(IME-UERJ)Calculo Diferencial e Integral

of 438/438
  • date post

    26-Nov-2015
  • Category

    Documents

  • view

    25
  • download

    4

Embed Size (px)

Transcript of (IME-UERJ)Calculo Diferencial e Integral

  • !"

  • i"Por favor, poderia me dizer que caminho devo seguir agora?Isso depende bastante de at onde voc quer chegar."Lewis Carrol - Alice no Pas das Maravilhas

    Atravs dos sculos a Matemtica tem sido a mais poderosa e efetiva ferra-menta para a compreenso das leis que regem a Natureza e o Universo.Os tpicos introdutrios que apresentamos neste livro originaram-se, inicial-mente, dos problemas prticos que surgiram no dia a dia e que continuaramimpulsionados pela curiosidade humana de entender e explicar os fennemosque regem a natureza.Historicamente, o Clculo Diferencial e Integral de uma varivel estuda dois ti-pos de problemas: os associados noo de derivada, antigamente chamadosde tangncias e os problemas de integrao, antigamente chamados de qua-draturas. Os relativos derivao envolvem variaes ou mudanas, comopor exemplo, a extenso de uma epidemia, os comportamentos econmicosou a propagao de poluentes na atmosfera, dentre outros. Como exemplosde problemas relacionados integrao destacam-se o clculo da reas de re-gies delimitadas por curvas, do volume de slidos e do trabalho realizadopor uma partcula.Grande parte do Clculo Diferencial e Integral foi desenvolvida no sculo XVI-II por Isaac Newton para estudar problemas de Fsica e Astronomia. Aproxi-madamente na mesma poca, Gottfried Wilhelm Leibniz, independentementede Newton, tambm desenvolveu considervel parte do assunto. Devemos aNewton e Leibniz o estabelecimento da estreita relao entre derivada e inte-gral por meio de um teorema fundamental. As notaes sugeridas por Leibnizso as universalmente usadas.O principal objetivo do livro foi apresentar os primeiros passos do Clculo Di-ferencial e Integral de uma varivel com simplicidade, atravs de exemplos,mas sem descuidar do aspecto formal da disciplina, dando nfase interpre-tao geomtrica e intuitiva dos contedos.O livro inclui a maioria da teoria bsica, assim como exemplos aplicados eproblemas. As provas muito tcnicas ou os teoremas mais sofisticados queno foram provados no apndice, foram ilustrados atravs de exemplos, apli-caes e indicaes bibliogrficas adequadas e esto incluidos como refernciaou leitura adicional para os leitores interessados.Os conceitos centrais do Clculo Diferencial e Integral de uma varivel so re-lativamente profundos e no se espera que possam ser assimilados de uma s

  • ii

    vez. Neste nvel, o importante que o leitor desenvolva a habilidade de calcu-lar e adquira a compreenso intuitiva dos problemas. As expresses do tipo "facil ver"ou semelhantes, que aparecem no texto, no devem ser encaradas deforma literal e tem o propsito de dar um aviso ao leitor de que naquele lugara apresentao resumida e os detalhes, perfeitamente acessveis, devero serpreenchidos.Esperamos que o livro permita ao leitor um acesso rpido e agradvel ao Cl-culo Diferencial e Integral de uma varivel.No podemos deixar de recomendar aos alunos a utilizao, criteriosa, dossoftwares de Clculo existente no mercado, pois eles so um complemento tilao aprendizado da disciplina.Desejamos agradecer aos nossos colegas do Departamento de Anlise e doIME-UERJ que, de algum modo, nos motivaram e deram condies para es-crever estas notas e Sra. Sonia M. Alves pela digitao. O texto foi digitadoutlizando Amstex e a maioria dos desenhos foram feitos utilizando o softwareMathematica. Certamente, todos os erros so exclusivamente de responsabili-dade dos autores.

    Mauricio A. Vilches- Maria Luiza CorreaRio de Janeiro

  • iii

    Copyright by Mauricio A. VilchesTodos os direitos reservados

    Proibida a reproduo parcial ou total

  • iv

  • Contedo

    1 Introduo 11.1 Desiguldades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Intervalos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Valor Absoluto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Distncia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Plano Coordenado . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Equao da Reta . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.6.1 Equao Geral da Reta . . . . . . . . . . . . . . . . . . . . 81.6.2 Equao Reduzida da Reta . . . . . . . . . . . . . . . . . 91.6.3 Paralelismo e Perpendicularismo de Retas . . . . . . . . 10

    1.7 Equao das Cnicas . . . . . . . . . . . . . . . . . . . . . . . . . 111.8 Trigonometria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.9 Exerccios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    2 Funes de uma Varivel Real 252.1 Definies e Exemplos . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Grficos de Funes . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3 Exemplos de Funes . . . . . . . . . . . . . . . . . . . . . . . . . 39

    2.3.1 Funo Modular ou Valor Absoluto . . . . . . . . . . . . 392.3.2 Funes Polinomiais . . . . . . . . . . . . . . . . . . . . . 402.3.3 Funes Pares e mpares . . . . . . . . . . . . . . . . . . . 47

    2.4 Interseo de Grficos . . . . . . . . . . . . . . . . . . . . . . . . 492.5 gebra de Funes . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    2.5.1 Funes Racionais . . . . . . . . . . . . . . . . . . . . . . 532.6 Composta de Funes . . . . . . . . . . . . . . . . . . . . . . . . 532.7 Inversa de uma Funo . . . . . . . . . . . . . . . . . . . . . . . . 57

    2.7.1 Mtodo para Determinar a Inversa . . . . . . . . . . . . . 582.8 Funo Exponencial . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    2.8.1 Crescimento e Decaimento Exponencial . . . . . . . . . . 652.8.2 Funo Logstica . . . . . . . . . . . . . . . . . . . . . . . 66

    2.9 Funo Logartmica . . . . . . . . . . . . . . . . . . . . . . . . . . 67

    v

  • vi CONTEDO

    2.9.1 Desintegrao Radioativa . . . . . . . . . . . . . . . . . . 692.10 Funes Trigonomtricas . . . . . . . . . . . . . . . . . . . . . . . 72

    2.10.1 Funo Seno e Co-seno . . . . . . . . . . . . . . . . . . . . 722.10.2 Funo Tangente e Secante . . . . . . . . . . . . . . . . . 732.10.3 Funo Co-tangente e Co-secante . . . . . . . . . . . . . . 74

    2.11 Funes Trigonomtricas Inversas . . . . . . . . . . . . . . . . . 802.11.1 Funo Arco seno . . . . . . . . . . . . . . . . . . . . . . . 802.11.2 Funo Arco co-seno . . . . . . . . . . . . . . . . . . . . . 812.11.3 Funo Arco tangente . . . . . . . . . . . . . . . . . . . . 822.11.4 Funo Arco secante, co-tangente e co-secante . . . . . . 83

    2.12 Funes Hiperblicas . . . . . . . . . . . . . . . . . . . . . . . . . 852.13 Exerccios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    3 Limite e Continuidade de uma Funo 953.1 Limites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    3.1.1 Definies e Exemplos . . . . . . . . . . . . . . . . . . . . 953.1.2 Limites Laterais . . . . . . . . . . . . . . . . . . . . . . . . 1023.1.3 Limites no Infinito . . . . . . . . . . . . . . . . . . . . . . 1063.1.4 Limites Infinitos . . . . . . . . . . . . . . . . . . . . . . . . 1093.1.5 Smbolos de Inderminao . . . . . . . . . . . . . . . . . 1133.1.6 Limites Fundamentais . . . . . . . . . . . . . . . . . . . . 1143.1.7 Assntotas . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

    3.2 Continuidade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1213.2.1 Teorema do Valor Intermedirio . . . . . . . . . . . . . . 126

    3.3 Exerccios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

    4 Derivada 1394.1 Reta Tangente . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1394.2 Funes Derivveis . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.3 Regras de Derivao . . . . . . . . . . . . . . . . . . . . . . . . . 1494.4 Derivada da Funo Composta . . . . . . . . . . . . . . . . . . . 151

    4.4.1 Derivada da Funo Exponencial . . . . . . . . . . . . . . 1544.4.2 Derivada da Funo Logartmica . . . . . . . . . . . . . . 1564.4.3 Derivada das Funes Trigonomtricas . . . . . . . . . . 1594.4.4 Derivada das Funes Trigonomtricas Inversas . . . . . 1614.4.5 Derivada das Funes Hiperblicas . . . . . . . . . . . . 162

    4.5 Derivao Implcita . . . . . . . . . . . . . . . . . . . . . . . . . . 1654.5.1 Clculo da Derivada de uma Funo Implcita . . . . . . 165

    4.6 Famlias de Curvas Ortogonais . . . . . . . . . . . . . . . . . . . 1704.7 Derivadas de Ordem Superior . . . . . . . . . . . . . . . . . . . . 1724.8 Aproximao Linear . . . . . . . . . . . . . . . . . . . . . . . . . 175

  • CONTEDO vii

    4.9 Velocidade e Acelerao . . . . . . . . . . . . . . . . . . . . . . . 1784.10 A Derivada como Taxa de Variao . . . . . . . . . . . . . . . . . 1814.11 Exerccios I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1864.12 Variao de Funes . . . . . . . . . . . . . . . . . . . . . . . . . 1944.13 Funes Montonas . . . . . . . . . . . . . . . . . . . . . . . . . . 2004.14 Determinao de Mximos e Mnimos . . . . . . . . . . . . . . . 2044.15 Concavidade e Pontos de Inflexo . . . . . . . . . . . . . . . . . 2094.16 Esboco do Grfico de Funes . . . . . . . . . . . . . . . . . . . . 2134.17 Problemas de Otimizao . . . . . . . . . . . . . . . . . . . . . . 2214.18 Teorema de LHpital . . . . . . . . . . . . . . . . . . . . . . . . . 2314.19 Exerccios II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

    5 Integrao Indefinida 2465.1 Definies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2465.2 Mtodos de Integrao . . . . . . . . . . . . . . . . . . . . . . . . 250

    5.2.1 Mtodo de Substituio . . . . . . . . . . . . . . . . . . . 2505.2.2 Integrais que Envolvem Produtos e Potncias de Funes

    Trigonomtricas . . . . . . . . . . . . . . . . . . . . . . . . 2535.2.3 Integrao Por Partes . . . . . . . . . . . . . . . . . . . . . 2545.2.4 Substituio Trigonomtrica . . . . . . . . . . . . . . . . . 2575.2.5 Integrao de Funes Racionais . . . . . . . . . . . . . . 2625.2.6 Tangente do ngulo Mdio . . . . . . . . . . . . . . . . . 271

    5.3 Aplicaes da Integral Indefinida . . . . . . . . . . . . . . . . . . 2725.3.1 Obteno de Famlias de Curvas . . . . . . . . . . . . . . 2725.3.2 Outras Aplicaes . . . . . . . . . . . . . . . . . . . . . . 273

    5.4 Exerccios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

    6 Integrao Definida 2826.1 Introduo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2826.2 Definio e Clculo da Integral Definida . . . . . . . . . . . . . . 288

    6.2.1 Teorema Fundamental do Clculo . . . . . . . . . . . . . 2906.3 Contruo de Primitivas . . . . . . . . . . . . . . . . . . . . . . . 2976.4 Aplicaes da Integral Definida . . . . . . . . . . . . . . . . . . . 300

    6.4.1 Acelerao, velocidade e posio . . . . . . . . . . . . . . 3006.5 Clculo de reas . . . . . . . . . . . . . . . . . . . . . . . . . . . 3036.6 Volume de Slidos de Revoluo . . . . . . . . . . . . . . . . . . 319

    6.6.1 Clculo do Volume do Slidos . . . . . . . . . . . . . . . 3216.6.2 Outros Eixos de Revoluo . . . . . . . . . . . . . . . . . 3276.6.3 Mtodos das Arruelas . . . . . . . . . . . . . . . . . . . . 330

    6.7 Comprimento de Arco . . . . . . . . . . . . . . . . . . . . . . . . 3346.8 Logaritmo Natural . . . . . . . . . . . . . . . . . . . . . . . . . . 337

  • viii CONTEDO

    6.8.1 Logaritmo Natural como rea . . . . . . . . . . . . . . . 3386.9 Trabalho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3396.10 Integrais Imprprias . . . . . . . . . . . . . . . . . . . . . . . . . 341

    6.10.1 Integrais Definidas em Intervalos Ilimitados . . . . . . . 3416.10.2 Integrais de Funes Descontnuas . . . . . . . . . . . . . 348

    6.11 Exerccios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

    7 Exerccios Resolvidos 365

    8 Apndice 401

    9 Respostas 411

    10 Bibliografia 429

  • ! #"%$

    &('*),+

    .-/ #",0*1324135

    '

    #0*176892

    )

    6: .;,04170*17923

    )

    c

    )

    c

    )

    aW

    urv

    >xVZ~p7>y

    )

    ?

    '

    92Z2

    )

    ;e395a`

    )

    5

    '

    92pD,18f27B COD,17G5,?AD,92p

    '

    0L !"eC0

    '

    C5

    '

    172

    23B Cr92s?^5

    '

    104"jC0l

    L

    $1ZD,17G5,?^D,>"eC0!

    LL

    !

    fTC

    w=

  • !"$#!

    a b[ ]

    -5

    '

    1704

  • ! "

    ! #"%$ &$')(*,+ .-/'1032

    1

    '

    170*68?^5,136892>795a`

    )

    5

    '

    % 24

    +A)

    k#B C:D,1C

    T)(

    T (

    $1H13

    )

    ?^

  • !"$#!

    ?A?

    ( I

    cG?^2

    '

    o$1/

    I

    175

    '

    B C,c#^

    I

    Qbs

    )( I

    cND,1Z95,D,1bC;

    '

    176892

    dc>

    W

    F

    ,cG

    395a`

    )

    5

    '

    % 2M

    +A)

    kCB C $1

    L

    q

    dc!

    I

    W

    ba%Y

    L,1Z r24

    +^)

    kCB C8D,1C

    )( I

    )(

    G

    U

    1724

    +

    92

    )( I

    (

    G

    cN

    )

    1J$1Z13

    )

    ?(92

    H

    )

    G,W

    F

    ,cG>395a`

    )

    5

    '

    % 2M

    +A)

    kCB C $1

    L

    ' !dG XM

    4

    W

    urv

    ~p7>

    y:!}E

    H#

    {{

    "j9242!$

    &

  • ! "

    I

    Id

    G

    W

    1

    +

    p",0*C",0*?^13DG CD,1b?^?A?

    c

    Id

    G

    $1Z13

    )

    ?^175

    '

    041Z92g5$

    )

    68170*920*1! C?^2

    G

    $1

    W

    T5

    '

    B C d$1Z rD,?^2

    '

    C5,3?A rD,1b pC0*?

    F

    136

    W

    %Y

    D,?A2

    '

    C5,3?] p135

    '

    0*1b92g5$

    )

    68170*921

    $1

    w I

    W

    I

    Y

    D,?A2

    '

    C5,3?] 8135

    '

    0*1l925$

    )

    6>170*92

    b

    1

    Io$1

    b/

    I

    =

    ^ ^81 8D,?^2

    '

    C5,3?A 8135

    '

    0*1

    92g5$

    )

    68170*92

    c

    1

    Q$1

    5c

    a

    c

    a

    W

    urv

    7~pO .>VQxHO~lQ

    6 "N #0sC0*D,135G CD,>D,1H5$

    )

    68170*92h0*13 C?A2m$1

    )

    6: D

    )

    "

    +

    pD,1H5$

    )

    6>170*920*1! C?A2

    ,

    c

    '

    C?A2

    )

    1

    ,

    2411s24968135

    '

    1s241t.

    jW{

    1

    +

    1368135

    '

    ZD,Z"N #0C0*D,135G CD, $1tLG C6: CD,H",0*?A6817?^0L [email protected],1 %

    5G CDG tD,t"N #0 1

    $1VLG C6: CD, s241

    F9)

    5,DG [email protected]*D,135G CDG D,s"N #0

    W 2

    1T[C0*68 t C5g$

    +

    F

    l g0*1",0*1324135

    '

    ekCB C

    F

    1396o$1

    '

    0*?A3 ZD,92T0*1! C?^23c"[email protected],136>92T0*17",0*1724135

    '

    #0

    F

    139681

    '

    04?A! C68175

    '

    1g92T"N #0*172hC0*D,135G CD,92

    W{

    #0L Z?^2

    '

    395,24?^D,170L C6892ZD

    )

    C2b0*1

    '

    C23c

    )

    1>"eC0b395 "j96892H

    )

    18241:?^5

    '

    10*2413

    '

    136"e104"e135,D,?^

    )

    %

    +

    #0468135

    '

    1

    WZY

    0*1

    '

    ,C0*?^n395

    '

    +

    $1G C68 CDG m17?(,DG C2/ #;G243?^242* C2/

    )

    13? ,mD,92/1r :0*1

    '

    m

  • !"$#!

