... s : xj cn No. 175. Notice of Transfer of Separate Estate to Joint Estate for G-azette.* . (Title.) Notice is hereby given that there being hi the hands of the trustee in the above bankruptcy a surplus estimated at £..... arising from ...
... ( cN - d'eM ) / d many j . Hence V A xj = 0 . ( 8 ) SC { 1 , ... , N } jes | S | > ( cN - d2eM ) / d is Similarly if ẞr = then it follows from ( 7 ) that the rth coordinate of Xj non - zero for at most Md ( f − e ) + cf Σ ? 2 ± 1 Ni ...
... s xj cn of ostis aur ; & c . METS γενόμεθα τ τῷ λύτρα . σε χάσεις Chryfo demus fecundo Chryfoftomi mentem effe , [ ftiam nos conjungi Chrifto nova quadam & vera Chryfo- tomus . Chriftum per proprium corpus ac fanguinem vnione . Sed ...
... ( S ) , ( xj ) jЄT € V ( T ) } . x and y . ) ( Here x ; and Y1 respectively denote the i - components of the vectors ... C N ; S ( x S \ ¡ ( × § - × § ̃3 ) = 1. ( × 3 − × § − 1 ) , VS C N , vi e S , vj e S - i . Condition ( 10 ) ...
... S × S → C is said to be a kernel of positive type , abbreviated φ > 0 , if ∑ij ( xi , xj ) Ci Cj ≥ 0 for every x1 , ... , xn ∈ S and every C1 , ... , Cn ... S × S → R is said to be a kernel of negative type , and we write ψ < 0 , if : ( a ) ...
... c.n. ( c ) . Mars , Adm . John L. , c.B. ( m ) , M.v.o. ( 4th ) , D.S.o. Masefield , Col. Robert T. , c . B. ( c ) . Massy , Col. Harry S. , c.B. ( m ) . Massy , Col. William G. , C.M.G. Masters , Br - Gen . Alexander , c.B. ( m ) ...