Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

Let W be a finite Coxeter group, P a parabolic subgroup of W, and N _W (P) the normalizer of P in W. We prove that every element in N _W (P) is strongly real in N _W (P), and that every irreducible complex character of N _W (P) has Frobenius-Schur indicator 1.     

Lattices Derived from Hyperlattices

In this article, by considering the notion of a hyperlattice and a superlattice, we give some examples of them, and we study their structures and their quotient structure with a regular relation. We introduce the relation ν on a hyperlattice L, and we let ν* be the transitive closure of ν. We show that ν* is a fundamental relation on a hyperlattice. The quotient L/ν* is called the fundamental lattice. Notice that the most important relations in hyperstructure theory are the fundamental ones. Finally, we give some interesting results about the fundamental lattices.     

ALMOST OPTIMAL LOCAL WELL-POSEDNESS OF THE MAXWELL-KLEIN-GORDON EQUATIONS IN 1 + 4 DIMENSIONS

Abstract

We study strong solutions of the Navier–Stokes equations for nonhomogeneous incompressible fluids in Ω ? R ³. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω =R ³) or the initial boundary value problem (for Ω ? ? R ³) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

整值随机变量序列的一类强律

本文引进似然比作为整值随机变量序列相对于服从Poisson分布的独立随机变量序列的偏差的一种度量，并通过限制似然比给出了样水空间的某种子集．在这种子集上得到了一类用不等式表示的强律，独立随机变量序列的一类强律是其特例．     

ON THE STRONG LAW OF LARGE NUMBERS FOR SUMS OF INDEPENDENT BANACH SPACE VALUED RANDOM ELEMENTS

For a sequence of independent random elements {V _n ,n≥1} in a real separable Banach space X, necessary and, separately, sufficient conditions are provided for the strong law of large numbers ∑ _i=1 ⁿ (V _i ?c _i )/b _n →0 almost certainly to hold where {c _n ,n≥1} and {b _n >0,n≥1} are suitable sequences of centering elements in X and norming constants, respectively. The necessity result extends a real line result of Martikainen[14] Martikainen, A.I. 1979. On Necessary and Sufficient Conditions for the Strong Law of Large Numbers. Teor. Veroyatnost. i Primen., 24: 814–820. (English translation in Theory Probabl. Appl., 24 (1979) 820–823) [Google Scholar] to a Banach space setting. The sufficiency result assumes that X is of Rademacher type p (1≤p≤2) and is new even when X is the real line. It is general enough to include as special cases a strong law of Adler, Rosalsky, and Taylor[2] Adler, A., Rosalsky, A. and Taylor, R.L. 1989. Strong Laws of Large Numbers for Weighted Sums of Random Elements in Normed Linear Spaces. Int. J. Math. Math. Sci., 12: 507–530. [Crossref] , [Google Scholar] for sums of independent and identically distributed random elements and a strong law of Heyde[9] Heyde, C.C. 1968. On almost sure convergence for sums of independent random variables. Sankhya¯ Ser. A, 30: 353–358.  [Google Scholar] for sums of independent (real-valued) random variables. Illustrative examples are provided showing that the results are sharp and an example is presented satisfying the hypotheses of the sufficiency result but not those of Heyde's[9] Heyde, C.C. 1968. On almost sure convergence for sums of independent random variables. Sankhya¯ Ser. A, 30: 353–358.  [Google Scholar] theorem.     

Prosolvable subgroups of free products of profinite groups

In this paper we establish several equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of prime power ideals to be a general ZPI-ring. Using these results, we establish some equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of primary ideals to be a general ZPI-ring.     

关于任意随机变量序列的强极限定理的一个注记

主要说明两两NQD随机变量序列的一些收敛性质是任意随机变量序列的强极限定理的推论.     

(∈,∈∨ q(λ,μ))-模糊强正则子半群

本文是正则半群的模糊化研究工作的继续,首先给出了广义模糊强正则子半群的概念,其次基于模糊点理论给出了(∈,∈∨ q(λ,μ))-模糊强正则子半群的概念,并且讨论了它们的相关性质.最后获得了(∈,∈∨ q(λ,μ))-模糊强正则子半群的同态像与同态原像的有关性质.