    B

    D

    A2

    1

    -1

    -2

    -2 1

    C

    0

    2* C5,D,J

    '

    13C0*136: OD,1

    ?

    '

    $

    F

    C0L C2Z"[email protected],136892D,17G5,?(08 PD,?A2

    '

    C5,3?] P135

    '

    0*1mD,9?A2"e95

    '

    92D,P"

    +

    C5,

    3C0*D,135G CD,

    W

    B

    x

    y

    x

    y

    1 2

    1

    2

    A

    d

    1`M C6

    1

    B

    B

    "e95

    '

    92gD,>"

    +

    C5,

    W{Y

    D,?^2

    '

    C5,3?A 8135

    '

    0*1 1

    $1C

    p

    B

    B

    (

    B

    B

    Y

    D,?^2

    '

    C5,3?A p"j9242

    )

    ? C2s241

    F9)

    ?A5

    '

    132t",0*C",04?A13DG CD,132t?A6813D,?A

    '

    C23

    ?

    pV

    1

    p

    241H1H24968135

    '

    1/241

    :W

    ?A?

    p

    :

    W

    ?A?^?

    pT

    !Z

    (

    !H pW

    R

    +

    ),+

    1b pD,?A2

    '

    C5,3?] p135

    '

    0*1Z92"e95

    '

    92

    I

    !

    ^

    1

    I

    W

    Y

    "

    +

    ?^! C5,D,8 p[w$C0*6

    ),+

    r

    I

    I

    B

    (

    ^

    4

    B

    ^=I

    I

    2

    1

    '

    170*68?^5,1Hp"e95

    '

    >c,

    )

    1ZD,?^241

    F

    6>135

    '

    >D,1H041

    '

    r

    )

    1

    +

    ?

    F

    p92g"j95

    '

    92

  • ! "

    G,!

    1

    wI

    A

    W

    1`M C6

    ,

    :"e95

    '

    :",0*

    )

    0L CD,1

    L

    !

    c

    wI

    !

    "j95

    '

    92/

    )

    ?

    +

    ?A #0*1327968

    5,>D,1724135,,,

    P S T

    R

    Q

    2

    '

    0*?

    C5

    F9),+

    92

    L

    123B Cr2413681

    +

    G C5

    '

    132

    N+

    F

    ,

    L

    1

    L

    C0s

    )'

    0*

    +

    CD,,c

    ^

    G

    1

    G

    W{Y

    "

    +

    ?^! C5,D,: p[w$C0*6

    ),+

    DG >D,?A2

    '

    C5 %

    3?A

    L

    )(

    G

    c

    L

    (QH1

    wI

    WV

    ;

    '

    136892tr24?A2

    '

    136:

    )(

    G

    wI

    (Q

    )

    1

    '

    136 3968p24

    +^)

    kCB C,{m

    G+

    F

    W

  • !"$#!

    urv

    }P~

    ~l J~ _x~

    urvvau

    }O~

    ~l x/V~p Q~ _x~

    1`M C6 T

    1

    B

    B

    B

    D,9?A2"e95

    '

    92tD,?^2

    '

    ?A5

    '

    92g5,>"

    +

    C5,,

    x x1 2

    2

    1P

    P

    1

    2y

    y

    Y

    17

    )

    ekCB CrDG p0*1

    '

    r

    )

    1/"N C242* r"j1

    +

    92"e95

    '

    92 t1

    B

    $1#

    T (

    ( Dg

    95,D,1b

    B

    c

    B

    s1 D

    B

    B

    W

    "e95

    '

    t

    "e10

    '

    135,31m p0*1

    '

    >T)(

    ( Dg

    241ZT (

    ( Dg

    %Y

    L,1Z r13

    )

    ekCB C8DG p041

    '

    r

    )

    1/"N C2M2* r"e1

    +

    92s"j95

    '

    92

    ^

    1

    B

    I

    !dG W

    ^ (

    G

    c

    I (Rt ^r1Dg

    I

    G+

    F

    ,cG p13

    )

    ek#B C $1C

    (^

    Z

    IH

    W

    I

    2

    1

    '

    170*68?^5,1

    '

    +

    )

    1/r"e95

    '

    ^

    "j170

    '

    175k! J p041

    '

    :^)(

    b b

    wI/

    W

    "e95

    '

    ^

    "e10

    '

    135,31m 041

    '

    )^ (

    b /

    wI/

    241H^ ^(

    b

    wIH

    ,+

    F

    ,c

    ^

    b

    W

    2

    1324135,,92tD,1:

    18 I

    c0*132M"j13

    '

    ?(

  • ! "

    -1 2

    3

    -4

    1 3

    1

    3

    urvv7

    }O~

    ~l _x}z7J~ Q~ x~

    1

    )

    68 0*1

    '

    r5 B Co$1"N #0L

    +

    1

    +

    r Cr13? ,rD,92

    c,175

    '

    B C

    W

    a Cn3135,D,,

    B

    B

    1

    B

    B

    B

    cGC;

    '

    136>92s

    X @ V-?$ S%$ V$! ]-?=

    (

    $1LG C6: CD,[email protected]?A135

    '

    18 C5

    F9),+

    #0/DG m0*1

    '

    1

    [email protected]?A135

    '

    1

    +

    ?^5,1! #0/DG m0*1

    '

    W

    $

    [w$ C3?

    +

    DG r041

    '

    r

    )

    1/"N C2M2* r"e1

    +

    r"j95

    '

    s

    1

    '

    176317G3?^135

    '

    1b C5

    F9),+

    #0 $1C

    b

    s

    ;

    '

    135,G : p13

    )

    ek#B Cr0*13D

    )

    n7?ADG >DG r041

    '

    r

    )

    1/"N C2M2* r"e1

    +

    92"e95

    '

    92 T

    I

    1

    B

    cNb9W

    Z1Z[\ Cn3136>92 t s

    )

    B

    135

    '

    B C,cN241ZIp1

    t 9c

    '

    1768923c

    l

    (R

    )

    W

    I

    V2470*15G p[C0*6: 0*13D

    )

    n3?^DG 8 r13

    )

    ekCB C,

    G

    )( I

    (

    b

    W

    Y

    [C0*6: 0*13D

    )

    n3?^DG $1mD,

    '

    ?^"e

    (

    135

    '

    B C,c

    I

    b

    I

    WW2

    1324135,,92rD,1

    1Q I

    c

    0*132"e13

    '

    ?^

  • !"$#!

    2 6

    1

    5

    -2 2

    -2

    2

    urvv

    ~lT~p7xH!z7y x

    x/oxHOz }Q7~lz7y Qx _x~ly

    1`M C6

    N (

    g1

    B

    (

    B

    C2g17

    )

    ekCB9132gD,1D

    )

    C2g041

    '

    C2

    W{Y

    2h0*1

    '

    C223B Cp"N #0L

    +

    1

    +

    C2h241

    124968175

    '

    1241 h

    B

    WY

    20*1

    '

    C2h23B C"e104"e135,D,?^

    ),+

    #04132s2M11/2M968135

    '

    1241

    B

    W

    F

    ,c

    C20*1

    '

    C2D,1p13

    )

    ek#B9132Z , (

    (ED

    1p

    B

    (

    B

    ( D

    B

    23B C"j1704"j135,D,?A

    ),+

    #0*1323c 241p1

    24968175

    '

    1/241Cc N

    B

    (

    B

    W

    @Y

    L,1gD,?^0*17?

    '

    W

    -0.5-1 0.5

    1

    -1 1

    1

  • ! "

    urv

    }P~

    >xy J~lyi :Jz t~ly

    Y

    13

    )

    ekCB CpD,p241

    F9)

    5,D,

    F

    0L

    )

    136D

    )

    C2

    95,?A3 c

    )

    `M m5G

    '*)

    0*13n3 mD,1"e135,D,1pD,[email protected]?A135

    '

    132 lc

    !

    c

    #

    c:cj1

    W

    @D,136892t395,24?AD,10L #0/D,9?A2! C24927

    1

    !

    1

    !

    W

    1

    !

    W

    Rh96>"

    +

    1

    '

    C5,D,/

    )

    CD0L CD,92D,92;G?A5

    968?^92d5G C2

  • !"$#!

    95,D,1b'Bs

    1

    Bs

    !

    W

    ?A?

    1

    1

    !q

    )

    1

    =

    cN r13

    )

    ekCB C

    "[email protected],1H24170172470*?

    '

    r396>,

    ,G

    (

    B

    B

    )(

    B

    B

    95,D,1rBZ

    1

    BZ

    !

    WZY

    213

    )

    ekCB9132

    ^

    1

    ,G

    0*17",0*1724135

    '

    C6

    )

    6:

    D,113?(92

    "N #0L

    +

    1

    +

    92s C92s17?(,92g3C0*D,135G CD,92

    W

    ?A?^?

    1

    c b13

    )

    ekCB Cb"eD,124170h132M70*?

    '

    7968,

    (

    B (

    !

    (

    B

    c

    )

    1t0417",0*1324175

    '

    D

    )

    C2s041

    '

    C2g

    )

    1Z2M1Z?A5

    '

    17042413

    '

    C6

    W

    !

    W

    1

    1

    !

    r13

    )

    ekCB C $1C

    !

    B

    (

    #

    )(

    (

    )

    10*17",041324135

    '

    )

    6:

    D,1H17?(,p"N #0L

    +

    1

    +

    8 Cp13? ,>D,92g

    W

    I

    1

    1

    !

    r13

    )

    ekCB C $1C

    P

    B

    (

    #

    )(

    (

    )

    1J$1Z p13

    )

    ek#B C>D,1

    )

    68

    D,1H13?(r"N #0L

    +

    1

    +

    r C>17?(,rD,92

    W

    ^

    1

    !

    cN p13

    )

    ekCB Cp0*17",0*1724135

    '

    )

    6: l0*1

    '

    W

    2

    ?

    F

    rr

    )

    10*17",0*132M135

    '

    C6 C2t2M1

    F9)

    ?A5

    '

    132s13

    )

    ekCB91723

    G

    CB (

    B

    ^=I

    wI

    (

    G

    W

    I

    CB (

    B

    Im ^

    W

    _^

    B

    5G

    B

    ^

    cW

    GC

    B

    VG

    B

    )(

    b

    ^t

    W

    ba

    B

    B

    I

    5G Z

    ^b

    W

    c#

    B

    W

    CB

    5G b

    ^b

    W

    G

    c

    !

    9c

    ! #

    ^[email protected]

    wI>1q

    G,N+

    F

    ,c

    G

    c >

    c

    c

    c

    c

    Bg

    G

    1

    Bg

    cWVY

    13

    )

    ekCB C>0*17",041324135

    '

    )

    6: p1

    +

    ?("G241Z7135

    '

    0L CDG >5,r"j95

    '

    ,G, c=

    D,1Z17

    )

    ekCB C,

  • ! "

    5G

    B

    G

    (

    b c=

    B

    c

    I

    !

    9c

    ! #

    [email protected] i

    1 _

    ^

    h+

    F

    ,c

    G

    c

    9c

    1

    Bg

    Bg

    G,WY

    13

    )

    ekCB Cb0417",0*1324175

    '

    )

    6 C$

    &

    0*

    ),+

    p7135

    '

    0L CD,r176

    L=

    c D,10L C?ApIZ1

    '

    136 b[C0*6:

    B

    (

    B

    G,

    2

    1324135,,92tD,1:

    18 I

    c0*132M"j13

    '

    ?(0*17",041324135

    '

    )

    6: p,?^"$170M;e

    +

    1H1/"[email protected],1H24170s132470*?

    '

    >396>,

    B

    G

    B

    GC

    Rh968 c

    !

    dG

    c

    #

    c r1

    ^9c

    '

    1368923^c"

    !

    c >

    9cp

    9c

    ^

    c

    cG

    B

    G

    1

    B

    WVY

    13

    )

    ekCB Cp0*17",0*1724135

    '

    )

    6: ,?^"$1704;j

    +

    1C

    B

    G

    b

    B

    2

    1324135,,92tD,1:_^

    18

    GC

    c0*132M"j13

    '

    ?(

  • !"$#!

    -2 2

    -2

    2

    -2 3

    -2

    2

    ba

    R968

    !

    1

    c% m13

    )

    ekCB Cm0*17",041324135

    '

    ED

    )

    C20*1

    '

    C2395,7C040*135

    '

    132

    D,1r[\

    '

    ,

    CB

    B

    Id

    8G

    ^Z

    B

    (QI

    Bs

    W

    F

    ,c

    Bs

    (JI

    B

    175

    '

    B C,c

    ^

    )

    W

    c#

    R96>

    c

    !

    9c 813

    )

    ek#B Cm0417",0*1324175

    '

    )

    6: >"N #0N$ #;j

    +

    8D,1l13? ,:"N #0L

    +

    1

    +

    m C:13? ,mD,92

    W 2

    1324175,,92D,1:

    ba

    1:

    c#

    c0*132M"j13

    '

    ?(135

    '

    1C

    -3 -2 -1 1 2 3 4

    -5

    -4

    -3

    -2

    -1

    1

    2

    -2 3

    -2

    2

    Rh968

    !

    c p13

    )

    ek#B Cr0*17",041324135

    '

    )

    6: l"N #0N$ #;e

    +

    rD,1H13?(p"N #0L

    +

    1

    +

    > C>13? ,rD,92

    W

    -2 2-1 1

    -1

    1

    2

  • ! "

    urv

    hz7|>8P xz7~

    -5,?A3?A

    +

    68175

    '

    1Z[\ #0*136892

    )

    6: >0417

    C5

    F9),+

    >3135

    '

    0L

    +

    23B C:2413681

    +

    G C5

    '

    1321H

    )

    1l r0* CnCB C8DG >2417681

    +

    G C5k3 $1b

    0L CnCB C>135

    '

    0*1l92s0L C?^92

    W

    )

    6C$

    &

    0*

    ),+

    :D,1b3135

    '

    0*1H0L C?^@c241`M 8396>",04?A68135

    '

    8D,8 #0*3

    2

    )

    ;

    '

    175,D,?AD,8"e1

    +

    C5

    F9),+

    >3175

    '

    0*

    +

    I

    W

    O A

    B

    l

    r

    J$1OD,?(0*1

    '

    C6>135

    '

    1",0*C"eC0*7?A95G

    +

    1 6813D,?^DG D,

    C5

    F9),+

    ZI

    W Y

    D,68?

