This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...

Let V be a finite dimensional vector space. Given a decomposition V ⊗ V = ⊕i Ii, define n quadratic algebras (V, Jm) where Jm = ⊕i6=mIi. This decomposition defines also the quantum semigroup M(V ; I1, ..., In) which acts on all these quadratic algebras. With the decomposition we associate a family of associative algebras Ak = Ak(I1, ...In), k ≥ 2. In the classical case, when V ⊗ V decomposes in...

Let $p$ be a prime, let $K$ discretely valued extension of $\mathbb{Q}_p$, and $A_{K}$ an abelian $K$-variety with semistable reduction. Extending work by Kim Marshall from the case where $p>2$ $K/\mathbb{Q}_p$ is unramified, we prove $l=p$ complement Galois cohomological formula Grothendieck for $l$-primary part N\'eron component group $A_{K}$. Our proof involves constructing, each $m\in \math...

Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minim...

The minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of C(X). The necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) I is an intersection of O , s, when X is basically disconnected. (iii) I=O , when x X h...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

Let $G$ be a locally compact abelian metric group with Haar measure $\lambda $ and $\hat{G}$ its dual $\mu ,$ ( G) is finite. Assume that$~1<p_{i}<\infty $, $p_{i}^{\prime }=\frac{ p_{i}}{p_{i}-1}$, $( i=1,2,3) $\theta \geq 0$. L^{(p_{i}^{\prime },\theta }( small Lebesgue spaces. A bounded measurable function $m( \xi ,\eta ) defined on $\hat{G}\times \hat{G}$ said to bilinear multiplier of type...

This paper addresses the problem of designing a submodule of a given system of communicating timed I/O automata. The problem may be formulated mathematically by the equation (C||X)rA under the constraint IX=In, where C represents the specification of the known part of the system, called the context, A represents the specification of the whole system, X represents the specification of the submod...