pp 429-441
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.
pp 443-455
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.
pp 457-470
Structure of a Code Related to $Sp(4,q),q$ even
N S Narasimha Sastry R P Shukla
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.
pp 471-483
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.
pp 485-493
Positive Linear Operators Generated by Analytic Functions
Let 𝜑 be a power series with positive Taylor coefficients $\{a_k\}^∞_{k=0}$ and non-zero radius of convergence 𝑟 ≤ ∞. Let $𝜉_x,\,0≤ x < r$ be a random variable whose values $𝛼_k, k=0,1,\ldots,$ are independent of 𝑥 and taken with probabilities $a_kx^k/\varphi(x), k=0,1,\ldots$
The positive linear operator $(A_\varphi f)(x):=E[f(𝜉_x)]$ is studied. It is proved that if $E(𝜉_x)=x,E(𝜉^2_x)=qx^2+bx+c,\, q, b, c\in R, q>0$, then $A_\varphi$ reduces to the Szász–Mirakyan operator in the case 𝑞=1, to the limit 𝑞-Bernstein operator in the case 0 < 𝑞 < 1, and to a modification of the Lupaş operator in the case 𝑞>1.
pp 495-503
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 $Tx=y$.
pp 505-515
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.
pp 517-543
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.
pp 545-554
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).
pp 555-574
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.
pp 575-581 Subject Index
pp 583-585 Author Index
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Volume 127 | Issue 5
November 2017
© 2017 Indian Academy of Sciences, Bengaluru.