    '

    ?^5,D,

    )

    1P #0*3 1O

    0L C?^.241 `M C6_6817D,?AD,92/396 .68132M6:

    )

    5,?ADG CD,1>1rD,135,

    '

    C5,D,E"jC0

    I

    6813D,?^DG D,

    C5

    F9),+

    ITc

    '

    136892

    I

    c95,D,1: E395,2

    '

    C5

    '

    1 PD,17"j135,D,1:DG

    )

    5,?^DG CD,18D,186813D,?^DG .D,1

    C5

    F9),+

    92

    13247

    +

    ,?ADG

    W

    $1r

    )

    5,?ADG CD,1pD,1r6>13D,?ADG mD,1

    C5

    F9),+

    92"N #0L E m

    )

    +

    . 9c%

    )

    241 `M c

    '

    +

    )

    1

    I

    W

    V60*132

    )

    68,ce 86817D,?ADG 8D,

    C5

    F9),+

    I 1760L CD,?A C5,92$1bDG CDG 8"e1

    +

    >0L CnCB C,

    c

    95,D,18$1rE396>",04?A68135

    '

    D,O #0*3.2

    )

    ;

    '

    135,D,?^D,P5,E9$

    &

    0*

    ),+

    E

    )

    `3135

    '

    0* $1r.6813D,?^DG >D,1

    )

    6

    C5

    F9),+

    136 0L CD,?] C5,92s5 B C8D,17"j135,D,1bDG

    )

    5,?^DG CD,1bD,1Z396r",0*?A68175

    '

    r395,24?^D,170L CDG

    W

    >"

    +

    C5,>3C0*D,135G CD,

    395,24?^D,170*136>92

    )

    6 9$

    &

    04

    ),+

    .C0*?A135

    '

    CD,5,.24135

    '

    ?AD, C5

    '

    ? % ,C0N$ #04?A,c%3135

    '

    0L CD,5G .C0*?

    F

    136 1rD,1r0L C?^

    ?

    F9)

    +

    W

    T2

    '

    1m9$

    &

    0*

    ),+

    $1mD,135,968?A5G CD,PC$

    &

    0*

    ),+

    '

    04?

    F

    95,96o$1

    '

    0*?A3

    WJ

    "e95

    '

    lc?^5

    '

    10*241kCB CJD,

    9$

    &

    0*

    ),+

    >396 82M1368?&% 13?(r"j924?

    '

    ?(DG C2 #;G2M3?A2424 C2$1ZLG C6: CD,8C0*?

    F

    136

    W

    2t"j95

    '

    92 lc

    c

    !

    c

    #

    c

    ?A5

    '

    1704241kCB9132tD,>9$

    &

    0*

    ),+

    r396 92s13? ,[email protected],135G CD,92trD,?^

  • !"$#!

    A

    B

    D

    III

    III IVC

    Rh968> r13

    )

    ekCB CrD,89$

    &

    0*

    ),+

    o$1/

    B

    (

    B

    9cN241

    )

    796>",0*?A6>135

    '

    $1 I

    W{

    C0

    '

    C5

    '

    ,cN >6813D,?^DG

    D,1Z

    )

    +

    )

    170 #043>D,132

    '

    1ZC$

    &

    0*

    ),+

    $1H?

    F9)

    +

    r2

    )

    r6813D,?ADG p1360L CD,?] C5,92

    W

    Rh95,24?AD,17041H

    C5

    F9),+

    :I

    )

    1HD,1

    '

    170*68?^5G l24C;,0*1Zp9$

    &

    0*

    ),+

    pD,10L C?A9c,> #043rD,1/C0*?

    F

    136

    L=

    1/1

    '

    041368?ADG CD,1

    ,T'

    C?^2g

    )

    1 w P1 a

    c,7968r5,>D,1324135,,,

    M

    O

    P A

    H#

    V

    g

    24135,8D,

    C5

    F9),+

    Iq$1ZD,135,

    '

    CD,r"eC0

    {

    I

    1/D,17G5,?AD,8"jC0!

    {

    I

    ;

    g

    7 % 24135,>D,

    C5

    F9),+

    :Iq$1/D,135,

    '

    CD,>"jC0 D

    I

    1ZD,17G5,?^D,>"eC03

    D

    I

    hY'

    C5

    F

    175

    '

    1HD,

    C5

    F9),+

    I $1/D,135,

    '

    CDG p"eC0

    I

    1/D,17G5,?ADG >"jC0!

  • ! "

    I

    13

    )

    ?^92

    )

    1TD,9?A2 #0*792d395

    F

    0

    )

    135

    '

    132

    '

    176 68132M6: sC0*?

    F

    1361 t68132468 t1

    '

    0*1368?^DG CD,1Cca"jC0

    '

    C5

    '

    6813246>

    24135,,[email protected] % 24175,,c1

    '

    W

    $

    396

    )

    60*1",0*1324135

    '

    #0

    '

    D,92T92h #04392395

    F

    0

    )

    175

    '

    172s Cb #0*3Z"jC0(JI {c

    95,D,1 $1

    )

    6 5$

    )

    681704>?A5

    '

    13?(0*

    W

    H#

    {{

    Y

    "N #0

    '

    ?(0pDG C2r0*1

    +

    ekCB9132r C5

    '

    170*?AC041323cD,17G5,?^6892r Q24133 C5

    '

    1.1E J3 % 2M13! C5

    '

    1D,

    C5

    F9),+

    :I "jC0!

    D

    I

    D

    I

    1 D D

    I

    {

    I

    95,D,1 D

    I

    1

    {

    I

    c,0*172M"e13

    '

    ?^

  • !"$#!

    I

    D

    I

    I

    1 I

    I

    (

    D

    B

    I

    d

    B

    I

    ^

    1 I

    D D

    B

    I

    d

    D

    B

    I

    ;G241704

  • ! "

    I

    c

    G

    1^ 9I ^

    G

    {

    I

    w9I

    I99I

    ^=9I

    I99I

    D

    I

    ^=9I

    I99I w9I

    I99I

    I

    b

    G G

    1^ ^ 9I

    b

    1^

    G

    A

    c

    I

    {

    I

    I99I

    ^=9I

    ^=9I

    I#9I

    w9I

    D

    I

    I99I

    w9I

    w9I

    I#9I

    ^=9I

    !z t~

    ~l

    >

    gd

    e

    #0L r

    )

    +

    )

    170

    '

    0*?

    C5

    F9),+

    !

    2M1

    F9)

    ?A5

    '

    1ZD,1724135,,,

    C

    B

    D

    b

    a

    A

    c

    1`M

    #

    >"j95

    '

    :C;

    '

    ?AD,8"e1

    +

    8?A5

    '

    1704241kCB C:DG >0*1

    '

    8

    )

    1Z"N C2M2* >"eC0

    !

    1$1Z"e104"e135,D,?^

    ),+

    #0/ C

    +

    CD,

    8W

    F

    ,

    {

    I

    ! #

    !

    {

    J

    ! #

    !

    >

    )

    1H?^6>"

    +

    ?^!

    !

    {

    I

    !#

    #

    !

    {

    J

    W

    C0

    '

    C5

    '

    ,

    {

    I

    {

    J

    W

  • !"$#!

    Y

    5G

    +

    F

    C6>135

    '

    1Cc,C;

    '

    1368927

    {

    I

    {

    J

    {

    D

    W

    N

    j

    Rh968> #"

    +

    ?A! ek#B C>D,?^041

    '

    rDG

    +

    13?%D,92g24135,923cNC;

    '

    136>92t $ #0*1! rD,

    '

    0*?

    C5

    F9),+

    !

    I

    {%

    I

    D

    {

    I

    I

    3D

    {

    J

    urv

    x

    z7>y

    jY

    L,1 2M

    +A)

    kCB ClDG C2h241

    F9)

    ?A5

    '

    132D,1324?

    F9)

    +

    DG CD,13210*17",041324135

    '

    15,13?([email protected]*D,175G CD,p395a`

    )

    5

    '

    24

    +^)

    kCB C,

    XB

    ;

    CB

    I

    B

    (o

    I D

    Z

    b9

    )(R

    =

    1

    )( I

    [

    Zb

    )(R

    F G

    CB (R

    c

    TB

    Id (R

    ?

    ^

    Zb

    Id (

    G

    `

    B

    (R

    ICB

    I

    CB

    +

    (

    I

    6

    XB

    )(

    c=

    B 5

    XB

    I

    CB

    Zb

    (

    G

    B

    VG

    "

    ( )( I

    I

    I

    (R ( )( I

    0

    B

    I

    2

    1

    '

    170*68?^5,1H92g

  • ! " !

    h

    #0L

    '

    D,pc

    1 )(

    ( # (

    ( 1

    ;

    "N #0L

    '

    D,pP1

    W

    GC

    J #0*

    )

    1Z92g241

    F9)

    ?^5

    '

    172t"e95

    '

    92g5,>"

    +

    C5,[email protected]*D,175G CD,81H3

    +

    ),+

    1b rD,?^2

    '

    C5,3?A r135

    '

    0*1H1

    +

    1723

    H%G,Nb9 dG,! b9

    ;

    Z c=

    ^

    !dc=

    /

    I

    !

    ^

    !dc=

    D

    Z [email protected]

    G,

    ^

    1

    /

    I

    [

    H

    ^

    ^

    F H [email protected]

    ,G,!

    Z

    !

    =

    I

    ?

    /G,Nb9 dG,

    `

    Z

    I9I

    b

    ^

    [email protected]

    ^

    ba

    '

    ?

    +

    ?An318 P[w$C046

    ),+

    DG OD,?A2

    '

    C5,7?] "N #0L DG 0*1

    '

    "e170M"e135,D,?^

    ),+

    #0> l0*1

    '

    8Id (

    b b

    t

    1/

    )

    1/"N C242* p"j1

    +

    p"e95

    '

    W

    GC

    SV170*?(G

    )

    1/

    )

    1Z C2g0*1

    '

    C2Id)( ^

    Z1

    c

    5G Z

    23B Cr"j1704"e175,D,?A

    ),+

    #0*132

    W

    ba 2

    1

    '

    170*68?^5,1Z p5G

    '*)

    0*13n! rDG C2t

    )

    04

  • !"$#!

    ^

    B

    Ia

    wI

    (RwI/

    ;

    c

    CB

    B

    GAG

    B (

    B

    Ia

    Z

    D

    Ia B (

    G

    )( ^

    b5G

    1

    #XB (

    G

    B

    #

    c Z

    A

    [

    #XB

    c

    B

    ^

    c

    ^=I

    b

    wI

    G

    F

    #CB(R

    c

    B I

    b

    CB (

    B(R

    c

    )(Q

    c

    (

    c1G

    ?

    b

    XB( I

    b

    )(E

    B

    Zb

    `

    CB ( )(

    B ( ^

    XB(

    B

    5G

    5G

    +

    XB (

    B

    G

    (R ^

    6

    B

    (

    B

    ()(Q

    (

    G=

    5

    G

    B

    (

    G

    B

    (RwId

    ^=I

    ^

    c#

    1 `M

    )

    6 "j95

    '

    E5

    )

    6: "N #0N$ #;j

    +

    )

    5

    )

    6: .1

    +

    ?^"G241

    W

    68 m0*1

    '

    .

    )

    1p"N C242M1r"eC0 $1rD,?

    '

    D,1

    '

    C5

    F

    135

    '

    1 E"N #0N$ #;j

    +

    )

    O1

    +

    ?^"G241:5,"j95

    '

    241m E"N #0N$ #;e

    +

    )

    1

    +

    ?("G241:132

    '

    B CO395

    '

    ?ADG C2

    ?A5

    '

    13?(0L C68135

    '

    15

    )

    6 D,92{24136>?&% "

    +

    C5,92D,1

    '

    170*6>?A5G CD,"e1

    +

    /0*1

    '

    W

    ST10*?^G

    )

    1s

    )

    1s H 041

    '

    ( D

    $1

    '

    C5

    F

    135

    '

    1 "N #0L #;e

    +

    T

    B

    (

    ( D5,>"e95

    '

    X

    D

    W

    2

    CDG r p0*1

    '

    )( :1/>C$

    &

    0*

    ),+

    >CB (

    Bs cGD,1

    '

    170*68?^5,1

    '

    +

    )

    1C

    241`M C6 2413! C5

    '

    132

    ;

    241`M C6

    '

    C5

    F

    135

    '

    132

    W

    %

    #0* r

    )

    1

  • ! "

    I'

    %

    0*

  • !"$#!

    IJ

    G

    I

    Nb9 3

    IJ

    ^

    G

    I

    Nb9

    D

    IJ

    I

    I

    IJ

    c

    L=

    IQ

    G

    ^

    !

    I

    IJ

    ^

    ^

    I

    I

    c# 2

    CDG r r13

    )

    ekCB CmI>[\ #0*

    +

    D,p"e95

    '

  • ! "$#

    % & ' (

    )+* , -/. )0)

    132 4 5687

    9;:=< > :

    2 ? @ [email protected];[email protected]

    :IH

    B

    :

    @

    H

    JLKNM

    > OPRQS

    6

    T

    7

    U

    O+VWO :3XYO[Z \^]

    U

    V

    _`badce`gfihkjl

    m

    conqpsrt`badconquvhkwe`bxyrzanqxyhLuvh{a[|qr~}f{rz`banq|quvh{xy`b|ch{sa[uvhhkco`bxlhkcofih~rfrz|qfb`bceruq`

    nq|}f{h{rqxhnq|}f{h{ruq`+nqxh{hkweilhk`bpwo`ih{pl`nqxhwe`b{wh0nq`+uq`baefwo``+fbrzxyr0nqxh!nvh{|cesuvh{uq`

    l`uq`ce`woxy|vh{uvhjr{wrzncewohynvh{|cosuvh{uq`{uq`0xh{|q`bwohlnq|qsfihqadco`bxlhkweh{ah{pco`wo|vhkco{h{ajhkwh

    uq`v|qwr{woxh{pxy`b|co`+nqxhgnq|}fkh{rqadfbrzpsq`bxrzahae`bznq|co`k

    [+k

    ;

    `dh{x0vGxhLnq|}f{h{ruq`v|quvhY`bx/`gfbrzxGkh{psr{we`ba`bx/ l`

    nqxh0wo`b{whgnq`[h{aeaerfhhfih{uvhg`ps`bxy`|corYInqx

    +

    ~

    a|qr{ch}f{rz`banqaenvh{saabh{rqzI `

    |lnqxy`worl`fvh{xh{uqr{hkweilhk`bp!s|quq`j`b|quq`b|co`uvh+nq|}f{h{r`

    {hkweilhk`bp!uq`j`b|quq`|co`uvhnq|}f{h{rq

    b

    ae`bznq|ce`chk`bph!nq`xyrzacewh+h+kh{{h{rae`bxh{|vh{pquq`lh{znvh[uq`nqxhwo`jqwe`baoh!we`jqwo`bae`|ch[nqxh

    nq|}f{h{rq

    +h z

    zz

    {

    {

    +`hkcorqkhchk`bphwo`jqwo`ae`b|chnqxhnq|}fkh{rq{jrzsafih{uvhuqshco`xIh{aeadrfbsh{uvhnqxhlnq|qsfih!nvh{|cesuvh{uq`

    uq`kh{{h{rq_r{co`nq`{jrzaeae`bpsx`b|ce`{|~h{r`sadco`nqxhyNlr{woxnqphxyhkco`bxlhkcofihjhkwohy`jqwo`aeaohkwh

    nq|}f{h{ryuqr`q`bxgjvpsrqqxh{abvhuq`v|qd}fkh{ryuq`[nq|}fkh{rl`[aohkcesae`bch

    rz`bchLnqxhLj`bae!nqsaohuq`jqwo`}fbrzauq`gjqwor!uqncorzauvhf`badchtlh{adsfih`x;cewi`baaenj`woxy`wofih{uqrza

    uq`nqxuq`ce`woxy|vh{uqrgh{wdworqvr{qco`b|quqrkad`0hgae`znqs|co`[chk`bph

  • " de [+

    wor!uqncor

    nj

    nj

    nj

    z

    {

    z

    achchk`phY|~h{rwo`jqwo`ae`b|chnqxyhYnq|}f{h{rqjrzsahfbh{uvhjqworuqncorfbr{wdwo`badjrz|quq`

    jqwo`}frq

    k

    lhkwo`ihuq`nvh{pnq`wfzl

    m

    wofbnqpsrl`[nq|}f{h{ruq`ae`bntwh{srq

    +`hkcorq ae`rwh{ruqrf{l

    m

    wofbnqprYl`uq`b|qr{ch{uqrjr{wz`b|cbh{rq{ z

    "!

