... { 0x | ŴÊ | 0x ) – X { 0x | ÊŴ | 0x ) + ( 0x | ÊŴB | 0x ) ) a — b — C d Let us calculate the terms a , b , c , and d one by one . First , from eqn ( 11.55 ) we know that a = ( 0xW0x ) . The term b is given by = b = ( 0x | Ŵ B | 0x ) ...

... C", f(0) > 0 for any 6 e 0X. 2+(0X, d6) is equipped with a topology by embedding 2+(0X, d6) into L*(0X, d6). Note the space 2+(0X, d6) is path-connected, since any measure on a path between pu, pul: (1 - t)/w -- thul, 0 < t < 1, belongs ...

... C is weakly fair with regard to characteristic G at ( all levels of ) 0x , if a . ( CIL f ( X ) ) | ( @x , G ) b . ( Gƒ ( X ) ) | 0x C. ( GLC ) 0x ( group - wise local independence of f ( X ) and C ) ( measurement invariance of f ( X ) ...

... 0x 0 OX 0 0X, 0 f_ - Of + 0x of + “ f ox, ox, 6.x ox, 6x ox, ox, (C-6) where x, X and X, are the x components of the vectors r, R and Rc. From eqn (C-1), (C-2) and (C-3) we have 0x 0x 0x — = 0, — = –1 ... (C-9) we obtain, for 192 Appendix C.

... 0x { ( a , b + c , d ) ( ef ) ( gh ) } , N ON { ( ab ) ( cd ) ( efgh ) } + 0x { ( ab ) ( cd ) ( e , f + g , h ) } , Ox { ( abcd ) ( efgh ) } + 0x { ( abcd ) ( e , f + g , h ) } N + 0x { ( a , b + c , d ) ( efgh ) } + 0x { ( a , ...

... 0x { ( a , b + c , d ) ( ef ) ( gh ) } , = ON { ( ab ) ( cd ) ( efgh ) } = = = = + ON { ( ab ) ( cd ) ( e , f + g , h ) } , ON { ( abcd ) ( efgh ) } + 0x { ( abcd ) ( e , f + g , h ) } + 0x { ( a , b + c , d ) ( efgh ) } + 0x { ...

... 0x 0x | T 0x 0x L • Where the curvature is positive (a dip, Fig. 16C.3), - - - the change in concentration with time ... c 0c l 0°c 0°c cal formulation of the intuitive notion that there is a natural (#) - (#) — (#) * , i. |- (#) T2 oxo ...

... 0x)\eox) was chosen arbitrarily, so X = e(X) is closed in the space D(F, 0x) = Z.F(X). V.035. Knowing that 0x e F C C, (X, I) and 0; e G c Cn(Y, I), suppose that there is an embedding i : G → F with i (0y) = 0x. Prove that ZF(X) maps ...

... 0x | 2 3 0x^ 3 0x *0t 3 7 č 0x40t 21 č 0x" | 2 5 5 5 -os-os) o ***{-};}} #ovs-os) o = 0 (6) 45 7 0x"Ot 45 7 Ox' 45 7 0x"0t Neglecting the seventh-order terms in Eq. (4) and applying the above method to the thirdorder terms, Eq. (7) is ...

... 0x #u Λ y = 0 ^ ( e , f ) = ( 1,0 ) △ C 33 no , 2 12 л то Λ 0x #u Λ y = 0 ^ ( e , f ) = ( 0,0 ) A c 44 no , 3 5 5 no , 3 13 ^ то Λ 0x #u Λ y = x ^ ( e , f ) = ( 0,0 ) ^ C 4 lo ^ то Λ 0x #u Λ y = x Λ ( e , ...