• Volume 117, Issue 4

November 2007,   pages  429-585

• Bounds for Regularity and Coregularity of Graded Modules

Let 𝑀 be a finitely generated graded module over a Noetherian homogeneous ring 𝑅 with local base ring $(R_0,\mathfrak{m}_0)$. If $R_0$ is of dimension one, then we show that $\mathrm{reg}^i+1(M)$ and $\mathrm{coreg}^{i+1}(M)$ are bounded for all $i\in\mathbb{N}_0$. We improve these bounds, if in addition, $R_0$ is either regular or analytically irreducible of unequal characteristic.

• Explicit Representation of Roots on 𝑝-Adic Solenoids and Non-Uniqueness of Embeddability into Rational One-Parameter Subgroups

This note generalizes known results concerning the existence of roots and embedding one-parameter subgroups on 𝑝-adic solenoids. An explicit representation of the roots leads to the construction of two distinct rational embedding one-parameter subgroups. The results contribute to enlighten the group structure of solenoids and to point out difficulties arising in the context of the embedding problem in probability theory. As a consequence, the uniqueness of embedding of infinitely divisible probability measures on 𝑝-adic solenoids is solved under a certain natural condition.

• Structure of a Code Related to $Sp(4,q),q$ even

We determine the socle and the radical series of the binary code associated with a finite regular generalized quadrangle of even order, considered as a module for the commutator of each of the orthogonal subgroups in the corresponding symplectic group.

• On the Compactly Locally Uniformly Rotund Points of Orlicz Spaces

In this paper, locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.

• Positive Linear Operators Generated by Analytic Functions

Let 𝜑 be a power series with positive Taylor coefficients $\{a_k\}^\infty_{k=0}$ and non-zero radius of convergence $r\leq\infty$. Let $\xi_x,\,0\leq x &lt; r$ be a random variable whose values $\alpha_k, k=0,1,\ldots,$ are independent of 𝑥 and taken with probabilities $a_kx^k/\varphi(x), k=0,1,\ldots$

The positive linear operator $(A_\varphi f)(x):=E[f(\xi_x)]$ is studied. It is proved that if $E(\xi_x)=x,E(\xi^2_x)=qx^2+bx+c,\, q, b, c\in R, q&gt;0$, then $A_\varphi$ reduces to the Szász–Mirakyan operator in the case $q=1$, to the limit 𝑞-Bernstein operator in the case $0 &lt; q &lt; 1$, and to a modification of the Lupaş operator in the case $q&gt;1$.

• Compact Solutions to the Equation $Tx = y$ in a Weakly Closed $\mathcal{T}(\mathcal{N})$-Module

Given two vectors $x,y$ in a Hilbert space and a weakly closed $\mathcal{T}(\mathcal{N})$-module $\mathcal{U}$, we provide a necessary and sufficient condition for the existence of a compact operator 𝑇 in $\mathcal{U}$ satisfying $Tx=y$.

• Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals

By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.

• Central Limit Theorems for a Class of Irreducible Multicolor Urn Models

We take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.

• Some Nonlinear Dynamic Inequalities on Time Scales

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).

• Dynamics and Bifurcations of Travelling Wave Solutions of $R(m, n)$ Equations

By using the bifurcation theory and methods of planar dynamical systems to $R(m, n)$ equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.

• Subject Index

• Author Index

• # Proceedings – Mathematical Sciences

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