    $#kx f{l

    m

    wofbnqpruq`wh{rsznvh{ph

    zco`bx lhkwo`bh[

    z

    !&%

    ('

    nqx f{l

    m

    wofbnqpr[uq`wh{r[znvh{pqh

    zz

    {co`x lhkwe`ih

    zz

    zzz

    !)%

    ('

    %

    ('

    nq|qsuvh{uq`bauq` lhkwo`ih$

    x coh{|qnq`0jhkwh `badcor!fih{z`bx uq`griqv`b|qsrLp l

    m

    nquqrL|nqx qrzadjvcoh{puq``gco`wh r{woxh uq`nqx

    fbpss|quwergfbwofbnqpshkwwo`corguq`

    C

    x`ceworzauq`[h{pconwohqfbrzx nqxq`bxysadbl`wosrg`bx fih{uvh`cewe`bxy

    uvh{uq`{

    rzpsnqxy`uqrgch{|q!nq`l`uq`baefwecorg`bx nq|}fkh{ryuqrwh{r*!

    r

    rzpnqxy`uqrgfsps|quwor l`

    $#

    !

    `+rguqrzauqrzaq`xysael`wosrzayl`

    !

    t+qpsrzzrqrrzpnqxy`cor{ch{p

    l`{

    , z

    +# .-

    !

    t

    r{w`q`bxgjvpsrqqae`[rgwh{rgr{w/

    vrgrzpsnqx`l`0,

    !

    t{

    +rzsaaohkcl`psce`bahkwdcovfbsh{sa`badcih{rtfbwefbnqph{|quqrh{rtwo`buqr{wuqrt!nvh{uqr{w`bx;nqxhlr{wevchLuq`gwh{r

    sznvh{ph

    21435

    fbrzxjqwoxy`b|cor !nq`ad`jhkwh rzaLaehkcl`bpsco`babae``bps`a ce`wo`x nqxh

    ae`jhkwoh}f{h{rh{|qznqphkwuq`76t`bxwh{uqsh{|qrzal`

    6qrz|quq`0 l`[rgwh{srq

  • ! "

    s

    rzzrqvjruq`bxrzauq`aefwo``wrfbrzxgjqwosxy`|cor`bxnq|}f{h{ruvhae`jhkwh}f{h{ryh{|qznqphkwi

    6

    1R

    3

    6

    k

    `buq`7rp`

    rzpsnqxy`uq`nqxyhxh{adaohgh{aerzaeh l`s|`woaoh{xy`|co`jqwor{jr{wefbsrz|vh{phjqwe`baeabh{r

    h!nq``bpshg`badcvlhaenvxy`cesuvhsadcor l`{rgjqwor!uqncoryuvhgjqwo`aeabh{ryj`psrrzpnqxy`l`fbrz|qadcoh{|co`kae`hgco`bxg

    j`whkconwhuqr[lh{al`fbrz|qadch{|co`{+`b|qr{ch{xyrzah+jqwo`baeabh{rjr{wg!rrzpsnqxy`jr{w, `hco`bxgj`whkcenwh

    fbrz|qadcoh{|co`jr{w*v`b|cih{rq

    1

    ,

    ruq`xyrza`baefwo``w+hjqwe`baeabh{ry`x nq|}fkh{ryuqrrzpsnqx`{

    ,0

    ,

    rznYrgrzpnqxy`+`bxnq|}f{h{ryuvhgjqwe`baeabh{rq ,

    `bquqrvnqr[ph{xy|vhkwuq` rzae`bnqspps`$

    psnr[aoh{|qzn~l

    m

    |q`br0hkcewoh l`bauq`nqx=kh{aerq!frzxyrhkwecl`wosh{a

    rzn `bh{a2rzxyrh{anvh{|couvh{uq`ba`b|rzpuvh{aabh{rYj`nq`b|vh{abjr!uq`bxyrzafrz|qaesuq`wohkwnq`ykh{aerza

    co`bxr{woxyhkcorgfsp l

    m

    |quwosfr|~h{r`pilh{adcofbrq

    R

    +`b|qr{co`bxrzayjr{w;r woh{sr `r fbrzxjqwesxy`b|corq3+`suqr h wosf}f{h{r |vh{a jhkwe`buq`ba uqr {h{aerqh

    `bprfbuvh{uq`Luqryaoh{|qznq`^l`xyh{sr{wh{rypsrz|qzryuqr`bryfb`b|cewh{puqr{h{adr`uq`bfwe`baefb`ae`0hguqsadckh{|qfh

    uqr`qrhjhkwo`uq`fwo`aefb``l`[`wory|vhjhkwo`buq`{

    wo`bpsh}f{h{r`|cewe`h`psrfsuvh{uq`uvhfbwefbnqph}f{h{rg`

    l`uvh{uvhjr{wi

    7#

    #b

    rz|quq`l`0hgaefbr!fbsuvh{uq`uqraeh{|qznq``hguqs`wo`|}fih`b|cdwo`hgjqwo`badabh{r uq``b|cewh{uvhy`0huvhyaehql

    m

    uvh

    uqrYaoh{|qznq`|qrY{h{aerqj`woxy`b|ch{psxy`|co`kjhkwhtrYaoh{|qznq`ynqxh{|qr|nqxhL`bsh

    z

    1R

    `

    1R

    vpsrzzrq

  • " de [+

    z

    1^

    1R

    #

    zN

    k

    `bxyrza

    zz

    xy`cewerzauq` hkwh{xy`jhkwohh{`wnqxfbnwewoh{puq`r{woxhkcorYwe`ch{|qznqphkwbruq`bxrza

    `baefwo``wh lhkwe`ihuqrYfbnwdwh{p `x/nq|}f{h{ruq`ynqxGuqrzapsh{uqrzab+`yhkcorqad` `

    abh{rYrzapsh{uqrzauqr

    fbnwewoh{p vae`bnj`wl

    m

    xy`cewor l`

    -

    zz

    `hlhkwo`bhguqrgwe`ckh{|qznqpsr l`

    qprzzrq

    z

    ^~

    z

    yR

    #

    aesrzprzzsadcoh{auq`bae`b|rzp`woh{x nqxhNlr{woxnqph0jhkwhuq`co`woxs|vhkwhadnj`wol

    m

    fbs`[fbr{wejr{wh{puq`h{|q

    xh{a`x nq|}f{h{ruq`ae`bntj`baerq

    `uq`|qr{ch{xyrzajr{whgaenj`wo l

    m

    fs`fbr{wdjr{wh{pq`b|cbh{rq

    5

    #

    rz|quq` l`rj`baer`x !nqsprzatuqr h{|qxh{p`

    5

    l`nqxhfrz|qadch{|co`^!nq`^uq`j`b|quq`Ruqr h{|q

    xh{pj`woxy`b|ch{psx`b|ce`{ l`fbrz|qq`bfsuqr!nq`

    5

    z

    jhkwh !nqxyh{|qrzat`

    5

    z

    jhkwh

    jqwoxhkch{ab r{w`$q`bxjvprqqnqx qrzx`bxuq`

    {

    !nqsprzaco`x nqxhaenj`wo l

    m

    fb`fbr{wdjr{wh{phkjqworiqsxyh{uvh

    uq`

    {

    z 1

    {

    #

    zz

    # nqxhfwoh{|}fihRuq`

    nqpsrzaco`bx nqxh^aenj`wo l

    m

    fs`

    fbr{wejr{wh{phkjqworiqsxyh{uvhuq`

    z 1

    #

    # v`cofk

    z&1

    #

    z 1

    #

    #

    z 1

    #

    z

    #

    {

    z 1

    {

    #

    zzz

    #

    z

    z 1

    z

    #

    N

    #

    z 1

    #

    #

    z 1

    #

    {

    #

    k

    `dh

    8`LhYwo`b{whnq` h{adaerfbshhYfih{uvh|lnqxy`worwo`bh{p 0rae`nfbnrqsadcorl`k

    r{wg`q`bxgjvpsrq h{r^|lnqxy`wer

    h{aeaer!fbh{xrzar|lnqxy`wer

    h{r|lnqxy`wer

    h{aeaer!fbh{xrzarg|lnqxy`wory

    vh{r|lnqxy`wer

    h{aeadrfbsh{xyrzarg|lnqx`wor

    h{r|lnqx`wor

    -

    h{adaerfbsh{xyrzar|lnqxy`wor

    -

    -

    v`cof{

  • ! "

    ~

    d

    -

    -

    #

    -

    -

    zb

    `dh

    - `+th[wo`b{wh!nq`h{aeadrfbsh0hfih{uvh|lnqxy`werwo`ih{p

    aenvhwh{nvh{uwoh{uvh

    sacor l`{

    r{w`q`xjvpsrqqh{r|lnqxy`wer

    h{aeaerfh{xyrzar|lnqxy`wor

    vh{rg|lnqx`wor

    h{aeaer!fbh{xrza

    r |lnqxy`wort

    #

    `h{r |lnqxy`wor

    |~h{rjruq`bxyrza+h{adaerfbshkw+|q`b|qnqx;|lnqx`wor wo`ih{p

    jrzab

    |~h{rl`nqx |lnqxy`worwo`ih{p

    s|quq`v|qsuqr

    #

    -

    -

    -

    -

    -

    -

    ` dh

    `hae`bznqs|co`[nq|}f{h{r

    # ae`

    ae`

    r |lnqxy`wor

    h{aeadrfbsh{xyrzar |lnqxy`wor

    #

    h{r |lnqx`wor

    h{aeadrfbsh{xyrzayr

    |lnqxy`wer

    h{rg|lnqxy`wor

    h{aeaerfh{xyrzar|lnqx`wor

    #

    v`cef{

  • de [+

    ~

    #

    #

    d

    d

    #

    k

    ` dh

    `hae`bznqs|co`[nq|}f{h{r

    ad`

    ad`

    r{w+``bxjvpsrqh{r |lnqxy`wor

    h{adaerfbsh{xyrzar |lnqxy`wer

    h{r|lnqxy`wer

    h{aeadrfbsh{xyrzar

    |lnqxy`wer

    h{ry|lnqxy`wer

    h{adaerfbsh{xyrzary|lnqxy`wor

    jrzsa

    l`[wewh{fsrz|vh{p

    !

    _rza`$q`bxjvprza

    k

    k

    k

    k

    zb

    `

    h{anq|}fkrz`baabh{ruq`v|qsuvh{ajr{w`b!nvh}f{rz`ba

    !nq`r{wo|q`bfb`x

    !nvh{|quqr0abh{r0hkcewovnqsuqrzakh{psr{we`bah_r0`q`xjvpsr

    !hnq|}f{h{r|~h{rRl`uvh{uvh

    jr{wnqxh0`b!nvh}f{h{rqvxh{abqhuq`v|qd}f{h{ruq`[nq|}f{h{rl`[aohkcesae`bchxz`wh{pq|q`bx coruvh{ah{anq|}f{rz`ba

    abh{rg|q`bfb`baeaehkwoh{xy`|co`k uq`v|quvh{auq`xyh{|q`bwh`jvp l

    m

    fchr{w`q`bxgjvpsrq

    `{uqnwh{|ce`r`wih{ruq`

    zz

    !|qrsruq`h{|q`bworq!we`bzsadcdwlh{aeae`bxrzah[co`xj`wohkconwhxlh sxh

    rfr{wewosuvht`bx/fih{uvhYuqshr{qco`wil

    m

    h{xyrzanqxhnq|}f{h{rqL+`yhkcorqhtfih{uvhYuqh`adclhYh{aeadrfbsh{uqrnqxh

    lnq|qsfbhco`bxgj`whkcenwhx lh qsxyhsadcorl`{hco`xj`wohkconwhl`tnq|}f{h{r^uqruqsh x0r{wh|~h{r^`$qsach

    nqxhYNlr{woxnqpshY`jvp l

    m

    fbchjhkwh`jqwe`baeaohkwghnq|}f{h{ruqr`$q`bxjvpr

    huq`v|qd}f{h{ruq` nq|}f{h{r l`

    aohkcoae`bch

    x z`wh{p0h xh{sr{wehuvh{anq|}f{rz`banqaoh{uvh{a|vh{ahkjvpsfih}fkrz`baabh{ruvh{uvh{ajr{wNlr{woxnqph{arzn

    `b!nvh}f{rz`bab

    s

    l

    jqwo`bfbaer[co`w nqx=jrznqfbruq`fbnqsuvh{uqrqzjrzsa|q`bx=coruvh+`bnvh}fkh{r[uq`uqnvh{akhkwoblhk`bsauq`v|q`nqxh

    nq|}f{h{rq r{w`$q`bxjvprqh`bnvh}fkh{r

    #

    L|~h{ruq`v|q`nqxhnq|}f{h{rqjrzsa jhkwoh

    co`xyrza uqrza

    kh{psr{wo`bajhkwh

    hgaohk`wi

    g

    xyh{a

    #

    ulhr{woz`bx hguqnvh{anq|}fkrz`bab

    g

    `

    #

    ruq`xyrza+sxh{z|vhkw+nqxhLnq|}fkh{rfbrzxyrLnqxh xlh{nq|vhnq`ncospsih nqxhfb`wecohtxhkcl`wohyjqwoxh

    |jvnc$jhkwh`bpshkr{whkw+h{pznqx jqwor!uqncoryv|vh{przncdjvnc$`r fbrz| nq|cor uqrza|lnqxy`worzawe`ih{safrzxyr

    nqx uq`jlrzaecor uq`xhkcl`wosh{ajqwoxh{ab

    sfih `suq`b|co`nq`3l`nq|quvh{xy`|ch{puq`co`woxy|vhkwi`vhkch

    xy`b|co`{|q`baco`uq`jlrzaecorqnvh{pxhkcl`wohLjqwosxhYh{ nq|qfbrz|vhkw|qrzaeaohxlh{nq|vh fih{aerfbrz|cdwlhkwosrq

    fbrzxfb`wdco`bih hg`bacewh{hkwo`bxrza q`badchgh{|vh{psrzzsh|qrzaps`khh{aae`bznq|co`auq`v|qd}fkrz`bab

  • !

    x f(x)

    [+k

    fbrz| nq|coruq`coruqrzarzanq`aohkcoaeh{b`bxhuq`v|qd}f{h{r+uq`nq|}f{h{rl`fvh{xh{uqr

    +

    L

    `l`[uq`b|qr{coh{uqrjr{w ^ ~

    s

    frz| nq|coruq`coruqrzarza

    t coh{sanq`

    ~Nrz|quq` ^ ~l` fvh{xh{uqr

    L

    `l`[uq`b|qr{coh{uqrjr{w!^ ~

    l

    fphkwor!nq` ^ ~R ~`!nq` ^ ~l`rfbrz| nq|corguqrza {h{pr{wo`bauvhkhkwoilhk`p |quq`

    j`|quq`b|ce`jhkwh+rzanvh{al`uq`v|quvh R ~l`r+fbrz| nq|coruqrzakh{psr{wo`bauvhkhkwoilhk`bpuq`j`b|quq`|co`

    fih{pfbnqph{uqrzahjhkwecowuqrza`bp`bxy`b|corzauqryuqrzxl

    m

    |qrq

    +nvh{anq|}fkrz`ba`abh{rguqch{a

    v

    ad`[co`bx rgxy`baexr0uqrzxl

    m

    |qr `~

    ~~$jhkwh

    cor!uqrL2jr{w[`q`xjvpsrth{a[nq|}fkrz`ba0

    #

    q

    `~

    #

    e abh{ruq`wo`b|co`ba

    jrzaad`bnqauqrzxl

    m

    |qsrzaabh{ruq`wo`b|co`ba

    |co`bauq``wh{pznq|qa`q`bxgjvpsrzabrzpch{xyrzahs|qaeadcownq`jhkwh`baconquvhkwnvh{ps!nq`wnq|}f{h{rqquq``

    xyrzaae`bxgjqwo`uq`ce`woxy|vhkwrzafbrz| nq|corza ^ ~`^ ~

    b

    lhkwo`ihuq`nqx fzl

    m

    wofnqpsruq`wh{sr* l`[ {

    "!

