz쟄 5Ѣz'S 29\ :B}[-_$8AW'˅~d|q$gg;J =ZE Y=[⸭k1DQ9S,]z8zO¯2c2_xX-`p[NJP:TkO[u?;8T^N,>dYA0> \©^cgE"]t23 וyW=ҹv+e ` z'aЍIib'H8j.%kRʾSŃ[jV8ei+bvɀF3Ҷ|_ԶX( ~k^gI[ߓ1+7]-Y; endstream endobj 291 0 obj << /Type /FontDescriptor /FontName /WONXQY+LMMathItalic12-Regular /Flags 4 /FontBBox [-31 -250 1026 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 59 /XHeight 431 /CharSet (/C/D/H/K/L/Q/T/a/b/comma/d/e/f/g/gamma/greater/k/lambda/less/mu/p/r/slash/t/theta/u/v/x/y) /FontFile 290 0 R >> endobj 292 0 obj << /Length1 1828 /Length2 3825 /Length3 0 /Length 5653 >> stream %!PS-AdobeFont-1.0: LMMathItalic8-Regular 1.200 %%CreationDate: 16th September 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. 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Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMMathItalic8-Regular)readonly def /FamilyName(LMMathItalic8)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle -14.0362 def /UnderlinePosition -117 def /UnderlineThickness 36 def end readonly def /FontName /WAWKNV+LMMathItalic8-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 84 /T put dup 97 /a put dup 98 /b put dup 44 /comma put dup 105 /i put dup 222 /pi put dup 47 /slash put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp^h?qFg :*ۆ.ۈ`e&6{҇ J+9SC?+310r5,;2ۉ3 #,vgKf $5c@!;\]K*95tBY-ЃQ m6B֍QqWw3sd ͻog0\EB~$15 3gwf9`6Msk%e8cͧ\OA վ]ޱץ[Z΢KxsӋ={Wtـ#jsFv>,n_^?3qYf}>L^UKug 3oN&HR,dotw1+anP{Q6K¡#?WFZw ?\5%p9 U ϷynQ븧۹W5_UE-D~%go=okݘ1F3=)ہTMSd~ wҚzS}#XѮ'U4FU1 tWE.t_ƐFÒVqoPaOjQPԣpRI>s&{T!F#| J-IbPd7oY)RNGhQ+wB FuJot$^T66E 0FfJRvl{}c@Re-Hams"".WBAEqn:'-k[% r;=7mi8!\I[S;8`UJ,TsM7tYW!Nh.# cB{aa~pⱕ%oRV@0dƒaz|KK3M2 IN# Tx#4$Kv~eXeZа_atI357d78J'n5bdDtsHc9w\VsCݢ`{tAU֑;?5aâHE{$B [̸Yoy0\I31)*1g5 rfsR0WsK9H;|ykvi<5![0onyhoyi8[g<ȥ҈V;_G- Oq w!`<^e|X#|JtB`")h9cqEtV[^ϑ.'އ$X?hoК^Rkx,q(miq^@:}ʏPSBڄcK)| 8˔$ d܅p!Vb OWUڼ{urYҦa;H  dcKOG9bq{u~d ˲CBnr1D+"]3U="/PFZv:k BJP)?vEp]5s@%rDrJ|$̌ 8L;V  whL:.K5MH$-c4Tƪ3 yD|3HFt.®d![o Ο]z97.|>mjM>jEȕjT3UGu=U7 x=vJwD]xI/,X!MX̭8w-2eF.egX˱J>~3rqH~lE+qm.o-0y{~dp)p:j(. Wt4qX9+"_Z^ͳЛ4 u9'Rjmxy!p: x?qSM͖a&5% ῚdٖC|= qD6A-N'2I|qm>vs@6ҭůDCӹ#)? F5Yy!YH}z煈p*KjM)/3AQb-%SZWD] i;@$x}A`Xz"y`+~ 6mHX3f,17l7zpU?8Q=+5-#A7R%% H .$ٶu\q>8X̟;§:y$(h ~Ҽz.Ntw 'z5/eguMeIS)f(zS%X2As-Nfٹ=eX,> endobj 294 0 obj << /Length1 2351 /Length2 27911 /Length3 0 /Length 30262 >> stream %!PS-AdobeFont-1.0: LMRoman10-Regular 2.004 %%CreationDate: 7th October 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 806 194 0 %%EndComments FontDirectory/LMRoman10-Regular known{/LMRoman10-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.004)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMRoman10-Regular)readonly def /FamilyName(LMRoman10)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -146 def /UnderlineThickness 40 def end readonly def /FontName /JUREKA+LMRoman10-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 77 /M put dup 78 /N put dup 79 /O put dup 83 /S put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 58 /colon put dup 44 /comma put dup 100 /d put dup 101 /e put dup 102 /f put dup 129 /fi put dup 103 /g put dup 171 /guillemotleft put dup 187 /guillemotright put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 113 /q put dup 114 /r put dup 115 /s put dup 59 /semicolon put dup 47 /slash put dup 116 /t put dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-430 -290 1417 1127}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp?(:E(qU[s $gG '\ wMsuIC'93|Y@TۂEk$:mGzRg?x= w;*E JM8͛,uZmY `n.ˣ/J E: BO/g^Mj9Z6F脨0 BKBՈ[GOrEY86nXՔ*wFot8CF :g6}dPk]!$3h+ۆ^];JR*-uC4⚈u6Lj=!;͐`,7TZXV]w)ߧɍ)%NL߱VيӒI|5sBMedO&Ng$q&Y©Au(@HVqQy?>&_@GKf0Z E\$3eL :G(, f[M]ln uE~0Rt^S PjwWv6! 1nC22O՜QS tynG }=_nW?^‚2I=>]L-ͬIq^ ͘ EM ,|K93QbָZ׹pu P۫%Fj`(m->DI 3C6*ZrBYvc)7@#G `0ޣ/<6(.Fx@GۈZ<>VChY/>.((m`b[ Kh94BPA:@~ A)MN#dGa13q=c%fy5gYq-*cQ1sh֟KG.[׶dDk鼪;$Qk{Me|}2 ̳^;Nys?R=FykBSdl2įGeyeƲ?.{() {'}y=gN`}j0C&. rO\"6D෸*"qtAM6YI@$5F06pK"!y_ϵ;!.)3!9rBFpCO«;Q}9΍QľPwdlN{ aOI2{/=XH?~4JFLG ~bϽ pq:HCp3 2g\ܦ;vguzpR2 (vq6k+Տc&Euny:hCDUNv'Qz:BD;j ҙN%z&j^sI_GĚх/羯(l%|Dg&?L5#0$I0/ 1Pyԑ'TuHm9RHIlپCy W J ꫀ17ssdذC( !PeߌSv /u*1- b8 ruҺ`bi$1ӭýEq~FJ5-MUP;g I"W^T1w*oā;~X(/?8tlg ?n+QTiׯ>C2" FWGR7r]9ug6 j={Meaq?ևO'uT$7?//CΕnYO o Y2I`"jve-[NqWmZE7FY! lX*X?VE{ P( ~LKug,Q=̾9,ɬ &8 VoIq ˱՞,aKRK';k-] $& lp­olᎩ{WkDNu6G'TlW+.F`\uFǗ+Dϰ|+^uأiS`՛K;4F6%OM膻ɕ.i5 (NHBE;!P%҃y Ru˝oD~;?)ؒAkqd[`6~@wC?4aځa8ȸ7z6d"߇WLa+qz ЙibIҧƽcHn+dLyI.d;bѵx??w/Kt ]jm.&tjy@]=0hUS7Fbc ;xMQa((Dݾ)t&$8L ۿ;7=?ǿ^Tl^6Q껡Uk|ܧyf 9A F.(siѮ:}_5(85*(T7bI;vI4Jl ?f!*R*dڇ-xHw^f{u28vVohi:jC1LA1 ])\, P T?f6^2/"MP*)9rgUueSjKE1\[QC @#G'7^Ymc)6Tsnʿ}_&*'{lGy} O %bg>m(ң \='s 7ق 3sdP͛o QTƢ|uVlXA1 g>A%~m0 Rgq|:$N@#ysGr_"3z{=3ȶ?g, Q^;G2:z!~,lջ߇o9g y#<P b|מ[?{ج4ԶU1 V2nAcn8UPO@^w.r,"c+utT{(;uUB/xzFTMuDYwCxͩl"FRZW\ ǟeaJs PԶO5*tӃ11oO_"B(i(|pk _}sDNFG&[}OK$;ܜX*B=aSH?ER]q3Ҵ ?G9<- |%W%2{+c'%79͐lu rlM7|sċ3x5 f7Ï4eqJkyaj>W-ωB̆nVGkrTh [_?,v^@_VpWm' ;7*26Bn֔a\5Vhв5(3mI,Ojv5^pW3g1Hs"Hƴ߽Iw6 2,2o) j;uYl:rϢR J 5u Ô(#Ъ"Gs;۰K84pHΏ",K$FB[+`:ڮȋ<Ǵ0U>?,!wDܸΦ*}M-8py7ӻiB.k&OpkG0v&n㮄u*NG;nq+ӂ~IrԪae6@2;|2TxdfI!wi,R\\yְ$C©x{Σ)5"puHͿ}=kUQIA/|:*8L91E~YY8'K`.ZLÀ!+`)ꙃ%=7 lfu nHm98&6̹w]7"QXX֗HDĄfE[ @ѭH^x|Ї3`g4W/pI[^'K~ޞMD[:@,@vPPK̘56-2L {u9jaoLw\6iW;<j`O湢8ŒܻMg}Aq:i@W=_WFY h X d)Pw mo&UhJ~ܵxM[jPٸkgrʘʕi`"N?HU&ܗ5ƧKi;0wߩ nvXDLoMI}Rk/TQ՗S0@/|\zc0{6 sኝh0m伀 {nZ\ FE%#ΠAﳹiY8tY }m-MuU>\-rLiΟ w|&jb7D !3ɍ7a ~V -*ҲJvH KyKrJբiG;"`MPa?-<×sN%)Rɱ'o;bWU5WԼM Vidcu}ko&˱՞,aKRK'; R62b{\+OtAn2]?!r `L;ͭn$'2+AS1J2OLkjkﵱNon gMG^ Ɣ..Ba›8`p[MA2GA;_k+@{6NŖʑ@ΎIhD,] z[ll}wBh5v4ZBu.0O6y܀3Fx\|TYb}+`#L,wVdgNҁP;rs٘y)U2Z5c{e|nj;M~ܚ0412!{ϗGwn й1o*% iܼktc e9{e=0-ArN|R-!LDp\u}FR!JC\Pr ea+S\_F왃\9C1O<G$W|/$=2JY*sͽTc>Xƾua =m.󼂢9iy'@m˙dKCQ8d `i x( _q(!nQ>HYcGgwsZ,l# \ۥdKΡ&w?sD]LTn^C x* 5R(͛~|+(yƋ#Ж*K63zm ^vER= (;\]#fNO0&e-di8׺{\km+zɩ 4$4x~.L<Ӥ 옆誀A{7bfŅ{#kBy|OnH8,@ԃB ;XgpGiJ!,UÖMG.}&l4ȎR0ogkѠCݲ9k'H< !-uVVju 9oF 2d1E6nf5o|%hWm2}R<6`۴KKk&yR:*Ol9Y"AgMWiwy-^x&/en x-:YiZ4HyH  $HkvކyP(Z>;e@EzeV6_ʢM Sy*m֞gtw/iJoSiN.5z^NW":nQ$0S!]{suG~YEpqr)r4ŨSxM+ ~|0DIJK'p7v4Pپ0 j t NFb !TM#35[uZgjPkKcU-sFX:N*@bd9̦zz/G%3ud`۪r$L{;^ކvUSqWӖV5n"UhKVKiHQ,لbTWu@=^SQ׷p<5W]kxpK>z8ʃ .v$>A?EfܽU7µ6SrVŧBj9Tb2i-7LO'ݖS}kEAWQ89p],TS}mR3oA3: Xbys]6D:)}S?O~ݡ8RR}͏ӓ&5ҧdJv%w ?? 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Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 806 194 0 %%EndComments FontDirectory/LMRoman12-Regular known{/LMRoman12-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.004)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. 