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JOURNAL OF MATHEMATICAL STUDYJ. Math. Study, Vol. x, No. x (201x), pp. 1-74. Astrophysical Dynamics and Cosmology. Tian Ma1, Shouhong Wang2,. 1 Department of Mathematics, Sichuan University, Chengdu, P. R. China.2 Department of Mathematics, Indiana

p(m)qkd (kA,kB) = Pr(KA = kA,KB = kB|M = m). (1). ... KA, kA, KB, kB: output keys for Alice and Bob.

these points. Once the sample size n is fixed, either by cost or time considerations, and an op-.

p is a p-complete, nilpotent space and π1(BG. p )= G/Op(G). ... HBG = HBNG(D) = HB(NG(D)/Op′NG(D)) = HBDNG(D)/CG(D). Proof. See Swan [209].

dV (t) =. ((ıH 1. 2aKKa. )dt dB(t)Ka. aKSdB(t) Tr((S I)>dΛ(t)))V (t),. ... dY (t) = Ka(t)dt SdB(t). C Controllability and Observability. Consider a complex linear (time invariant state-space) system described by the differentialequation.

The geometri representation theory of these algebras has been studied in [Lu1, Lu2, Lu3 and fundamental re-sults have appeared in [HO, Op. ... The following proposition provides a graded He ke analogue of the results in [Ka,Proposition 1.20 and [Ka,