    +# ad`b|quqryrgwoh{srqco`bxrzab

    vprzzrq

    ^

    ^

    -

    rz|qaeuq`wo`yh nq|}f{h{r

    Y

    ~

    # l`fbphkworLnq`|~h{r`$qsaco`bx wo`bacewod}fkrz`ba[jhkwhLrt|lnqx`wor

    wo`ih{p~vpsrzzrqco`bxrza!nq`{

    NR ~

    `

    #

    jhkwh coruqrt `b|cih{rR ~

    - fbrzxyrLcoruqrt|lnqxy`wortwo`ih{p

    jrzadaenqwoh{snvh{uwh{uvhv`b|cih{rq

    ^ ~

    -

    k

    rz|qaesuq`wo`+hnq|}f{h{r

    xhwoh{s!nvh{uwh{uvh`sadce`aerzxy`|co`ae`

    !`b|cbh{rq

    ^ ~

    - |qrNkh{xy`b|co`{vfbrzxyr`bx

    co`bxyrza

    !^ ~

    -

  • " de [+

    rz|qaeuq`wo`Rh nq|}f{h{r

    ~

    #

    rzxyr |qrfih{aer h{|co`wor{wi

    #

    `$qsaco`

    aerzxy`|co`ae` #

    qwo`aerzp`b|quqryhgs|q`nvh}f{h{rco`bxyrzab

    ^ ~

    i

    bR

    - `k|qrkh{xy`b|co`{qco`bxyrza

    !^ ~

    -

    rz|qaesuq`wo`0hnq|}f{h{r

    g

    l`fbpshkworynq` l`uq`v|qsuvhyae`[`aerzxy`b|co`ae`

    przzr

    co`bxrza!nq`{

    NR ~

    -

    jr{wrznceworgph{uqrqvnqxhwh}f{h{rl`|nqphae``adrzxy`b|co`[ad`r|nqxy`woh{uqr{wtl`|!nqpr `|cih{r

    R ~

    k

    rz|qaesuq`we`hnq|}f{h{r

    #

    frzxyr|qr0fih{aerh{|co`wosr{wr0uq`|qrzxys|vh{uqr{wuvhwh}f{h{r

    |~h{rgjruq`[ae`w|nqpsr vprzzr

    #

    v`b|cih{rqq

    `{

    NR ~

    ^ ~

    rz|qaeuq`wo`thnq|}f{h{r

    fbrzxrhwh{s flnvfih^uq`Lnqx |lnqxy`worjrzaecorrzn

    |q`bhkcor l`+jrzaecokhrznY|q`bhkco{h

    ^ ~

    !^ ~

    k

    rz|qaeuq`wo`h+nq|}f{h{r

    ~

    -

    #

    nq|}f{h{rl`uq`v|quvhae`

    ` #

    aexnqpch{|q`ih{xy`|co`k `baerzp`b|quqrh{a|q`bnvh}fkrz`babvr{qco`bxyrza

    qpsrzzrq

    ^ ~

    - `

    !^ ~

    -

    zr{whnq`uq`co`wexys|vh{xyrza~|qrza``bxjvpsrzarzauqrzxl

    m

    |qrza` xh{z`b|qauvh{anq|}fkrz`babkjruq`bxyrzahi{h{phkwi

    ae`bxj`woszrqq`bach{anq|}f{rz`ab

    b

    `t~

    `b|cbh{rR

    !

    !

    `L # -

    #

    -

    jrzsa #/-

    l`

    ae`bxgjqwo`jrzaecerq

  • !

    `+~

    vfih{psfnqph{xyrza

    $ad`

    `~

    -

    -

    l

    ch{x0l`bx fbrzxnqx |qrzagco`cerzaguq`tlh{pfbnqpsrRuq`|qr{chkwh{agnq|}f{rz`bayfbrzxr IC rz|quq`k

    NR ~

    JLKJ

    E

    P

    TU

    VO

    1

    Q

    6

    T

    7

    U

    O+V

    we`jqwo`bae`|ch}fkh{rz`brzxl`cewesfihuq`nqxhnq|}f{h{ruq`nqxyhkhkwoilhk`pwe`ih{pl`uvh{uvhgjr{wae`n

    ~

    |qrgjvpsh{|qryfbr!r{wouq`b|vh{uqrg

    [+k

    {wlhkvfryuq`[nqxyhgnq|}f{h{r

    ~yl`[rgae`bznq|co`[aenfrz| nq|coruqrgjvph{|qrq

    ~

    !$~de ^ ~

    +`brzxy`cdwosfih{x`b|ce`

    ~tl`{`bx z`woh{p ~nqxh fbnwekhL|qr jvph{|qrq_rza`$q`bxjvprza

    b

    k

    `

    uvhgad`}f{h{r

    ~|~h{r l`nqxhfbnwekh_rzafih{aerza`bx !nq`

    ~yl`[nqxhfbnwekhs|conqco{h{x`b|ce`

    jr!uq`bxyrzaj`b|qaohkwgnq` rzafbrz| nq|cerza ^ ~`!^ ~[wo`jqwo`bae`b|ch{x hdphkwoznwh`eh{pcenwh

    xlh sxhuvhfnwe{hqwo`adj`bfcokh{xy`b|co`{

    |qsfh{psx`b|ce`{hLfrz|qadcewon}f{h{rtuqrza[{wvlhkvfbrza[ad`wlhwo`ih{psih{uvh h{b`b|quqrYnqxhychk`bphrz|quq`gh{a+`b|

    cewh{uvh{a0uvhYchk`bphYah{rrza0`bps`bx`b|cerza0uqruqrzxYl

    m

    |qsr` h{a0aohql

    m

    uvh{abh{awo`adj`bfcokh{a0sxh{z`|qabYaco`

    jqwor!fb`baeaer^l`uq`bxyr{wh{uqr[`s|q`vfs`b|co``ad`wlh0hkh{|quqrz|vh{uqr0|qrzafihkjl

    m

    conqpsrza ae`bznq|co`abnvh{|quqr0ad`wih{r

    uvh{uvh{acl`bfb|qfih{axh{sa`vfs`b|co`ba+jhkwh h{b`w[rL{wvlhkvfbrq

    l

    xjr{wecoh{|co`|~h{rtfbrz|qnq|quqwh nq|}f{h{r

    fbrzxae`bn{wlhkvfbrqqjrzar{wvlhkvfbr l`nqx adnfbrz| nq|coruqrjvpsh{|qrq

    b

    adrfb`r{wlhkvfbr uvhynq|}f{h{rLuvh{uvhj`bpsh ad`bznqs|co`chk`bph nq`xyrzacewhhkh{{h{rae`bxh{|vh{puq`

    lh{znvhguq`[nqxh0wo`jqwo`baeh

    +h

    z

    zz

    {

    {

    {wlhkvfrguq`bachgnq|}f{h{r|~h{rwo`jqwo`bad`b|cohnqxh0fbnwekh

    jqwoxy`bwh0fbrzpsnq|vhuvhcohk`bpsh0we`jqwo`bae`|ch

    hgr{weuq`b|vh{uvh`hae`bznq|quvhfrzpsnq|vhh{awo`badj`bfco{h{ahkvaefbaeaoh{a psrzzrqqr{qco`xyrzab

  • de [+

    1 2 3 4 5 6 7

    200

    400

    600

    800

    1000

    adr!fb`rg{wlhkvfbrguvhnq|}f{h{r

    #k NR ~

    ` ^ ~

    h{b`b|quqrhchk`bpsh

    ~

    #

    #

    jhkwh coruqr rza+jrz|corzauq`hkvaefbaeaoh{a[ `L ce`bx;htxy`badxhr{wouq`b|vh{uvh

    Y

    #N

    rzzrqr{wlhkvfbr uq`vfbh adconvh{uqr|qrjqwoxy`bwery`ae`bznq|quqrLnvh{uwoh{|co`k

    vad`wekh{|quqrhchk`bph

    fbrz|qfbpnq ae`!nq`ae`r[kh{psr{wuq` Nh{nqx`b|coh!rza{h{pr{wo`bauvh[fbr{wdwo`badjrz|quq`b|ce`r{wouq`b|vh{uvhh{nqx`b|coh{x

    xh{awhkjvuvh{xy`b|co`{

    `yrza[{h{pr{wo`bauq` hkjqwersxh{xg ae`ghb`worqrza[kh{psr{wo`ba[fbr{wewo`adjrz|quq`b|co`ba

    uvhgr{weuq`b|vh{uvhyhkjqworiqxh{xgad`xyh{sawhkjvsuvh{x`b|ce`[uq`[b`worq

    {wlhkvfbruq`l`{

    -1 -0.5 0.5 1

    0.2

    0.4

    0.6

    0.8

    1

  • !

    #

    k

    adr!fb`rg{wlhkvfbrguvhnq|}f{h{r

    NR ~

    R ~

    h{b`b|quqrhchk`bpsh

    ~

    `

    `b|cih{r

    `ae`

    `b|cih{r

    rzzrq ry{wlhkvfbr`adclhyaeconvh{uqry|qryjqwoxy`bwery`

    co`wefb`bwerynvh{uwh{|co`ba

    vae`wd{h{|quqrLhchk`bphq`bxyrzanq`[nvh{|quqry

    `fwo`baef`{rzakh{psr{we`ba

    fbr{wewe`badjrz|quq`|co`ayuvhr{weuq`b|vh{uvh

    coh{xl`xCfwo`baef`bx `txh{awhkjvsuvh{x`b|ce`{nvh{|quqr

    `

    uq`bfwo`aefb`{rza[kh{psr{we`bafbr{wewe`badjrz|quq`|co`auvhtr{wouq`b|vh{uvh

    uq`bfwo`badfb`bx`yxyh{sa+whkjvsuvh{xy`|co`k

    {wlhkvfbrguq`0l`{

    -1 -0.5 0.5 1

    -1

    -0.75

    -0.5

    -0.25

    0.25

    0.5

    0.75

    1

    adr!fb`rg{wlhkvfbrguvhnq|}f{h{r

    NR ~

    R ~

    h{b`b|quqrhchk`bpsh

    ~

    z

    z

  • de [+

    `

    3

    `b|cih{r

    `ae`

    `b|cih{r

    rzzrq ry{wlhkvfbr`adclhyaeconvh{uqry|qryjqwoxy`bwery`

    co`wefb`bwerynvh{uwh{|co`ba

    vae`wd{h{|quqrLhchk`bphq`bxyrzanq`[nvh{|quqry

    `fwo`baef`{rzakh{psr{we`ba

    fbr{wewe`badjrz|quq`|co`aguvhr{wouq`b|vh{uvh

    hkjqwersxh{xg ae`uq``wor` hxy`buqsuvhY!nq`y hkjqworiqxh ad`uq`

    b`werqrzakh{psr{we`bafbr{wewo`adjrz|quq`b|co`bauvhr{wouq`b|vh{uvh

    h{nqxy`b|ch{x xnqcorq nvh{|quqr

    `fwo`baef`{

    rzakh{psr{wo`bafbr{wdwo`badjrz|quq`b|ce`bauvhr{wouq`b|vh{uvh

    uq`bfwo`baefb`x ` h0xy`buquvh0nq`Yuq`fwo`baef`{ rzakh{psr{we`ba

    fbr{wewe`badjrz|quq`|co`auvhgr{wouq`b|vh{uvh

    hkjqwersxh{xg ae`uq``worq

    {wvlhkvfbruq`l`{

    -3 -2 -1 1 2 3

    -3

    -2

    -1

    1

    2

    3

    adr!fb`rg{wlhkvfbrguvhae`bznq|co`[nq|}f{h{rY

    ~

    R

    #

    ae`

    ae`

    # - ae`

    -1.5 -1 -0.5 0.5 1 1.5

    -0.4

    -0.2

    0.2

    0.4

    k

    +`ce`woxy|q`hnq|}f{h{rLfn ry{wlhkvfbrl`k

  • !

    -1 1 2 3 5

    2

    phkwh{xy`|co`k~

    ae`[

    `[

    +`co`woxys|q`xyrzarzaae`bzx`b|cerzauq`[we`chg!nq`psh{xrza

    jrz|corza

    `

    $

    `y

    wo`baj`bfcekh{xy`b|co`{

    `nvh}f{h{rguvhwo`cohgnq`jh{aeaohjr{w

    `

    l`

    s

    `b!nvh}f{h{ruvhgwe`chg!nq`jh{adaohgjr{w

    `

    l`

    q`b|cih{rq

    ~

    ae`

    ae`

    ae`

    ae`

    ay{wvlhkvfbrzauq`~ -

    -

    `Y

    t

    Ljr!uq`bx ae`w

    r{qcouqrzauqwo`ch{xy`|co`uqry{wlhkvfruq`0~+`hkcorq

    {wlhkvfbrtuq`~

    -

    jruq`ae`w[r{qcosuqrthLjhkwecewuqr{wlhkvfruq` cewoh{|qaeph{uvh{|quqrk rYh{r

    psrz|qzr uqr `b qruqrzaR`bx

    nq|qsuvh{uq`ba+jhkwh h`bae!nq`wouvh ae`

    rzncewh{|qaepsh{uvh{|quqrkrth{rLprz|qzr

    uqr`qrguqrza`bx

    nq|qsuvh{uq`bajhkwhhuqwo`chae`

    {wvlhkvfbruq`~

    ~ -

    jruq`ad`wr{qcosuqruqr{wvlhkvfbruq`Lcewh{|qaepsh{uvh{|quqrkrh{r

    psrz|qzrguqr`b qrguqrza

    `bx

    nq|qsuvh{uq`bajhkwhfbxhad`

    rzn

    nq|quvh{uq`bajhkwhh{rgae`

    {wlhkvfbruq`~

    ~$

    jr!uq` ae`wr{qcouqr z`bacosfih{|quqrk ae` r{wlhkvfbruq``wecofih{psx`b|ce`

    j`psrhkcer{w

    {wlhkvfbrLuq`0

    ~

    jruq`ae`wr{qcosuqr zfbrzxjqwesxy|quqrkae` rL{wlhkvfbrLuq`y qr{wo

    brz|ch{psx`b|ce`j`bpsrghkcor{w

    {wlhkvfbrYuq`g~

    ~$

    jruq`gae`w0r{qcesuqr zfbrzxgjqwosxy|quqrkae` rY{wlhkvfruq`

    `wecesfih{pxy`b|co`j`bprhkcor{w

  • de [+

    {wlhkvfruq`Y~~

    jr!uq`ae`wtr{qcosuqr z`badcesfih{|quqrk ae` r {wlhkvfruq`

    qr{wobrz|coh{psxy`b|co`+j`bprhkcor{w

    {wlhkvfbrguq`+~

    jruq`ae`wr{qcosuqrj`bpshwo`v`~h{rguqr{wlhkvfbrguq`0`bxcor{wo|qruqry`br

    uqrza

    {wlhkvfbrguq`+~

    jruq`ae`wr{qcosuqrj`bpshwo`v`~h{rguqr{wlhkvfbrguq`0`bxcor{wo|qruqry`br

    uqrza

    xfih{uvhfih{aerl`fbrz|`b|qs`|co``badj`fbvfihkwrzauqrzxYl

    m

    |qsrza`xh{z`b|qab

    b

    _+hy`bae!nq`wouvh~rza{wlhkvfrzauq`

    h{bnqp uq`

    ~

    `woxy`bpqr`

    -

    -

    `wouq`i

    _+huqwo`bchvrza{wlhkvfrzauq`

    g

    #h{bnqpvuq`

    -

    -

    #`woxy`bpqr

    `

    g

    y

    #`wouq`

    -1-2 1 2

    -2

    -1

    1

    2

    -3 -1-2 1 2

    1

    k

    aY{wlhkvfbrzatuq`

    h{bnqp$uq`

    -

    -

    `wox`bpsqr`

    `wouq`

    -1-2 1

    -2

    -1

    1

    -2

    ae`znqwuvhkwe`bxyrza+lhkworza[``bxjvprzauq`nq|}fkrz`babfbrzx;ae`bnqawe`badj`fcorzauqrzxl

    m

    |qrzabxh{z`b|qa`

    {wlhkvfbrza

    sul`hl`r{woxyhkwnqx zfbhkclh{psrzzr +uvh{anq|}f{rz`baxyh{sanqaoh{uvh{ab!h{anvh{saae`wbh{r[ncopsih{uvh{a

    |qrza`$q`bxjvprza```wofzl

    m

    fbsrzab

  • !