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Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMRoman8-Regular)readonly def /FamilyName(LMRoman8)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -117 def /UnderlineThickness 36 def end readonly def /FontName /EASNAP+LMRoman8-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 56 /eight put dup 52 /four put dup 49 /one put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 51 /three put dup 50 /two put dup 48 /zero put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-456 -292 1497 1125}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp^h?Y+A+caDT27x]3 I6;/vCY*2ȔnM"/֋SvtJOŇ%be)^ I5(/,P&+GCZ UYt1] [ yo 㒆߁sjMԕӥ)ڼ[GY/$M?,TW[%_I\Y䃱?5أsBC -iXT2HG׍7h(L7ֱmYTsd_ϗ@&X $\x$n> PRtk!HѸ/JY*_>T|8P 'p+#5(bW0ςnLL{][S{kWf0miYMA8bh*q·ehdJ|PNXˁ}CtTz_Jւ]ON(5? _$_s<ӸT;@l[Ig0h+T&%_ЁX@wё-88ͼ J Vh$ƋNAk$og& 'zubs3>Acz).Uz ^9&:;!\̱+Ykm$ ItYJ㬰Lr~""dsc;Ǒw #Ϸ1 yA1T>%<[ǯBC'Q2O/EX!{uyZB%I_Ttri+?<9<|sH}ȃ`l4BQa=WD_}yTڿ}OPN$Sus4RCW-zr[B$@3>>I qؙRw~stkHEjVFaI bF^(b[bfЉ|f `UY1:$58Kܠk']#s3;Y gHXds8P\`z ]FAX @N9̎ԙv!]ɮKN5AM\Fp}xy0 q҄hprYx}JuH5Г2kX>S8JXI8t! -i~u@ǹ a3pmZ}r:|FIΘxcK)k 4k_Mg }Ӻ2JQBn'W@=7[RTB? ,,`+7w;R**FX11ۄ7WacKu6/ܛWO=5$ٽY,⛅,0Q> m5S(-"oEZ™x  |Ũp缕i 'rJI(oj='è2%x3_B&T'y)ֻ$?pHۏ<\V9-Cn&'TFovKpҼcK?ȁl^f>A0Jb[1  k< gKg~Qm.x8J'jnim?Gj0u,eOmX2{NMFO^ kv G7&ڗq PQn?At>"o?p,%E8@%qܕC3b Z<{X [9צcv&ycb yrzL˴'d-yo4At{5EC ٔ?)OJpe.!]r ,`h:ү,o|BuP >'OzҜTiNےpx@/"e8s :4?kSƌtK%<FHw"pɐFބ<6@s>r` ˉ*::jji'8͊kh_qbbWpQk?rf2wj>)-$ެ!l'CwRB܃x3*\!'R[fg ~WiP9{P艉&GhʇA@LtWa*!C*T%WR[`-1,ԍiuWK+SQd9Z`7e>R^IowfJҍR`OѸ}P&pEUgVZ#1&\ 9Oڨ=/^^t(}v/ Go(b66}? mp G g6m3*箖wh 9l01r2(!-H?< gĨbLTC,=l`qR8J=ɓPKDy dF j93N W @ mp A.we+՞,VB; F\U` ,eY;9MX#ꔗBYA:hg<-%`4v<a$]1f L:DD2(WHC`b bgx#R^U9= .*Z6#k3[#;)sLXpV, MDS34?i-M/]ST.}Eyɵ.mY^~TeRUՄA rqz\#IO< ]IVWJ7(Zb/ OX[V軕e]Y l=m9 Njn΄? .B CC8OVaꖿ O>v l"I WH\9{.H VH p.b R.}`=b{Vq 8|E J"xXm\c<8z][YU@2kq9V1m켭v6 =.C GJ dˉ;:Cv݌E4r&dU)F#DCawD Ԡ~Ҝ} 5~sŜGdjO k |f3~ڙ!}f=EC:'xy̽PF@[vipmf2@øܯPs\8@NjvSz+7'Q%'ґ6ie^쾀0zơinNJt" "VPP4x#Y /O,S'ϢKG%:c}"(ra3r?uvc|:_!~c0Șnxc۸^b͈Zez7Fa$NSVe?i5GQ3aJ3g(|#@1ITF+9v,?*NP1rrveYaMBE%zq2k`DR5g؞j*΃n*RPvZKIDmP&]nrն6"sA 6f֐; Sf2f SqQU¹M YqFV܀VI|wܠ?ͅ OMg4:^zS/堎]En"իgw~(oGϗԻKs9}s[/v4?@<(TɕSBSI̘\FG6a5 zU&L*+WZ OF$.GQ/\gw3:i]Zi[^+//]?᷹&ahFOWc_,M]_2Wwצt_re }qj3܉."- /&(d.@~]XO۬_X"an%AQy#'j(0\Wz=܀䆎b S:ɧ>"~Z@Kx>HwY50cʸi'?_+$YnB6Q\K'.vqW/Re.lܣ%!b6$&=TLp놿`h= ؟rvCK_Ș&FAy:% 0ǓBJBUUrbj :Hk;$.uD O <:s$NKV@J7=Yιƽ/cqf^ظnѴcFhL%*N}%+ 5Zׇ3uZ@:5itBd"56>>\X|aXF6n1`IBԧ݃OC9vjq?|(\z0:(Y$ Oivc`a[LC/NU>5x5lI1\ُi8j&g1"1#D%ZzD| )&t+}} 16C.gcC[jj7!~: ς dӇD)k qwE:8Y (DЋ?dkJL3OO]-|:"d:8eA77Sji+f&fE4k䰄D#ԟjȔ!ǂ[nj``__0 zˇ4@d?I\~XQ+!S$1(n6VO`hǥBI?<:n*[E#^W$Lk^B8sp>ʰ귡*#a9$DZ <th:5/< (_¬r^zqt5BLl籔)bh0׈5TUKe3V*@B qxly`% 8ٱ<Ҥ\ѩtq >r-+>C<.B|PPۻu ( A>'NࠜXx_-lz]\  UY)#mZ5ETk8? 15<ۜO;,&F-wu3e9ךW߽G {I/w[醈R?$g3Ud?VaM(ګSE1;,z80oZ^{t!HB\8\3rEs&2aIں-eį&*@~n1z Ap~_n[낕p[AJ~nإ! 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Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 806 194 0 %%EndComments FontDirectory/LMRoman12-Italic known{/LMRoman12-Italic findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.004)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. 