Resolucao Halliday Comentada

 

FNCCGMNW & \JXKGHE

XACZÏÈA

O\NYG]NÏÈA, AKMNX J ]J\DAMGKÌDGHN  Hgrcjg Vnvgjr Lnhfnrjc j Djstrj jd Iäsghn pjcn Zkgvjrsgmnmj Ijmjrnc mn Lnfgn Dnrnhîs Lnfgn Autulra mj :

 

Xudîrga >

  Jqugcälrga j Jcnstghgmnmj

 

>.>   Ncouks Jxjdpcas Jxjdpcas mj Jqugcälrga Jqugcälrga Jstîtgha Jstîtgha   . . . . . . . . . . . . . . . . . . . . . >.<   Rralcjdns Nmghgakngs Nmghgakngs   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

>

8

8 ?

 

Xudîrga

Ornvgtnïèa, Akmns j ]jrdamgkìdghn 

<



 

 Hgrcjg Vnvgjr

 

Hnpätuca > Jqugcälrga j Jcnstghgmnmj

Rjrouktns >.>   Ncouks Jxjdpcas mj Jqugcälrga Jstîtgha :.  Kn Igo. >2∜< )<  + > 4 7, =   K  (6, 2 ¿ >2∜< )<

Noarn, n iarïn quj n pnrjmj jxjrhj kn lacn ç  r   =, < >2∜< I  4  4 do   4 2 , 6: 7, 6  4 = , =   K  C 6, 2 >2∜<

¿

¿

¿ ¿

 , .   Kn Igo. >2∜< ) (8, 22 >2∜< )< I  4  4 (9, 22 8, 22) >2∜<  4 >8, 9   K  I  4

¿

 ¿

∜

¿

.

a had n vjrtghnc. vjrtghnc. Xj a hadprg hadprgdjkt djktaa C mn lnrrn ç 9,>2 d, hnchucj n mgstìkhgn  x jktrj n jxtrjdgmnmj jsqujrmn mn lnrrn j a sju hjktra mj dnssn.

N iarïn rjsuctnktj tnkta ka jgxa x qunkta ka jgxa  y  ç kucn, au sj`n, sj hnkhjcnd, jktèa0

 

I x 4 ] >x + ]  sj sjk k(ζ ) + ] < has (ω ) 4 2 ] > 4 ] < sjk (ω ) /sjk  / sjk (ζ ) I y  4  ] >y + ]  has (ζ ) + ] < has (ω ) do  4  4 2 ] > has (ζ ) + ] < has (ω ) 4 do 

∜

Ornvgtnïèa, Akmns j ]jrdamgkìdghn 

∜

⇜

⇜

 

 Hgrcjg Vnvgjr

  

>.>.  Ncouks Jxjdpcas mj Jqugcälrga Jstîtgha

 

:

Nssgd, sulstgtugkma ] > kn sjoukmn jqunïèa, jkhaktrnrjdas n tjksèa  ] < 0 ] > has (ζ ) + ] < has (ω ) 4 do  ] < sjk (ω )   has (ζ ) + ] < has (ω ) 4 do  sjk (ζ ) ] < sjk (ω )has (ζ ) + ] < sjk (ζ )has (ω ) 4 do    dosjk(ζ ]  ﬎hn0 ] > 4

 sj k(ω )   dosjk(ω )   dosjk(ζ  sjk  4 sjk (ζ + ω ) sjk (ζ ) sjk (ζ + ω )

 ¿

A tarquj rjsuctnktj jd rjcnïèa na hjktra mj dnssn ç kuca, jktèa0



ύy  4 2

] >y x + ]  has (ζ ) x + ] < has (ω ) (C x) 4 2

∜U] >has (ζ ) +¿ ]  j mjpags jcgdgknkma ]  has (ζ ) + ] < has (ω )   ] < Chas(ω ) x 4 U] < sjk (ω ) /sjk  / sjk (ζ )Thas (ζ ) + ] < has (ω ) x 4

  Chas(ω ) Usjk (ω ) /sjk  / sjk (ζ )Thas (ζ ) + has (ω )   Chas(ω )sjk (ζ ) x 4 sjk (ω )has (ζ ) + has (ω )sjk (ζ )  Chas(ω )sjk (ζ ) x 4 sjk (ω + ζ )

x 4

Xulstgtugkma as vncarjs kudçrghas, altjdas0  9 , >2 ¿ has (:8, >a ) ¿ sjk (89, 7a ) x 4    . As cnmas N =>. As NH H j HJ mn jshnmn mn Igo. >.

 Jqugcälrga j Jcnstghgmnmj

 

9

N iarïn rjsuctnktj kn vjrtghnc j kn fargzaktnc sj nkucnd, nssgd, tjdas pnrn a cnma jsqujrma mn jshnmn0

  ∜    ∜∜

I  ]   4 2 I   4  ]  I  +  + I  N do  4  4 2 I  +  + I  N 4 do 

∜

⇜

⇜

j pnrn a cnma mgrjgta0 I  I J  4 2 I  ]   4 2

⇜ I  4  4 I J ⇜ I   4 ] 

A tarquj rjsuctnktj pnrn a cnma jsqujrma jd rjcnïèa na pakta H ç0  C I  N Chas(ζ ) do (C m )has (ζ ) ]  sj sjk k(ζ ) 4 2

∜

∜

∜

<

@î pnrn a cnma mgrjta ﬎hn0  C I J Chas(ζ ) ]  sjk (ζ ) 4 2

∜

sjk sj k(ζ ) ⇜ I J 4  ].