    JLK

    :XO[Z \^]

    U

    V O

    1

    Q

    6

    T

    7

    U

    O+V

    e

    achgnq|}f{h{rl`uq`v|quvhgjr{wi

    rzxyr[r{h{pr{w hkvaerzpsncor[uq`nqx |lnqxy`worwo`ih{pl`ae`bxjqwo`|~h{r|q`bhkcerqzco`bxyrza!nq` ^ ~

    R ~

    - `ad`bn {wlhkvfbr l`fbrz|qadcoconqsuqruq`+uqnvh{aae`bx we`ch{auq`fbr!`vfbs`|co`ah{|qznqpshkwo`ba

    `

    vwo`badj`bfco{h{x`b|ce`{vnq`ae`|co`woae`bfcoh{x `bx/

    -2 -1 1 2

    1

    2

    vae`we`nq`rza{wlhkvfbrzauq` ~ b`uq` jruq`bx ae`w r{qcouqrzauqr{wlhkvfbruq`~$+`hkcorq

    ~~

    ~ l`[r{qcosuqrgwo` v`co|quqrhkcewhi l`auqry`b qrguqrza |qrjqwesxy`bwor`ae`bznq|quqr!nvh{uwh{|co`ba

    hjr{wz}f{h{ruqr{wlhkvfruq`nq``badce`dhg|qrco`wofb`worg`[!nvhkwecornvh{uwh{|co`bab

    rzxr`$q`wof{l

    m

    fbrqquqsh

    fbrzxyrjr!uq`ae`wr{qcouqrrg{wlhkvfbryuq`

    adrfb`rza{wvlhkvfbrzauq`+

    y

    -

    `uq`~

    `dh

    (przzrq~

    -

    `|cih{rqr0{wlhkvfbr0uq`l`r{qcouqrhjhkwecowuqr0{wlhkvfbr

    uvhnq|}f{h{rgcewh{|qaepsh{uvh{|quqrkr[h{rpsrz|qzruqr+`br+uqrzay`bx

    nq|quvh{uq`jhkwohhuqwo`bch`

    nq|quvh{uq`ba

    jhkwhyfbxh

    {wlhkvfbrl`0fbrz|qacoconquqruq`0uqrzsaad`bzxy`b|corzauq`wo`coh{auq`0fbr`vfbs`b|co`bah{|qznqpshkwo`ba

    `

    jh{adaoh{|quqryjr{w0

    `

    qwo`badj`bfco{h{x`b|ce`{r{wrznceweryph{uqr~

    wlhkvfbrza

    uq`` wo`baj`bfcekh{xy`b|co`{

  • de [+

    -2 -1 1 2 3 4

    1

    2

    3

    4

    5

    -1 -0.5 0.5 1

    0.05

    0.1

    0.15

    0.2

    JLKLKJ

    1

    Q

    6

    T

    7

    U

    O+V

    U

    ]iSiQ

    U

    Z S

    SV

    1

    Q

    6

    T

    7

    0U

    U

    ]iSiQ

    U

    Z S

    ] O SiZ O[S

    U

    U

    @

    P Z

    achgnq|}f{h{rl`uq`v|quvhgjr{wi

    ~

    *-

    rz|quq`

    ^ ~

    R ~

    aoh{|quqr hyuq`v|q}f{h{r uq`0uqsadc h{|qfbhy`b|cewo`jrz|cerzauqryjvph{|qr|~h{rl`uq l

    m

    fbpjqworkhkw+nq`uvh{uqrzacewi`ba

    jrz|corza|qr{wlhkvfruq``badce`baabh{rfbrzps|q`ihkwo`a r{wlhkvfbr uq` l`0hwe`chyuq`0fbr!`vfbs`|co`h{|qznqpshkw

    jh{adaoh{|quqrjr{wL

    Lwo`bfbjqworfih{x`b|ce`{uvh{uqrza0uqrzsajrz|cerza0nq`yuq`ce`woxy|q`bxnqxhtwe`ch

    |~h{rg`wecosfbh{p`$qsaco`[nqxyhnq|}f{h{ryhkvx fbn r{wlhkvfbr l`hwo`ch`wov!nq`

    jhkwhgceruqr

    s+

    -N

    -

    - `bx z`wh{p

    5

    -

    5

    -

    jhkwhcoruqr

    5

    rzzrq

    $v

    v$

    r{woxh{x nqxhjqwerz{wo`baeabh{rhkwocexl`cofihuq`

    wh{{h{rg

    s

    jqwor{jqwo`buvh{uq`nq`fihkwh{fco`wosihh{anq|qf{rz`bajrzps|qrzxysh{sauq`jqwoxy`bwer{wh{n^l`{- q

    uq`j`b|quq`hkj`b|vh{auq` sadcorRl`+hh{fwl`aefbsxrzasznvh{sauvh{uqrzahfbr{wewo`adjrz|quq`bx h{fwl`baefbxyrzasznvh{a

    jhkwh

    l

    `badcohgfihkwh{fco`wl

    m

    adcosfbhgnq`uq``[ae`wncespsih{uvhg|vh{ahkjvpsfih}f{rz`ba

    q +nvh{|quqrg

    hnq|}f{h{rl`+fvh{xh{uvh

    ~

    `ae`bnt{wlhkvfbr l`+nqxh0wo`cohjhkwh{p`bphh{r

    `b qruqrzanq`jh{aeaohgj`bpsrjrz|cor

    b

  • !

    copssbh{|quqrYhr{vae`we{h}fkh{rYuvhjlh{zs|vh

    `bae!nq`wouvhrza[{wlhkvfbrzauq`y

    -

    h{bnqp

    `

    ~

    -

    `wexy`bpsqr`

    ~

    -

    pspilh{ao wo`adj`bfcokh{xy`b|co`{

    uqwe`bch rza

    {wlhkvfbrza[uq`

    -

    h{bnqp`

    -

    `woxy`bpqr`

    psspblh{a

    wo`baj`bfcekh{xy`b|co`{

    -2 -1 1 2

    -1

    1

    2

    -1 1

    -1

    1

    2

    v nvh{|quqr

    r{qco`bxyrza0nqxGcojrxjr{wdch{|ce`yuq` nq|}f{h{rq fvh{xh{uvh

    d

    r{wech{|corqvhnq|}f{h{rps|q`ihkwLl`uq`v|quvhjr{wi

    `l`xyruq`bpr xhkco`bx lhkcosfbrjhkwh we`baerzp`wLjqwer{vps`bxh{a!nq``b|rzp`bx jqwor{jr{wofbsrz|vh{psuvh{uq`{

    `bn

    {wlhkvfbrl`[nqxh0wo`cohguq`fr`vfb`b|co`0h{|qznqphkw jh{aeaoh{|quqryj`bphr{wosz`xY

    hkwhcoruqr

    q

    #

    t

    -

    #

    -

    #

    s

    -3

    `bxz`woh{p +~

    jhkwhYcoruqrYF`

    s nvh{|quqry

    co`bxyrzab

    nq`l`[fvh{xh{uvhnq|}f{h{r

    q

    `bn{wlhkvfr l`nqxhwo`chguq`[fbr`vfs`b|co`h{|qznqpshkw

    b

    njrz|qvhy!nq`rzaad`bznqs|co`bauvh{uqrzar{woh{xWfbrzp`ch{uqrza|nqx `j`wesxy`b|corq

    `0hco`br{woshaendh

    fb`b|co`hg`j`wo `b|qfbshgs|quqfihg!nq`[rzauvh{uqrzace`bx nqxhgfr{wewo`bpsh}f{h{rgps|q`ihkwb h{fq`+ch{pnq|}f{h{ryps|q`ihkwi

  • " de [+

    z

    z

    `dh

    ~

    '

    - N `ph{ajqwor{jqwos`uvh{uq`bauvh{anq|}fkrz`baps|q`ihkwo`ba

    '

    -

    '

    -

    `aerzp`b|quqrraeadco`bxhqr{qce`bxyrzab

    '

    `

    vpsrzzrq~

    -10 10 20 30 40

    -50

    -25

    25

    50

    75

    100

    _r{co`nq`+j`bpsh{ajqwer{jqwos`buvh{uq`auvh{anq|}fkrz`baps|q`ihkwo`bavjruq`bxrzacorzxyhkwnvh{ps!nq`wjhkwuq`jrz|corza

    `r{qco`bxyrzarxy`aexyrwo`baenqpch{uqr qjr{w`q`bxgjvpsrq

    z

    '

    -

    '

    -

    hk`bxyrza!nq`hjqwo`aeabh{ruvhlh{znvh0uqrxhkwl`+nq|}f{h{rguvh0jqworznq|ququvh{uq`{+`b|qr{co`bxrzajr{w =h

    jqwo`badabh{rg`Ghjqworznq|ququvh{uq`wo`phkco{h0h{r|l

    m

    `puqrxhkwij`wesxy`b|ch{pxy`b|co``wevfih ae`+nq`+h

    jqwo`badabh{ruvhlh{znvhgh{r|l

    m

    `p~uqrgxhkwl`+uq`

    '

    '

    hkcoxrzae`wh`nq`h{fwl`aefbsxrzaznvh{sa|vh

    jqworznq|ququvh{uq`0fbr{wewo`bajrz|quq`bxWhyh{fwl`badfbsxyrzasznvh{a|vhjqwo`baeabh{rq rzzrqh{rgjh{aeaehkwuq`nqxjrz|cor

    uqrxhkwjhkwhrznceweradconvh{uqrh

    xy`cdwor[uq`jqworznq|quqsuvh{uq`k vhi`wlhnqxCh{nqxy`b|coruvh

    jqwo`badabh{r^uq`thkjqworiqsxyh{uvh{xy`b|co`

    '

    h{aeaeh{|quqr^uqr^|~l

    m

    `bpuqrxhkwghnqxhjqworznq|ququvh{uq`uq`

  • !

    Ihjqwo`baeabh{rh{nqx`b|cohkwlh

    1g

    jqwo`badabh{ruvh lh{znvh`bxFhkcoxyrzae`wh{abl`uvh{uvhj`bpshnq|}f{h{r

    jrzps|qrzxysh{puqrgjqwesxy`bwor{wh{n~

    &1

    -

    20 40 60 80 100

    2

    4

    6

    8

    10

    jqwe`baeabh{ryuvhlh{znvhhgnqxyhjqworznq|ququvh{uq`0uq`

    z

    l`

    z

    1Rz

    -

    z

    '

    `hjqwo`baeah{ryuvhlh{znvh l`uq`

    '

    vhjqworznq|ququvh{uq`l`

    &1

    -

    przzrq

    k

    hk`ad`Ynq`

    z

    {wh{xh{aouq`aerkdh^fbrz|co`bx

    uq`tjqwer{co`zl

    m

    |vh{ag`

    z

    uq`tps`b|cospvh{a

    fbrz|co`bx

    uq`tjqwor{co`{l

    m

    |vh{abx h{uqnqpcor^xl`buqsr|!nqx fbpsxhxyruq`woh{uqr^|q`bfb`aeaecohRuq`

    {

    uq`

    jqwor{co`{l

    m

    |vh{auqblhkwoh{a[`bx;aenvhh{psxy`b|ch}f{h{rqxyh j`baeaerhYuq`bad`dhYjqworN`w`badcoh{a

    {

    uq`jqwor{co`{l

    m

    |vh{a

    aerzxy`|co`fbrzx aerkdh`

    rznps`|copsvh{ab

    `l`hnvh{|couvh{uq`uq`aerkdh`

    h!nvh{|cesuvh{uq`uq`ps`b|cospvh{a

    uqilhkweh{a`

    xy`uqsuvh{a`bxnq|qsuvh{uq`bauq`

    z

    q!nvh{pl`hwo`bph}fkh{r`b|cewo``

    !nvh{|cesuvh{uq`uq`jqwor{co`{l

    m

    |vh|vh[adr{dhl`

    `hnvh{|cosuvh{uq`uq`jqwor{co`{l

    m

    |vh|vh{a ps`b|cospvh{al`

    jr{w

    uqh h{x0h{axy`buquvhL`x {wh{xh{a

    cor{coh{puq`0jqwor{co`zl

    m

    |vh{a[uqblhkwosrl`

    {

    psrzzrqco`bxrza+hL`b!nvh}f{h{r

    uq`[jqwesxy`bwor{wh{n~

    -

    {

    `{

    ~

    -

    {

    0.5 1 1.5 2

    0.5

    1

    1.5

    2

    2.5

    ajrz|cerzauqr{wlhkvfbrabh{rh{ajrzaeail

    m

    `bsafrzxv|vh}f{rz`bauq`aerkdh`p`b|cospvh{ajhkwhr{wo|q`fb`w

    {

    {woh{xh{auq`[jqwor{co`{l

    m

    |vh{auqilhkwosh{ab

  • de [+

    `buq`rr`$

    `[nqx j`baerguq`[nq|quvh{uq`bar{wj`b|quqnwoh{uqr`bxnqxhxrzph0`badchae`h{prz|qh

    `bx nqx kh{psr{w

    !nq`l`uqwo`ch{xy`|co`jqwor{jr{wefbsrz|vh{phg adcorl`{

    y

    5

    frz|qadch{|co`

    5

    uq`j`b|quq`uvhgwozsuq`buvhgxrzphtnvh{|corxyh{sawl

    m

    zuvhr{whgxyrzpshxy`b|qr{wae`wvlhgrgkh{psr{wuq`

    5

    $

    1

    Q

    6

    T

    7

    0U

    U

    ]iSiQ

    U

    Z S

    ] O

  • !

    #

    `

    '

    rzn

    qrza{wlhkvfbrzawo`badj`bfcorzaabh{rq

    b

    lhkwo`ihuq`nqxh`bae`wh l`[nq|}f{h{r!nvh{uwlhkcofihuq`[ae`bnwoh{srq`hkcorq z

    !

    +#k

    `bquqrvnqr[ph{xy|vhkwuq` rzae`bnqspps`$

    psnr[aoh{|qzn~l

    m

    |q`br0hkcewoh l`bauq`nqx=kh{aerq!frzxyrhkwecl`wosh{a

    rznt`h{ab

    l

    nqxhgnq|}f{h{rnvh{uwlhkcofih`bx

    7#

    #b

    hkwhraoh{|qznq`[!nqxh{|qrg|!nqxyh`bsh

    z

    *1^

    `

    1R

    przzrq

    z

    1^

    1R

    #

    zN

    k

    cewohk`clr{woh[uq`nqxFfbr{wejr0ph{|}fih{uqr0r{vps!nvh{xy`b|co`{uq`badjqwo`bbh{|quqrh[we`baeci`b|qfbh0uqrhkwil`uvh{uvh

    jr{wnqxh0nq|}f{h{rgjrzps|qrzxyh{puqrad`bznq|quqr{wh{n~

    jhkwecowuq`ae`bntuq`baeprfih{xy`|corqr{wobrz|coh{p h{r

    psrz|qzruqr`qruqrza~ r{qco`bxyrzaaenvhh{pcenwh

    r{w``bxjvpsrqnqxWr{`cer l`ph{|}fih{uqr|qr hkwi

    `

    aenvhLh{pconwoh`bx xy`cdworzab ae`bznq|quqrza[hkjlrza+rLpsh{|}fih{xy`b|corl`0uvh{uvhjr{w

    t

    d

    #N

    nvh{pl`[hh{pconwhgx lh qsxyh0hkcos|qzuvhj`bpsrgr{q`cory``bx !nq`[|qadch{|co``ps`[hhkco|qz`

  • de [+

    +`co`wexys|q`bxrzar l`wecofb`yuvhjhkwlhkrzph

    #

    z

    '

    `

    rzzrqhh{pconwhxlh sxh l`Luq`

    hkco|qzsuvh

    ae`bznq|quqrRhkjlrzagrph{|}fih{xy`|corq

    +`bae`b|qqr h`bae!nq`wouvh

    `bphhr{vad`wekh}f{h{ruvhjlh{zs|vh

    zk

    a{wvlhkvfbrzauq`

    # h{bnqp`

    #

    `wexy`bpsvh`

    #

    y

    psspblh{awe`badj`fcokh{xy`b|co`{

    1 2

    10

    5

    -1 1

    2

    1

    Q

    6

    T

    7

    0U

    U

    ]iSiQ

    U

    Z S

    ] O

    Q

    achgnq|}f{h{rl`uq`v|quvhgjr{wi

    '

    -

    '

    -

    -

    '

    |quq`

    '

    '

    '

    '

    ^ ~

    xh{ahR ~~`r{wvlhkvfbruq`uq`j`b|quq`bx

    `baead`b|qfbh{pxy`b|co`uqrg{wh{nYuqrjrzps|rzxysr`[uq`

    '

    achnq|}f{h{r l`{fbpshkwh{xy`b|co`{hz`b|q`wh{psih}f{h{r|vhkconwoh{puvh{anq|}f{rz`bah{|co`wor{wo`bab rzxyr``bxjvpsrq

    `dh{xyrzah{anq|}f{rz`ba~

    `g~

    -

    !^ ~

    F` ^v

    -

    `bnqawo`badj`bfcorza{wlhkvfbrzaabh{rq

    1-1

    -0.5

    0.5

    1-1

    1

  • !