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[[P2Ox%nܷ`(Ps⊗ISxN@I} N%ߑ;npscdjpGseqL?^A Fn P7r(Ro= ((fٞ TEx\c?"+/ N}7r8v7ȱ7p`L(82㊲:135dnc)+"#+|'6a5XyNeC/ ɚޭv ~\#<&H#Ë)MjC>-kŋdп:Kpm{6Cij% y~l#[b]˵[0 a >G Z.(ݞK:LlwM 2C2Q/ %KanG3G+M.H}E,z:Ob DdVV>#>,{Yb=yuPDoI9F9 4r{S)4I;7]krdylni锐*LB[v+wY))mXĝ$f+=wh;v${q,?DbPsVЩa{ ]c ̤sZ/{ڭٷ4[&B&&EB B#t7ltۀG7b}8ro*[nK0 21-&i}H<#*`$-mL]A9ʞ鶹\ Ru{LыXWY$t*? %'CJz V^3xy PJ?p ױin~60Ū3ޟr.ɺ+PĵكORxf aV-)nAȻ`2E%3"|!iQd?&O|ء Dn-ijB1 ۘ#m=D ({Ė֪֝P T5ųERr],:W-^7c)['Ň&'r*  j9HudW{Z$dG`Jfm'rKK;쟥D.Шrh;5e&%8f,}uH[7lz QᎆIeHaI$b>ޔAF⇓ރuyʼn:ʕS*8iɶg1ǟ^ʹu(?&$疒޳2ya L=jr嬲fL NJbo[R%c-#~meC;W1 o9gҜ3 TUlB,ܜ s*E!Z͆}b. VFkߜʑ+᫗& 9 NlQ*\gr[Me)űFFLvvc [r: kElVg@00ϐ67dfX}jfJw)*g>0L1̢]Iz5 LvWѸYi TZ ٢Ip.ogMLJV#\R2I"S8cFwB6X]c/'gi9lfϏPxѷ1y2$[BQS e)F3(we2Z6-Wh(bF>םmF&h-[E'pThfU~*sd/BV  PFr\Nֈd{xvf.~sF^5@jQLtHlٯ]O}u,0œ`̪6TvWeu2s+"v_/(SUF^6x:co7u!m<0OXsn(IӆIFf[HYPsp bk !ɆRPݟ8 ;>zK2{5ǩœo:ʦ D86wڌ]n>d$W6F;UD4&bPb!q(q RbP/bש :ϳ8 I& qeq6kc\#-.=QT5Zhl}GȣX<1`z`KDpaXD7073z. dt`ɴWT闤|]ƫ HqI$aZjZ@7|߅ ) SI- vgP)XB&'γ-0HxVY+ U$[gu|4@9QIQ:H qpX>0(!Э> endobj 304 0 obj << /Length1 2003 /Length2 3567 /Length3 0 /Length 5570 >> stream %!PS-AdobeFont-1.0: LMMathSymbols10-Regular 1.200 %%CreationDate: 16th September 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 694 194 0 %%EndComments FontDirectory/LMMathSymbols10-Regular known{/LMMathSymbols10-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.003)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMMathSymbols10-Regular)readonly def /FamilyName(LMMathSymbols10)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle -14.0362 def /UnderlinePosition -146 def /UnderlineThickness 40 def end readonly def /FontName /PJVCAM+LMMathSymbols10-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 198 /arrowdblright put dup 190 /arrowright put dup 123 /braceleft put dup 125 /braceright put dup 207 /element put dup 175 /greaterequal put dup 206 /infinity put dup 174 /lessequal put dup 173 /minus put dup 211 /negationslash put dup 166 /openbullet put dup 183 /periodcentered put dup 177 /plusminus put dup 239 /radical put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp[Kk‹5⩫ ?RRӀTw%jP `O`\ "vTn7B$EM9*V+\2k}SypHYa-yG03wYsv"xu"%Ԅ;+r?6_դeP\ ה ř]rb!~~mW(K=mX Pg$B%݃j[)3]d'l.)}boo4s Ʌm#-{93hfKHܪ.j 4.%wYti>!:LS>tWEo/ٵAKlq,s9'$ ~Kmzqz =N Buj-K*Ŕs(rU%6!+5l%--f-k],?TޚTZE QH0p`}6'"RltPvuT.VjRY_Kf3h҃Pڪ;d0_1ɓ/0O-QcE:cMU >~ F@nf#6~T?&ߩ9eCx'>H n}Q-IpQ'6y񬌯u | }M1ה %zhkj {~jd*D:=XC ;|PO[,8y*-!Da!KO:6-XBزJ0fb>mZC;f'ZឃΦ 'Tu"+\06c6I9mVĉ_A쐆.7>uȡ0 ?h<0KUЛ6y[8&qp4>Lҏ>ܷm9*!{ 2b#Eig 0c=w @#6g[ SSpwrL^tH,r G]\mc<۷"k $8UJn$傷]:tﱱj3',p#clK,+-, O,$O52Y%H"``/X'Vi!l@iU5a>BKCOeC/oI+9ΞbQL}䊻׽:&~ dZ`ʺey+BbF?_bߒψѱuHgݟ`@R}$B%&Pl6:zF?[(lؽؔ2 / ?Jx qFWj-9K  |,oM< sPɠHcTæL <^XήD4 pN)v;AR>p' (B4P h>b-4?>2.o%Пj.W;+\4},D}1?pt +/י>e2CF(L:'dgܡ@0ϨAR7`$8m + \ ]og$W*֣~LåmU j&Ϗtzt8ꁹd~󉺓.c'Kl2kˣKo|rd<)Y9ͷ䪱?n/ cHЯwS5=(@XL bVJp7 Mmبۘ\EusR.}!GIvSH'(*0tL4~9p쐨Jp~77=\JrzŲŁFq%<7ۢe oX82/ jj ƆTKnUw30ALH4\M6Um$Uzt uӖF[BFp6{|@|74@U/ȋdDٯIqlRE g&u&!PIQ,8k̑ ߱҄m|)Azؑ-Z]"3߸. uĐ"Z\&IMltJʇɅ{eP{A%Dd3:sZVr"5c'BFڇc -{2=Ǥ2at.