Read e-book online Antenna Theory: Pt. 2 PDF

By Robert E. Collin, Francis J. Zucker

ISBN-10: 0070118000

ISBN-13: 9780070118003

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T. m) for m=p 2 (p: odd prime) shows (see be1ow). l\n m is of the form 52 ----- a~ (l, ... •. • ,v, ... ,m-l, ... -' xv x1 we set ~(a) Then we have (x 1 , ... ,xm_ 1 ; i + 1) a Eil<=~ (a) E Mm. m M' m Let M m denote the submono i d of generated by the following condition on (Pn) We call m Every (indecomposa ble) element If Theorem. n, ~iEMm m satis- with is satisfied, then the Hodge Conjecture for (Pn) m (cf. [6, Th. ) is true. ;;;-I+l with M : (Pn). (n : even) Thus we have IIE,ill < 11~11. llnll = 1, Xn or ~EM~ fies either of ~ n m and We say that the condition n hold for all holds if the conditions (Pm) By ( II I) and (IV), we also have even.

T ... ; , ~ II• ~ .. 1 :t • •} o:-1, I>'' ~ I .. I :r .... I U 1 ' •· : I • • 10 lt :- ;j .. ' ll I ~ ..... ' Ii . ·t ~ ll fi /-A d c ,. ( t I~ I~ , ... IK I' I (' ... :J .. ,, ... ~ .. I. " t•l • :,• ' 1 ,. " ........ r,.. , :- 7 -1 - " ) " . " .. J .. ~: I '! • 6 •I ob .. 1 ~ '-';tll s :-- I Jtl , .. ' I · ... ~ .. • .. '. _ Jt (" .. • I "' •11 ~ /,,1 ... >'"' #I~ "'I 6 -t lf I) I. :/J ~ I) i'tt /r {:. ~ .. II J{ '· ~ I II ("- ~ ~(IIC. 't tl :1 I fJ .. i. c_1 .. lt ,.. u! , • I : :. ' '! /l • 1 t /:.

Pm) (Pm) Actually the above results hold if we replace following weaker condition is stably generated by Mm (Qm) M~, (a). ~L Hence M~. Mm=M~, is Mm and the condition is true. , every element of expressed as a difference of two elements of Example. ;;;p-1) M m is generated by M ( 1) m where ( i , i +p , i + 2 p , ... , i + ( p- 1 ) p , ( p- i ) p) EI~~- 1 holdsif n

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Antenna Theory: Pt. 2 by Robert E. Collin, Francis J. Zucker


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