    JLKLK

    1

    Q

    6

    T

    7

    U

    O+V

    O+V O

    ED

    Z \

    O+V

    xh0nq|}f{h{rLl`[uqch

    ae`{qjhkwhceruqrg ^ ~`|cih{rt NR ~`{

    sxhnq|}fkh{r l`[uqch

    ae`{vjhkwhcor!uqr ^ ~`|cih{rNR ~`

    `bpsh{auq`v|qd}f{rz`bauq`nq|}f{h{rtjhkw`uq`nq|}f{h{rRl

    m

    xjhkwl`Nlh{fbsp`w[!nq`rt{wlhkvfrtuq`nqxhnq|}f{h{r

    jhkwYl`0aexl`cewofbry`bx wo`bph}fkh{r h{r`bruqrza

    `0r{wlhkvfbr uq`0nqxhynq|}fkh{rl

    m

    xjhkwl`adsxl`cdwosfbr`x

    wo`bpsh}f{h{r hr{wosz`xY

    b

    `dh

    L

    #-

    #

    ~fbrzxyr ^ ~

    hyjqwoxy`bwohgjhkweco`0uvh{auq`v|q}f{rz`bal`

    `wovfih{uvh`~

    ~

    #

    -

    ~

    #

    #

    -

    #

    vprzzrql`nq|}f{h{rjhkwi

    `dh

    ~

    y

    fbrzxrNR ~

    hjqwoxy`bwhjhkwece`uvh{a uq`v|qd}f{rz`ayl``wovfih{uvh

    `

    -

    psrzzrq l`nq|}f{h{rl

    m

    xjhkwi

    awo`baj`bfcerza

    {wlhkvfbrzaabh{rq

    -2 -1 1 2

    1

    2

    3

    4

    5

    6

    -1 1

    k

    `dh

    ch{p!nq`

    I

    nq|}f{h{rl`jhkw+ae` l`jhkw+`Rl` l

    m

    xjhkwae` =l`

    l

    m

    xgjhkwi

    hkwh

    ${co`bxg ae`{ #

    Nsadcorl`{nvh{|corxh{sr{wr{h{pr{w

    uq` x`b|qr{wrYkh{psr{wuvhYnq|}f{h{rqrz|qae`b!nq`b|co`bxy`b|co`{rY{wvlhkvfbruq`

    `adclhhkh{rYuqr

    {wlhkvfbruq`

    y

    !nq`ch{x0l`bxW`adclhhkh{ryuqr{wlhkvfbr uq`

    y

    `0h{aeadsxWadnqfb`baeae{h{x`b|ce`{

    hkwh^kh{psr{wo`auq`jqwlrksxyrzayuq``worqh{ayjr{ci`b|qfh{axy`b|qr{we`bauqrzxys|vh{x `nvh{|cor xh{r{wyr

    `jr`|co` qrza{wlhkvfrzavfih{x fih{uvh`bxh{a jvph{|qrza Ynvh{ae`+jhkwh{p`bpsrzah{r`b qrguqrza

  • de [+

    s hkwhL3

    - ~co`xgae`k+ #

    rzn^ae` dhtjhkwhLkh{psr{we`ba

    {wh{|quq`bauq`[h{ajr{c`b|qfbsh{auq`xyh{sr{w{wh{ntuqrzxys|vh{x h{auq`xy`b|qr{w{wh{n~

    +`bae`b|qqrzajhkwh

    `

    we`badj`fcokh{xy`b|co`{

    -1 1

    1

    1-1

    1

    -1

    psznqxyh{a`bb`babjhkwhL`badr~}fbhkwrL{wlhkvfbrtuq`gnqxhnq|}f{h{r l`gfbrz|`b|q`b|ce`g`wovfihkw[ae`h nq|}f{h{r

    l`jhkwrznl

    m

    xjhkwbjrzsahtadsxy`cdwohyjqwo`bad`b|ce`y|qrza[{wvlhkvfbrza[uq`adch{anq|}f{rz`bah{fbpschkwlhruq`bad`b|qqrq

    _r{co`nq``qadco`bxxnqcoh{anq|}f{rz`anq`|~h{rabh{rjhkwo`ba`|q`bxGl

    m

    xjhkwe`bab

    r{w``bxjvprqz

    #$-0 fbrzxyr ^ ~

    hjqwoxy`bwhjhkweco`uvh{auq`v|qd}f{rz`a0l` `wovfbh{uvh

    ~

    #

    psrzzrq

    +`y~

    ~ `b|cih{rq|~h{r l`nq|}f{h{rYjhkw|q`bx

    l

    m

    xgjhkwi

    fvhkw0rza[ coh{sa!nq`

    l``b!nqkh{ps`b|co`yhLuq`co`wexys|vhkwrza`bp`bxy`b|corzauqr ^ ~+ch{p

    nq`rzajrz|cerzauqry{wvlhkvfbruq`q`badcih{rh{fbsxhuvhgwo`ch

    N

    s

    fvhkwrza+Rch{a!nq`y~ ^l``b!nqkh{ps`b|co`ghLuq`ce`woxy|vhkw[rza+`bp`bxy`b|corzauqr NR ~ch{p

    nq`rzajrz|cerzauqry{wvlhkvfbruq`q`badcih{rhkh{qrguvhwo`ch

    N

    b

    `~

    # `b|cbh{rq~

    l`[`bnq{h{p`b|ce`0huq`co`woxys|vhkwrza`bp`bxy`b|corzauqr ^ ~ch{p

    nq`rzajrz|cerzauqry{wvlhkvfbruq`q`badcih{rh{fbsxhuvhgwo`ch

    +`bae`b|qqr h`bae!nq`wouvh

    ~

    #

    q`|cih{rq~

    l`+`bnq{h{p`b|ce`[huq`co`woxys|vhkwrza`bp`bxy`b|corzauqr ^ ~

    ch{p~!nq`rzajrz|corzauqrg{wlhkvfbruq`v`badcih{rhkh{qruvhwe`ch

    g

    +`bae`b|qqr huqwo`ch

    -1 1

    1

    -1 1

    1

  • !

    sruq`bxyrzahkqwoxhkw!nq`r0{wlhkvfbr0uq`nqxhnq|}fkh{r l`{!`bxz`woh{p nqxyhfbnwekh|qrjvpsh{|qr0fbrr{weuq`

    |vh{uqr h wo`fzl

    m

    jqwor!fih |q`bx ae`bxjqwe` l`0`wouvh{uq`whsacor l`{|q`bx coruvh fbnwekh |qrLjvpsh{|qrtfbr!r{wouq`b|vh{uqr

    rznfbrz| nq|cer uqr^jvph{|qrRl`r{wlhkvfbrRuq`h{psznqxhnq|}f{h{rq +`brzxy`cewesfih{xy`|co` nqxhfbnwekh^|qr

    jvph{|qrgfbrr{weuq`b|vh{uqrl`rg{wlhkvfruq`nqxyhnq|}f{h{rae`ceruvhwe`ch0jhkwh{ps`bpshh{r`bruqrza

    s|co`woad`bfch

    hfbnwd{hy|qrxlh sxyr|nqx jrz|corjr{w!nq`

    r{w``bxjvprqhad`bznqs|co`fbnwd{hy|~h{rwe`jqwo`bae`|ch

    nqxhnq|}f{h{rq

    fbrz| nq|cer

    !

    t# #-

    #

    |~h{r l`[rg{wlhkvfbryuq`nqxhnq|}f{h{rq

    +` hkcerq

    R

    #

    psrzzrqijhkwhcoruqr

    `sadco`xxh{sauq`nqx

    ch{p{nq`

    Y0

    `dhgrjqwlrkqxyrguq`ae`b|qqrq

    -1 1

    -1

    1

    JLK

    D

    Q

    O VO

    6

    T

    7

    0U

    O

    E

    P

    TU

    V

    `dh{x

    g

    ~`

    g

    ~coh{sanq`ad`bnqa{wlhkvfbrzaae`|ce`woae`bfch{x |qrgjrz|cor * `b|cih{rqh{afrk

    r{wouq`b|vh{uvh{auq` abh{rq

    $

    e

    d

    eqpsrzzry

    ~

    v`b!nqkh{ps`b|co`bxy`|co`k

    l`aerzpsn}f{h{ruqraeadco`bxh

    g

    g

    ~

    b

    fvhkwrzajrz|corzauq`|co`woae`}f{h{ruqrza{wlhkvfrzauq`0~

    `

    #N

  • #

    de [+

    `aerzp`bxrzargaesadce`bxh

    #

    uq`rz|quq`[ # ^

    g

    qprzzr

    `|cih{r

    rzn

    ajrz|corzaabh{r

    `

    1

    1

    fvhkwrzajrz|corzauq`|co`woae`}f{h{ruqrza{wlhkvfrzauq`0~

    R`+~

    -

    `aerzp`bxrzargaesadce`bxh

    ^

    -

    uq`rz|quq`

    -

    psrzzr

    -

    -

    `b|cih{r0

    rzny

    ajrz|corza

    abh{rY

    `y

    -1

  • ! #

    JLK

    [email protected]

    ] O

    O

    1

    Q

    6

    T

    7

    U

    O+V

    `dh{x

    `

    ~nq|}f{rz`ba

    [+k

    k

    L

    vb~

    ~~

    d

    v[

    ~

    vb~

    ~~

    x jhkwecesfbnqpshkwivae`

    5

    5

    N~b

    5

    N~

    d

    ~

    L

    ~

    ~

    ~

    ae`+

    |co`bauq`hkjqwo`bae`|chkw`q`xjvpsrzauq`badch{auq`v|qd}fkrz`babuq`co`woxs|q`bxyrzarzawo`badj`bfcorzauqrzxl

    m

    |qsrzab

    ^

    q

    ^ $v

    ^ ~ NRq

    ^ ~ NRqei ^vdN

    `rzxy`cewofih{xy`b|co`Yr {wvlhkvfbr uvh aerzxyhuqs`wo`|}fihjqwor!uqncor rzn!nqrfb`b|co`

    uq` ` co`bxY `bx fih{uvhjrz|cer^nqxhr{wouq`b|vh{uvh^!nq`l` wo`baj`bfcekh{xy`b|co`{haerzxhuqs`wo`|}fih

    jqwor!uqncorrzn nqr!fbs`|co` uvh{ar{wouq`b|vh{uvh{auq` `yR|qrzajrz|cerzagfbr{wdwo`badjrz|quq`b|ce`bab

    hkjvpsfih}f{h{r

    uq`badcoh{auq`v|q}f{rz`batl`{v`bx z`wh{pqxnqcoraesxgjvps`babvfbrzxrgr{vae`we{hkwe`bxyrza|qrza``bxjvpsrza

    b

    h{uqd}f{h{rg`haenqcewh}f{h{rguq`nq|}f{rz`ahkv|qaabh{rgnq|}f{rz`bahkv|qa

    +`hkcorqqad`0

    -

    `

    #

    -

    #

    v`b|cbh{rq

    v~

    #

    -

    #

  • #$" de [+

    r{w`q`bxgjvpsrqqae`~

    -

    v`b|cih{rq - v~

    ^` y^vb~

    +wvlhkvfbrza`xWh{bnqpq`wouq``+`wox`bpsqrqqwo`baj`bfcekh{xy`b|co`{

    -6 4

    -10

    10

    -6 4

    -10

    10

    h{uq}f{h{r `h adnqcewh}f{h{r uq`nq|}f{rz`batjrzps|qrzxyh{anvh{uwvlhkcosfih{aah{rnq|}f{rz`aLjrzpss|qrzxh{sa

    nvh{uwvlhkcosfih{a

    +`hkcorqqad`0

    '

    #

    -

    -

    `~~

    '

    #

    #

    -

    #

    #

    v`b|cih{rq

    vb~

    '

    '

    #

    #

    -3

    #

    -

    #

    r{w`q`bxgjvpsrqae`

    #

    -

    # -

    q`b|cih{rq - qb

    #^

    ` vb~

    #

    -

    wlhkvfbrza`x h{nqp q`wouq`[`[`wox`bpsqrqwo`adj`bfcokh{xy`b|co`{

    -4 -2 2 4

    10

    20

    30

    40

    -4 -2 2 4

    -20

    -10

    10

    20

    k

    ` dh{x

    #

    `+~

    -

    0

    qb

    ~

    ~

    #

    -

    ~`t qb

    #

    -

    rza

    uqrzxl

    m

    |qsrzaabh{rNR

    q

    i

    bR

    -

    NR q

  • ! #

    ~

    #

    -

    vrguqrzxl

    m

    |qr l`

    i

    ^

    -

    JLK K M

    1

    Q

    6

    T

    7

    U

    O+V

    B

    0T

    S

    U

    Q

    SV

    `dh{x y`

    ~jrzps|rzxysrzauq`fbr!`vfbs`|co`awo`ih{sar!uq`bxyrzauq`v|qwhae`bznq|ce`nq|}f{h{rq

    fvh{xh{uvh

    y

    ~

    hRjhkweco`suvh uq`v|qd}f{h{rqco`bxyrzanq` ^ ~

    i

    ~

    `bx rzncdwh{a

    jh{phiwoh{abr uqrzxYl

    m

    |qsr uq`nqxh nq|}f{h{r wh{fbsrz|vh{ptl`r fbrz| nq|coruqrzaL|lnqx`worzawo`ih{aLx`b|qrza h{a

    whql

    m

    b`bauqr0jrzps|rzxyr!nq`hkjhkwo`bfb`|qr0uq`|qrzxys|vh{uqr{wi_r{co`nq`+h{anq|}fkrz`bajrzps|qrzxyh{a ah{r0nqx

    fih{aerjhkwecofbnqphkwuvh{anq|}f{rz`awh{fbrz|vh{sa qh{adchfbrz|qaeuq`whkw

    ~

    jhkwhcor!uqrg

    b

    nq|}f{h{rY~

    5

    5

    /l`xyruq`bpr xhkco`bxlhkcesfbruq`jqwor{vps`xh{a+nq``b|rzp`bx nvh{|co

    uvh{uq`bas|`woaoh{xy`|co`jqwor{jr{wefbsrz|vh{ab r{w``bxjvpsrqvhps`buq`0rp`{ lh{z|vh