}-q< fr|~kl>S32ۀ1 SVUR-`>ܘͲ檢D:1!Ww<8.r b3s/FӬy m*%Y1F TClV0t/%l0`llv5_]/3Vn bERH`>V"a)| /՞Abas<] endstream endobj 305 0 obj << /Type /FontDescriptor /FontName /PJVCAM+LMMathSymbols10-Regular /Flags 4 /FontBBox [-29 -960 1116 775] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 40 /XHeight 431 /CharSet (/arrowdblright/arrowright/braceleft/braceright/element/greaterequal/infinity/lessequal/minus/negationslash/openbullet/periodcentered/plusminus/radical) /FontFile 304 0 R >> endobj 306 0 obj << /Length1 1771 /Length2 2114 /Length3 0 /Length 3885 >> stream %!PS-AdobeFont-1.0: LMMathSymbols8-Regular 1.200 %%CreationDate: 16th September 2009 % Generated by MetaType1 (a MetaPost-based engine) % Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS). % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG. % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki % from GUST (http://www.gust.org.pl). % This work is released under the GUST Font License. % For the most recent version of this license see % This work has the LPPL maintenance status `maintained'. % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. % This work consists of the files listed in the MANIFEST-Latin-Modern.txt file. % ADL: 556 156 0 %%EndComments FontDirectory/LMMathSymbols8-Regular known{/LMMathSymbols8-Regular findfont dup/UniqueID known{dup /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 17 dict begin /FontInfo 9 dict dup begin /version(2.003)readonly def /Notice(Copyright 2003--2009 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def /FullName(LMMathSymbols8-Regular)readonly def /FamilyName(LMMathSymbols8)readonly def /Weight(Normal)readonly def /isFixedPitch false def /ItalicAngle -14.0362 def /UnderlinePosition -117 def /UnderlineThickness 36 def end readonly def /FontName /ZKRXWE+LMMathSymbols8-Regular def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 156 /asteriskmath put dup 207 /element put dup 173 /minus put dup 205 /prime put dup 239 /radical put readonly def /PaintType 0 def /FontType 1 def /StrokeWidth 0 def /FontMatrix[0.001 0 0 0.001 0 0]readonly def %/UniqueID 0 def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec oc;j~EЪ%9.>XJٚмD"e?&oLH:]~nX%l޹dQ@a~M~EA˟V.UM؀")JY4қ UC92"\ܡw1rlxнtaA*`Jp[Kk‹5⩫ ?RRӀTw%jP `O`\ "vTn7B$EM9*V+\2k}SypHYa-yG05uu`Y`'$Ą Ub*-l=&v,TI]aCm6#:\6`XA* v&,6oV&k`~ y+f⨜mI q8KZ &Ê,~ l0k7߰)~᫺e$|-x$fKHrktAUA[SiQ:m1ڱN&%3XA 8QZDj&8T/=gdfPxXy |fI,M߄. @ )$9vg޽ȭ2)QOvk6mGCUV}PjB$ 3 QPX-tיb*t:?d&g+ȌyFISm)2*_/>PtՓp!X6c=lfm,d 3~L&"TSF冰Lzb]>N^1 :f/-! gv 8Ÿ m I;#.*Ǐe xu+d )*qj gBD diGj\-Wu҃ybgs ZF I܇~sht`G.G&ܤU@fdr{]v;+oN+9)V5DK2'Ř&"tʻT3%~O{,%\ڬ9 ri{|bb@YDs$9ADZn)̨Xڪ_܏B{T}Bl&isA@b۽Avסs I_$M 987]ؓ|#q)$G'[}u ̌%[q^PeЯM4;8CvgIVş#~d !8Ah!ta$V};itE gkEzT[Τb@KwX| b:m;UgoLQ qb:iIa4ă>B4^ endstream endobj 307 0 obj << /Type /FontDescriptor /FontName /ZKRXWE+LMMathSymbols8-Regular /Flags 4 /FontBBox [-30 -955 1185 779] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 46 /XHeight 431 /CharSet (/asteriskmath/element/minus/prime/radical) /FontFile 306 0 R >> endobj 308 0 obj << /Length1 1306 /Length2 1345 /Length3 0 /Length 2651 >> stream %!PS-AdobeFont-1.0: MSBM10 003.002 %%Title: MSBM10 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name MSBM10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup /UniqueID get 5031982 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /QDTWCG+MSBM10 def /FontBBox {-55 -420 2343 920 }readonly def /PaintType 0 def /FontInfo 7 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name MSBM10.) