Journal of Mathematical Study JMS Volume 55, Number 2

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Volume 55, Number 2

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Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces

Yuqin Liu & Xing Fu

10.4208/jms.v55n2.22.01

J. Math. Study, 55 (2022), pp. 109-123.

Preview Purchase PDF 2639 32447 Abstract

Abstract

In this paper, we establish the boundedness of the bilinear fractional integral operator $B_\alpha$ and the subbilinear fractional maximal operator $M_\alpha$ on vanishing generalized Morrey spaces $V_{0}L^{p,\varphi}(\mathbb{R}^n)$, $V_{\infty}L^{p,\varphi}(\mathbb{R}^n)$ and $V^{(*)}L^{p,\varphi}(\mathbb{R}^n)$. The main novelty of this article is that we control $B_{\alpha}$ by the subbilinear maximal operator $M$ and $M_{\alpha'}$ with $\alpha'>\alpha$. Some specific examples for the main results of this paper are also included.

Gorenstein Hereditary Rings

Meiqi Yan & Hailou Yao

10.4208/jms.v55n2.22.02

J. Math. Study, 55 (2022), pp. 124-138.

Preview Purchase PDF 2882 33545 Abstract

Abstract

In this paper, we introduce the Gorenstein hereditary and Gorenstein semi-hereditary modules and study the properties of the radical of Gorenstein projective modules over left artin rings. As an application, we characterize when Gorenstein projective modules are projective and give some characterizations of the Gorenstein hereditary rings by radical and Gorenstein projective modules over the endomorphism algebra of a module, respectively. Meanwhile we study the projective complexes over Gorenstein hereditary rings. In the last part of the paper, we study the heredity, Gorenstein heredity and quasi-heredity of the Morita context ring $\Lambda_{(0,0)}$ which is a left artin algebra.

Modeling and Applications to Circular Data with a Wrapped Poisson-Lindley Model

Christophe Chesneau, Hassan S. Bakouch & Tassaddaq Hussain

10.4208/jms.v55n2.22.03

J. Math. Study, 55 (2022), pp. 139-157.

Preview Purchase PDF 2722 32259 Abstract

Abstract

In the recent years, researchers in many fields, including meteorology, economics, sociology, psychology, and epidemiology, have shown a keen interest in the analysis and modeling of wrapped data. This motivates the development of new wrapped distributions and related models. In this paper, a simple and new wrapped model based on the Poisson-Lindley distribution is developed. Many of its properties are obtained, such as probability mass and cumulative distribution functions, survival and hazard rate functions, and probability generating function. The estimation of the model parameter is investigated by the maximum likelihood method. Test and evaluation statistics are also considered to assess the performance of the distribution among the most frequently wrapped discrete probability models using three different circular practical data sets.

On Doubly Twisted Product of Complex Finsler Manifolds

Wei Xiao, Yong He, Xiaoying Lu & Xiangxiang Deng

10.4208/jms.v55n2.22.04

J. Math. Study, 55 (2022), pp. 158-179.

Preview Purchase PDF 2670 32436 Abstract

Abstract

Let $(M_1,F_1)$ and $(M_2,F_2)$ be two strongly pseudoconvex complex Finsler manifolds. The doubly twisted product (abbreviated as DTP) complex Finsler manifold $(M_1\times_{(\lambda_1,\lambda_2)}M_2,F)$ is the product manifold $M_1\times M_2$ endowed with the twisted product complex Finsler metric $F^2=\lambda_1^2F_1^2+\lambda_2^2F_2^2$, where $\lambda_1$ and $\lambda_2$ are positive smooth functions on $M_1\times M_2$. In this paper, the relationships between the geometric objects (e.g. complex Finsler connections, holomorphic and Ricci scalar curvatures, and real geodesic) of a DTP-complex Finsler manifold and its components are derived. The necessary and sufficient conditions under which the DTP-complex Finsler manifold is a Kähler Finsler (respctively weakly Kähler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained. By means of these, we provide a possible way to construct a weakly complex Berwald manifold, and then give a characterization for a complex Landsberg metric that is not a Berwald metric.

Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process

Guiding Gu, Wang Li & Ren-Cang Li

10.4208/jms.v55n2.22.05

J. Math. Study, 55 (2022), pp. 180-194.

Preview Purchase PDF 2655 31680 Abstract

Abstract

This paper is concerned with the quadratic matrix equation $A_0+A_1X+A_2X^2$ $=X$ where $I-A_0-A_1-A_2$ is a regular $M$-matrix, i.e., there exists an entrywise positive vector u such that $(I-A_0-A_1-A_2)$u $\ge 0$ entrywise. It broadly includes those originally arising from the quasi-birth-and-death (QBD) process as a special case where $I-A_0-A_1-A_2$ is an irreducible singular $M$-matrix and $(A_0+A_1+A_2)$1=1 with 1 being the vector of all ones. A highly accurate implementation of Latouche-Ramaswami logarithmic reduction algorithm [Journal of Applied Probability, 30(3):650-674, 1993] is proposed to compute the unique minimal nonnegative solution of the matrix equation with high entrywise relative accuracy as it deserves. Numerical examples are presented to demonstrate the effectiveness of the proposed implementation.

Several Optimal Bounds for Some Means Derived from the Lemniscatic Mean

Xueling Wang & Li Yin

10.4208/jms.v55n2.22.06

J. Math. Study, 55 (2022), pp. 195-205.

Preview Purchase PDF 2540 31856 Abstract

Abstract

In this paper, we present sharp bounds for some bivariate means derived from the lemniscatic mean by Neuman, in terms of the harmonic, arithmetic and contraharmonic means.

On Strong Deviation Theorems Concerning Arrays of Non-Negative Integer-Valued Random Variables

Jing Song, Shu Chen & Zhongzhi Wang

10.4208/jms.v55n2.22.07

J. Math. Study, 55 (2022), pp. 206-215.

Preview Purchase PDF 2531 31188 Abstract

Abstract

In this article, by using the notion of general relative entropy as a measure of dependence of random variables, a kind of strong deviation theorems for the averages of array of integer-valued random variables are established. At the end of this paper, we give the upper and lower bounds for general moving averages of the form.

Gorenstein Hereditary Coalgebras

Yexuan Li & Hailou Yao

10.4208/jms.v55n2.22.08

J. Math. Study, 55 (2022), pp. 216-228.

Preview Purchase PDF 2540 31329 Abstract

Abstract

Let $C$ be a coalgebra. We prove that a right $C$-comodule is an $n$-cosyzygy if and only if it is a Gorenstein $n$-cosyzygy. We study the Gorenstein global dimension of coalgebras and the class of Gorenstein hereditary coalgebras. As a generalization of Gorenstein hereditary coalgebras, we introduce the concept of Gorenstein semihereditary coalgebras and show that a coalgebra $C$ is Gorenstein semihereditary if and only if every finitely cogenerated factor of any injective comodule is Gorenstein injective.

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