    k

    ` dh

    g

    ~

    #

    -

    -

    -

    #

    ^

    hkcor{wh{|quqr

    -

    -

    #

    #

    b #.- -

    co`bxae`{

    ~

    ae`

    przzrq ^ ~

    k

    ` dh

    g

    ~

    -

    R

    #

    -

    hkcor{wh{|quqr

    #

    -

    b

    #

    ce`bxgad`{

    ae`+

    rznt

    vpsrzzrq NR ~

    ` dh

    g

    ~

    -

    -

    #

    -

    hkcor{wh{|quqr

    ~

    -

    # -

    # -

    b # -

    vco`bxg ae`{

    |~h{ryjrzaeaenqwohql

    m

    b`bawo`ih{sa

    psrzzr ^ ~

    JLK

    5

    U

    Z \

    U

    V

    O

    1

    Q

    6

    T

    7

    U

    O+V

    `dh{x

    `

    ~uqnvh{anq|}fkrz`bach{a!nq`{

    !^ ~ ^q

    [+k

    ~

    l`uq`b|qr{ch{uvhjr{wL`uq`v|qsuvhjr{wb

  • #

    de [+

    ~

    ~e

    vae`we`!nq`huq`v|qd}fkh{ryh{ae`|couqrjrza~NRq

    ^ ~

    i ^ ~ez~NRv

    `^ ~

    b ~ed NR ~

    achyuq`v|qd}fkh{ryjqworuqnq{hjhkwecowuq`nq|}f{rz`ba+fbrz|qq`bfsuvh{ab~|qr{h{anq|}f{rz`bab~fbrzxr`wo`bxrzaxh{a

    h{uqh{|co`{

    uq`v|qd}fkh{ruq`fbrzxjrzadchuq`nq|}f{rz`bal`uq`Nlh{fbspxh{|q`rq{frzxyr`we`bxyrza|qrza`q`xjvpsrzab

    b

    fbrzxjrzadchuq`nq|}f{rz`bahkv|qal`[nqxyhnq|}f{h{ryhkvxY

    +`hkcorq!ae`+

    -

    `

    #

    -

    #

    `b|cih{rq~ ~~

    #

    -

    #

    -

    #

    ` qb

    #

    -

    #

    -

    r{w0``bxjvpsrqae`L

    `g~

    -

    `b|cih{rq ~b

    7-

    `y v~

    z

    wlhkvfbrza`bxh{bnqpv`wouq`[``wexy`bpsqrq

    wo`baj`bfcekh{xy`b|co`{

    -6 4-6 4

    ` dh{xW~

    #

    `~~

    -

    qfih{pfbnqps` y`

    wo`baj`bfcekh{xy`b|co`{

    R ~

    - +` ^v

    +~b~

    ~ e

    #

    #

    -

    rzzrq

    ^ ~

    i

    b ^

    -

    s !^q

    3` ^ ~

    i

    b

    - !psrzzrq|~h{rjr!uq`bxyrzafih{pfbnqphkw hx`b|qrza

    nq`fbrz|qaeuq`wo`bxrzanqx uqrzxl

    m

    |qrgxy`|qr{wjhkwohLuq`xruqrnq`!^q ^ ~

    +`hkcorq vb~

    ~e

    -

    -

    #

    #

    -

    `xyrzab

    ^ q

    i

    ^

    -

    s+ ~b

    ~d

    #

    #

    #

    #

    rzzrq

  • ! #$#

    NR ~

    i

    =

    -

    q+ v~

    ~~~~de

    ~~ -

    e

    -

    -

    NR q

    v ~b~

    ~dee

    #

    NR ~

    i

    R

    -

    +rza`$q`bxjvprzah{|co`wesr{wo`bajr!uq`bxyrzafbrz|qfbpnqw!nq`{v`bx z`wh{p

    qb

    ~b

    k

    njrz|qvh nq`nqxhyxh{|qfvhuq`0jrzpsnq`|co`nq`0frz|ch{xs|vhnqxhyph{zrhyco`x hr{woxhuq`nqx

    uqsadfbruq`wh{sr g`bx

    `aenvh^lhkwo`ih+=`x

    #N[l`nq|}f{h{ruqrwh{srq

    `r[woh{srfwo`baef``bx nq|}f{h{r

    uqryco`bxgjr`x j`bphp`b

    qd

    -

    uq`co`wexys|q`h lhkwo`ihyuvhxyh{|qf$vhy`x

    nq|}f{h{ryuqrgco`bxjrq

    lhkwo`ihl`0 {

    !

    #

    uq``bxyrzafih{pfbnqphkw+ e$ jr{wrzncewor ph{uqrd

    {bd

    de

    psrzzrqq e

    de

    -

    !

    -

    #

    #

    nq|}f{h{r ~~

    -

    #

    -

    jruq`ae`w`baefwech fbrzxyrh fbrzxjrzadch uq`^uqnvh{arzncdwh{a

    nq|}f{rz`ba+`hkcorq

    ~brz|quq`L~

    - # -

    `~

    Y+`bae`b|qqrza

    `bae!nq`wouvh{wlhkvfbrzauq`0 h{bnqp$^`woxy`psqr`

    adrfb`Lr{wvlhkvfbruq`

    #+

    nq|}f{h{r

    #

    jruq` ae`wg`baefwechfbrzxyrh

    fbrzxjrzadchYuvh{a0nq|}f{rz`a~

    #+

    `~

    (psrzzrq

    [`phr{vae`wekh}f{h{ruvh

    jlh{zs|vh

    qr{wlhkvfbrguq`~

    ~ l`rguq`bae`b|qqruvhuqwo`bchY`woxy`bpqr

    -2 -1 1 2

    1

    2

    -1 1

    1

  • # de [+

    +`ce`woxy|q`

    ~$ad`{

    ~

    R

    `

    s

    #

    `

    `

    R

    v`b|cbh{rq

    ~

    b

    e

    R

    R

    R

    #

    ~

    b

    R

    R

    ~

    #

    b

    vae`wekh{|quqr h{a`$jqwo`badabrz`bah{|co`wor{wo`bajruq`xyrzahkqwoxhkwnq`{

    -

    +

    *-

    -

    s

    `0

    #N`|cih{rq

    ~

    b

    #

    #

    ~

    e

    {

    ~

    #

    e

    ~

    e

    #

    _r{co`nq`{

    #

    #

    `

    vae`wekh{|quqr h{a`$jqwo`badabrz`bah{|co`wor{wo`bajruq`xyrzahkqwoxhkwnq`{

    #

  • ! #

    JLK

    D

    QO V

    O

    Z

    1

    Q

    6

    T

    7

    0U

    vae`we`0h{aae`bznq|ce`bachk`bph{ab

    '

    t

    '

    z

    z

    z

    '

    '

    g

    z

    z

    z

    jqwosxy`whchk`bph+rzqr{qcosuvh+|nqx `adconquqradr{qwo`hjr{jvnqpsh}f{h{ruq`h{ps`h{afbr{wofbnq|quvh{a |!nqx fb`wecor

    ae`cer{wfbrzaco`bwerncopssbh{uqrfbrzxyr0jrz|coruq`wo`jqworuqn}f{h{rgj`bpshg`badjl`fbs`{

    ch{xh{|qqruvhjr{jvnqpsh}f{h{r

    uq`[h{p`bh{aLl`[x`buqsuqrh{|!nvh{pxy`b|co`{vuqnwh{|co`

    h{|qrza

    |lnqxy`worFuq`[h{p`bh{aLl`[nq|}fkh{ryuqrh{|qr

    '

    `x nq`^l`wo`bh{pssbh{uvhh x`buqd}f{h{rq

    L

    '

    $

    njrz|qvh nq`k`bx fb`wecor s|qadcoh{|co`krzavsrzpblrzzrza

    xnquvh{xr0jrz|coruq`+sadcoh`+vfbh{x s|co`wo`badaoh{uqrza|qr0co`xjr0`bacosxh{uqr0jhkwh0!nq`[hjr{jvnqph}f{h{ruq`

    h{ps`h{ahkco| dhnqxFf`wecor0|lnqxy`woruq`s|quq~l

    m

    uqnqrzarznae` dhuq`bae`dh{xFr{qco`w

    '

    `bxFnq|}fkh{r0uq`+

    '

    '

    g$

    h{pnq|}fkh{rl`[fvh{xh{uvhuq`|`weaohuq`[

    L

    '

    `dhhae`bznq|quvhgcohk`bpsh

    +wvlhkvfbryuvhjqwesxy`bwh`aeznq|quvhgcohk`bpshwo`badj`bfco{h{xy`|co`k

    1 2 3 4 5 6

    10

    20

    30

    40

    50

    10 20 30 40

    1

    2

    3

    4

    5

    6

    [+k

    nq|}f{h{rl`[uqchnq|}f{h{rs|`woaehguq`0ae`{

    Rq

    ^ ~` R ~

    NRv

    shkwhcor!uqrg NRv qb

    `+jhkwhcoruqr ^ ~ ~b~

    x ch{p~fbh{aer l`uqcohgs|`wecil

    m

    `bp

    ~

    `~

    -

    ~

    abh{r|`weaoh{abvjrzsa

    ^ ~

    Rq

    b

    NRq

    !^ ~

    i

    k

    `{

    s+ qb

    ~e

    -

    ~b

    ~ e

    ~

  • # de [+

    `dhnqxhnq|}f{h{rys|`wecil

    m

    `bp +`b|qr{co`xyrzajr{w+

    aenvhs|`woaeh

    s+sb`w+nq`

    l`h nq|}fkh{rt|`weaohuq`Il`0`nqkh{ps`|co`0uqb`w+!nq`

    `

    ^abh{rLh

    nq|}f{h{rsuq`b|couvh{uq`{ xFrzncewoh{ajh{phiwh{abl`

    !

    l

    uqsb`wihnq|}fkh{ryl`|`weail

    m

    `bp ae`

    `aerzxy`b|co`ad`jhkwhcoruqr

    q

    #

    ^ ~ qco`bxyrza

    #

    `b|cbh{r

    #

    s

    {wlhkvfbrguq`0

    l`aesxl`cewosfrh{rg{wlhkvfbruq``bx wo`ph}f{h{rhwo`coh

    q

    `0l`s|`wecil

    m

    `bp`b|cih{r

    l`[s|`wecil

    m

    `bp~`

    v

    ~d

    _rad`bznqs|co`uq`ae`b|qqrqrg{wlhkvfbrjrz|cospvh{uqrfbr{wewe`badjrz|quq`h

    JLKK M

    ?

    E

    O

    U

    U

    \

    > O

    O Z SiQ

    D

    QgO V

    adfwo`khh`bnvh}f{h{r

    ~!nq`[uq`v|q`hgnq|}f{h{r

    s `aerzpkhh`nvh}f{h{ruqrco`xjhkwhY`bxFnq|}f{h{rguq`

    jhkwh0r{qco`w

    `kqh0ae`bznqwb

    j`woxnco`jr{w

    `bnvh}fkh{rr{qcouvhguq`v|q`

    _r{co`nq`kh weszr{wih nq|}fkh{r

    corzxyh kh{psr{we`ba |qrza

    R ~$

    l

    jrzadail

    m

    `bpuq`co`woxy|vhkw

    z`brzxy`cewosfbh{xy`b|co`ad`nqxhnq|}f{h{r0jrzaeaenqrzny|~h{rnq|}fkh{r0s|`woaohhkwhadcorquq`bae`b|qq`!nvh{ps!nq`w

    wo`cohjhkwh{ps`bpshh{r0`b qruqrzaae`+hwe`chs|co`weae`bfchr0{wvlhkvfbr0uvhnq|}f{h{r|qr0xlh qxyr|!nqxFjrz|cerq

    `b|cih{ryhnq|}f{h{ryjrzadaenqs|`woaoh

  • ! #

    b

    nq|qfbsrz|vh{x`b|ceruq`nqx co`woxrzxy`ceworq

    rzpsnqxy`uq`nqxhnvh{|cosuvh{uq`uq`xy`weflnwosrl`nq|}f{h{r

    uvhtadnvhtco`bxj`whkwecenwhgaeh{|quqrYhnq|}f{h{rs|`woaohuq`co`woxs|vh{xyrzahLce`bxj`whkconwhLhkcewhi l`bauq`

    ae`bntrzpsnqxy`{

    s|`woaohguq`nqxhnq|}f{h{rhkvx |~h{rfbrz|qach{|ce`l`hkvx

    +`hkcerqae`

    ~

    - [`b|cbh{rq

    b `wexncoh{|quqrjr{w

    ~

    k

    ` dh

    ^

    hk`xyrza[!nq`gad` l`jhkwhLnq|}f{h{rl`jhkw`gae` l`l

    m

    xjhkw[htnq|}f{h{rl`tl

    m

    xjhkwb rzzrRjrzadaenq

    s|`woaehtjhkwhL

    ae` l`jhkw`jhkwhLcor!uqrt ae` l`Yl

    m

    xjhkwi

    |`weaohtjhkwhYh{x0h{al`

    `woxnch{|quqrgjr{w

    +`bae`b|qqrzajhkwh l

    m

    xjhkw`[jhkwbvwe`badj`fcokh{xy`b|co`{

    1

    1

    1

    1

    ` dhR

    '

    -

    -

    '

    h{b`b|quqr

    '

    -

    -

    ` wo`badrzp`b|quqr^h`b!nvh}f{h{r^`x

    wo`bpsh}f{h{ryhqco`xyrzab

    '

    vpsrzzr

    '

    ae`

    '

    rzn~v`bnq{h{p`b|ce`bxy`b|co`{

  • de [+

    ~

    y

    '

    ae`

    '

    v!nq`l`[hgs|`woaehuq`

    xyh+rzph+uq`r{wdwh{fvh`badclhae`b|quqr| h{uvh`ae`bnrzpnqxy` ,;l`nq|}fkh{ruqr[co`xjr `bx

    ae`b|quqr*,d

    -

    +nvh{|corco`xjr[uq`bxyr{whhrzphhkcl`hkco|qzw rrzpsnqxy`uq`

    +``bxyrzatuq`co`wexys|vhkwhnq|}fkh{r s|`woaoh uq` ,y

    rzxyr ,

    .-

    `b|cih{r

    ,

    `

    ,

    ,0

    ,

    `

    ,

    k

    l

    fbrzxnqxY`bx;uqs`wo`|co`a

    `b|qfbh{a[uvh_+hkconwo`ihncopsihkwuqnvh{a`baefih{psh{a[jhkwhx`buqwco`bxg

    j`whkconwh{ab

    h{wo`b|qq`bc`7

    `bpaesnqa

    +`co`woxys|q`[hnq|}f{h{r nq`+wo`bph{fsrz|vhh0co`bxgj`whkcenwh

    `x {woh{nqa `bpsadsnqa h0co`bxgj`whkcenwh

    `bx {wh{nqa

    h{wo`|qq`bcivaohk`b|quqrnq`ae`bn{wlhkvfbrl`nqxh0wo`ch

    s`co`woxy|q`

    `rg{wlhkvfbrl`nqxyhwo`cohhnq|}f{h{ruq``ae`wuqrcojrq

    g

    *- N r{wrzncdworyph{uqrq

    aohk`bxyrza!nq`{

    vjrzahlh{znvhae`fbrz|qz`phyh

    {wh{nqa)`bpsadsnqab

    z

    jrzahlh{znvhg`wd`h

    z

    {wh{nqa/

    `bpaesnqa r{wech{|corq

    `

    z

    psrzzrq

    s

    `dh

    `|cih{rqq

    -

    `

    -

    rzzrqq`badch{aabh{rgh{awe`b{wh{auq`[frz|`weabh{rg`|cewe`co`xj`wohkconwh{auvh{uvh{a`x {wh{nqa `bpaesnqa`{wh{nqa

    h{wo`b|qq`bci

  • !

    -100 -40 100

    -100

    100

    h{psfnqps`hs|`woaohuq`nqxhnq|}f{h{rjrzpss|qrzxh{puq`ae`bznq|quqr{wh{n~

    `dh

    '

    # - -

    '

    r{vae`wekh{|quqrry{wlhkvfbruq`0co`bxyrzanq`h{b`w0

    +'

    rzn

    +'

    jhkwhr{qco`whs|`woaeh`baerzp`b|quqr

    L

    '

    # - -

    rzn

    '

    # - -

    co`bxrza!nq`{

    #

    '

    -

    '

    +'

    |cih{rq

    -

    #

    '

    -

    '

    +'

    ae`

    '

    #

    #

    '

    -

    '

    +'

    ae`

    '

    |vh{psrzh{x`b|ce`ad`

    +'

  • " de [+

    1

    Q

    6

    T

    7

    U

    O+V :I]O[Z OQ

    OV

    JLK

    1

    Q

    6