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def currentdict end currentfile eexec oc;jAw-24 WEvQC<3A2kX0k^|:ٴfb,|=sLu2KZ`3ndgRw@),q՜G<&h'. ΍883 ABAԾI$s@F25ڪ,i pK>6K` %E((bsS=GquӁqb٤YJ NN=>3qk'4Xj̴\4 G`v׎Co.kC1bhF,+.5P.F2E"R ޢ f PZcc*w6Y_P-~|y,Bk[R4kg0<Ayy4}pge*f\Y3]@m;s{~悈."Tk/}DJU2WG3KUa>u0»[ykT 8~qK.mdL<*͛L}>@!vR.l}#q82U]*P{aS(TGp|G^ǟEh"\S>{xiR(8KTW!Ԫ瓫ڂ}MܵptR+^OEo͖i jY r["Nh,KC"m` \338t5(;LrS Ua{Pjx$ǔ(mR ֖ alC_-cI#g6R2ѷE09Vm4w%{-Oֆ@ѷoBJG5 rgH(ütiJ&lR:UF,/SĈfՁ: P8A9ӨVq5;ӜΒzAuuw$A^Y M/ ^v" endstream endobj 309 0 obj << /Type /FontDescriptor /FontName /QDTWCG+MSBM10 /Flags 4 /FontBBox [-55 -420 2343 920] /Ascent 464 /CapHeight 689 /Descent 0 /ItalicAngle 0 /StemV 40 /XHeight 463 /CharSet (/R) /FontFile 308 0 R >> endobj 310 0 obj << /Length1 1608 /Length2 10102 /Length3 0 /Length 11710 >> stream %!PS-AdobeFont-1.0: NimbusSanL-Bold 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Sans L Bold) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Bold) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -155 def /UnderlineThickness 69 def end readonly def /FontName /JDTXVX+NimbusSanL-Bold def /PaintType 0 def /WMode 0 def /FontBBox {-173 -307 1003 949} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec oc;jtD[1ƅpTo9`.:ypJ*l'e}#)&7+/^ W{LZ60VQR^λ3r)#v$p~c&'ſ+ %;a~!ty`rcw-:!c.$ $A@h]=3ߊc~CJ2]u, \wSBΤ4b/7!?gam%5GڄWbH\;i[ %= (0|/jm댺L6Y?ȺIB/FB@2gٟ#YX\3y=aGupcA Zwؔ;sk~e[3xޘK :ׂ/E`ҥ1n|11QҬb⒟ ݱ~:4B8BμKNʇiC-"@2HmEnG0Įlu&- B{ XC9Œ|}!ƻx6q)z/SWݥ~< OfiΛa@TvnOY_Ӭa;Bmr, ')DrזH^ nL6вNC96pfgm:0l"1i*/ QE}wBַi94#ND Si dU@-0^@K ُ4ou- Jֻ6KOt5Re̶ۮ&bmUd_*92UEkx:.8;#Ⱦx @ab@܋ずnY#J&@6{F~WAj:IjϬI-?! 2R7 sQ`Nrz"n?nrjJ0O+) zYF$/ɹ9UTɃk'yVk!ϭhCdqWO-gR9T#}VKDz=qY[ؠ-kD Ed8i>|(\iXؚJ 0 ַ;p=11!̃OűNSfx@n,<)n5Fp0`!w˄x.ybS[o5tHreK6br=inP(nxZUqk/ lYt|aN(e>voTzLу$UqVRxrm|V $)z4GZ$ihBP.pLRE퇴׸Wqӓ²\jJ_U0e=e[)U4ҵ G\bp/28\@().P]nW0WBքųD[0لi֙'Z#:#̺SGwnrqa}hMoM 5\p8 "R'Yњ erBQs9w#T5!,'OP؏`ĆgWPtX((~+cN2ywtgl2m7 1Bx%Xn{Pi)ņM 'B PHpJ->O3& f"v*++S#M4~Z]?koIyǾ]m[}В-?;"1 ']$ʼnRN "b%L)žUmO ZĐ;}' Ucq]Vf_r$׫?x4Z*7T> _x4!YD;ZbFwԝ,}#0_GHs' ̈́>5o/ByH5ZjY :"7Nm? $%l݀s6hI6p5ʘPUX0\GFkg,<;6U0m\Bɇ&'r* M:aKF]@с] 74>Ike.h)P vfgBݠw3>:h4q]VJ4R~hXeQY)?94$";O0+OMsGg61$98ni3OE ٯֿ8qquC2f`Q"@Nr$k}L3M>W"%4*\ ۇ7qq'eu:v 8 ]^&Wő-Fq-gIVJ>5؆ٵ:ӫ<[@ /~gyච6"6wM(ڀm#6Nt\BAN~&/#{1<=p)m~8aeTpc\'jbIלh3pvt4c,^r57o84^]9w^M&n=Goܫb=1EYFD)qc]bïLDҗUCǻxTwg=`b x*Mq% }pd3AF9t.N&6x?X^9?~@Tj P !0 cMilioR^ʗ7 5c7 ޯyɿ᳧` o+{ۧ!]Rcv$zyχs5S*eS"/3Ӌ$yFê lpJ,V"d^H0d-,ޭS'Xcʾ$w.&XQGu3e-aYր* .xEb7u5;?`ٓdMH& "ycsēe,O7K\SR]X W]0x8uaph ׯTz˝77%Wx©L.yutW|o5 :s@馏dϛNVr?Mp(RC@0SREv&.SJX>..kt Oz:ܝ2C~S$kSyY\jL,;_k-E :RnoC)m53bUIrgX)4A+m=rNoPjbJLБ EH,HV;cٰ x!86NI6nYn_ü,\4!gǠ}(_e8)pSgQ~'Eۋ+y@|3/7 ΑdIn}yrCnPOCjȹ}h>qN |C(R1E AzmL2M/Ex:=x@ֶK:FsyctS='5}$B1N*z8+18pP HLnQHU^Am&cԅXc.^yNe0'Ԁ礐;vS=;Q_6B7VY%;ٟ3#xmYh[Y^0eO[A_br*{,hD;] JRMD/,Cl@A0x|M=2CEO'kCހtp(o3Bh6fCmTrČYNkC|, ۏ7(u!0/&ь'Vd,CZ4YTMl?![6"w Hwe[4KsK,Iվ?N%#Q񟔨RwKg]a񀝚r50]v>H?~&mq%Z/@Nnx 38k2#.q TI'^u' B!M@_9zH8N i)P4 ZCЊW@ОuϪhU$dEK.+,%N .hW{RB+hzK-'b3 [yua A3 DXBmd!23Hs_[qd3 ZDnD%h<xֱ.6`lGV$2? f vWUY9OZ;RzG)w_ug+%?e5_jT=5\HbӛOv;r_59YfOFiݴL]a:DArLN%x޽p2}U8Kk5vJ>C];cMݱr{ wDAD"MMZc )/ 6p̥O.gUvu[)VJ"A3j&1}>V t7@N+AUԝ3S}ޱ:yS.^IyϜ=_`ro;lٷ ޻ s4#u89><2|2~TF.qb]ڼӊy5(Iƃ6?ZY\{Y$Lb&S2(L;hGi 5pc^GZD3"~j}.>6}buXxF|gXo癳ruum$VCLWfZ7[@1}''{^i)yKݻl~]Tx 0,0^nR -UE28br 8_r:2aޜ /r@yQ)l!`~r_b(2RJ+ȋN[ܼX (Uk{QM!qT]#ḵI7iYjjs8ߐq 7`wPѿ'Yf&R@u2J1,\^Ee,4fIּ94)79:x#p,+ +eD-7}78k6k7JSLR^ju#&>DѧP*p v{}Y.qo&^v7lzʙCpDՓI|_]50ތfߥ Đ~ƝouH*%nDGDۭ5#g4=,](aV9/iYTqD43H?^: %Oehu;he !~@W3-q1~Ϣuv2 ͅ+D"H~B䄴h#7IX#ÿQvIGQ<)j'A|[o'er}q(|R^GL҆Yp'؂)IA,̽־GwmLs?G1g,;D`V(K3w//w"E-&p-J$!6s1>~E 8# @/ p}фfu0?*gpY[nHpgw0 B0O]J?o]a{ AB Աut>!仾cd  #vrׂG0Q">EBs]'vBnt0KȄQ p%MyV1OawV"_VoF;<[UQ@%/ BU;+DeC+$@Q _ T4\A.\b"nb$޳m Ue+5QsXԮq\3L0i~1עJa-$O4ѫLt c{cx$&d+ڊ60/?`iOןTE=?<\5} 9CXģHF9T ̉1*r)?a XMD.S rIw{.D+䴇a+s+ёI+Ѣ>A&I&3;պTMb, NwxկDgT4FvH4#B o]Ŀk?c=yF7kX26G4ݖaUFڼscl cRIFXe{A1- YP ,q1LuAUk*4kf6T #5G|HߝT j$ѡKrs9ʄ^diԂ=0KS+YB. tz%ɌRvlpP@<z}Py(UFɡ6jP5﮵E—P+pQ34͇ M^ tLUp[qɐ":oE೉:6.ٲT.>6#%8W6#&׳-5(߷ȫ*ݸd/1H].ͳ<Ӥ + 8-@b|RAJj ѝ'nC8Q/fW>.%"QhB͝1|P#_ws&AZWL,z=k%~>' [3y ڕYB->_i,HқobP'b!\fGXdd(-t0 Ffla`8*h`V|; SP)[>۪Oaȕ6ٝ"PԱ< |Z !qSHoH]WtOnkՄZM[:Xp?1ejzޚ6`4t[u΋XsL^= XxRX%]h X[yl3{P&vM^3q (p}&z&YN_&~X. !kI20zv C\&O'_GN:}YYq2oܿ~}:px3 %Ö ^a0N[B }U [T4k'&Is6!Jeuzyr endstream endobj 311 0 obj << /Type /FontDescriptor /FontName /JDTXVX+NimbusSanL-Bold /Flags 4 /FontBBox [-173 -307 1003 949] /Ascent 722 /CapHeight 722 /Descent -217 /ItalicAngle 0 /StemV 141 /XHeight 532 /CharSet (/A/C/E/H/M/N/O/P/Q/R/T/a/b/c/colon/comma/d/e/eight/endash/f/fi/five/four/g/h/hyphen/i/k/l/m/n/nine/numbersign/o/one/p/parenleft/parenright/period/q/r/s/t/three/two/u/v/w/x/y/zero) /FontFile 310 0 R >> endobj 312 0 obj << /Length1 1144 /Length2 1721 /Length3 0 /Length 2865 >> stream %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /DVXUUP+NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & Development) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec oc;jAw-36Uu4 l.Nk48DPh>[7ɰ9..CSoZqO O)9OHl~Q:ɾD0j J'JZ `B 5ԆG tbY7:Ϳ2hK@,'/ *  ρ5Lm;cբĽ( 8-An`bw"z#uLG2׽ofg]Vm]vC¾K\Qov=o|IS_6G4j9A<`iS^^&,P{69oL(HGNnִLiB-Mylb̞u1S8' n[$uè&\r<[R&d+"B=0Rl'Wd۠HGSވTg  'N4>6lW% =*?Kv3`Jzb=NNV'߾um>p, Sn@*gh6l?&L_ϖ`g=/yZ^Aj| A>2AuBY:Bg7R,"1˸?8 Zw.05yzwz9jQl=.Nܰ5yjHr: !+gϏy dF@<ipAb )*$pWV:;$= [YY ^#_XTzO@kmQԯ/;(]3&WM.hM'_9ΝQqP:P CY  yɗbOfu[pҢ#́(3"Y:í>"]ʲe濳܏;Hݝ1&4#M^ .^;JgB n{Aǝ] ZF8U G[5Bk!DO"Ed=cҹB]XBTxF_yoq>wa0?X赑@Vg0.ϲJ{R5#oV)CgM !~;].gP[O[ <ydvLODa!蝕=>j9FOoI,2Sb70 Std8JEX@XdtOҟ-gY*-g66(Hw@*>LZV G3h'vA>7@IhK;5-޳ln?P> `5ck endstream endobj 313 0 obj << /Type /FontDescriptor /FontName /DVXUUP+NimbusSanL-Regu /Flags 4 /FontBBox [-174 -285 1001 953] /Ascent 712 /CapHeight 712 /Descent -213 /ItalicAngle 0 /StemV 85 /XHeight 523 /CharSet (/d/e/t) /FontFile 312 0 R >> endobj 260 0 obj << /Type /Encoding /Differences [2/fi 35/numbersign 40/parenleft/parenright 44/comma/hyphen/period 48/zero/one/two/three/four/five 56/eight/nine/colon 65/A 67/C 69/E 72/H 77/M/N/O/P/Q/R 84/T 97/a/b/c/d/e/f/g/h/i 107/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y 150/endash] >> endobj 277 0 obj << /Type /Encoding /Differences [19/guillemotleft/guillemotright/endash 27/ff/fi/fl/ffi 33/exclam 35/numbersign 39/quoteright/parenleft/parenright 44/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/K/L/M/N/O/P 82/R/S/T/U 87/W 89/Y 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 229/aring] >> endobj 264 0 obj << /Type /Encoding /Differences [16/parenleftBig/parenrightBig/parenleftbigg/parenrightbigg 32/parenleftBigg/parenrightBigg 48/parenlefttp/parenrighttp 64/parenleftbt/parenrightbt/parenleftex/parenrightex 90/integraldisplay 104/bracketleftBig/bracketrightBig 113/radicalBig] >> endobj 269 0 obj << /Type /Encoding /Differences [13/gamma 18/theta 21/lambda/mu 25/pi 59/comma/less/slash/greater 67/C/D 72/H 75/K/L 81/Q 84/T 97/a/b 100/d/e/f/g 105/i 107/k 112/p 114/r 116/t/u/v 120/x/y] >> endobj 267 0 obj << /Type /Encoding /Differences [0/minus/periodcentered 3/asteriskmath 6/plusminus 14/openbullet 20/lessequal/greaterequal 33/arrowright 41/arrowdblright 48/prime/infinity/element 54/negationslash 102/braceleft/braceright 112/radical] >> endobj 262 0 obj << /Type /Encoding /Differences [40/parenleft/parenright 43/plus 48/zero/one/two/three/four 54/six/seven/eight 59/semicolon 61/equal 65/A 73/I/J 87/W 91/bracketleft 93/bracketright 95/dotaccent 97/a 99/c 105/i 108/l/m/n/o 115/s 118/v/w/x 122/z] >> endobj 274 0 obj << /Type /Encoding /Differences [42/asteriskmath 136/bullet] >> endobj 314 0 obj << /Length 1966 >> stream %!PS-Adobe-3.0 Resource-CMap %%DocumentNeededResources: ProcSet (CIDInit) %%IncludeResource: ProcSet (CIDInit) %%BeginResource: CMap (TeX-ec-lmr10-lm-ec-0) %%Title: (TeX-ec-lmr10-lm-ec-0 TeX ec-lmr10-lm-ec 0) %%Version: 1.000 %%EndComments /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo << /Registry (TeX) /Ordering (ec-lmr10-lm-ec) /Supplement 0 >> def /CMapName /TeX-ec-lmr10-lm-ec-0 def /CMapType 2 def 1 begincodespacerange <00> endcodespacerange 11 beginbfrange <0E> <0F> <2039> <10> <12> <201C> <15> <16> <2013> <21> <26> <0021> <28> <5F> <0028> <61> <7E> <0061> <98> <99> <0178> <00C0> <00D8> <00E0> <00F8> endbfrange 94 beginbfchar <00> <0060> <01> <00B4> <02> <02C6> <03> <02DC> <04> <00A8> <05> <02DD> <06> <02DA> <07> <02C7> <08> <02D8> <09> <00AF> <0A> <02D9> <0B> <00B8> <0C> <02DB> <0D> <201A> 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297 0 R /FirstChar 19 /LastChar 229 /Widths 278 0 R /Encoding 277 0 R /ToUnicode 315 0 R >> endobj 316 0 obj << /Length 1971 >> stream %!PS-Adobe-3.0 Resource-CMap %%DocumentNeededResources: ProcSet (CIDInit) %%IncludeResource: ProcSet (CIDInit) %%BeginResource: CMap (TeX-ec-lmri12-lm-ec-0) %%Title: (TeX-ec-lmri12-lm-ec-0 TeX ec-lmri12-lm-ec 0) %%Version: 1.000 %%EndComments /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo << /Registry (TeX) /Ordering (ec-lmri12-lm-ec) /Supplement 0 >> def /CMapName /TeX-ec-lmri12-lm-ec-0 def /CMapType 2 def 1 begincodespacerange <00> endcodespacerange 11 beginbfrange <0E> <0F> <2039> <10> <12> <201C> <15> <16> <2013> <21> <26> <0021> <28> <5F> <0028> <61> <7E> <0061> <98> <99> <0178> <00C0> <00D8> <00E0> <00F8> endbfrange 94 beginbfchar <00> <0060> <01> <00B4> <02> <02C6> <03> <02DC> <04> <00A8> <05> <02DD> <06> <02DA> <07> <02C7> <08> <02D8> <09> <00AF> <0A> <02D9> <0B> <00B8> <0C> <02DB> <0D> <201A> <13> <00AB> <14> <00BB> 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