Abstract : In this paper, we study $\Delta$-transitivity, $\Delta$-weak mixing and $\Delta$-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.
Abstract : In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\mathbf{P}^{n}(\mathbf{C})$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.
Abstract : This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.
Abstract : Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers and let $P(A)=\left\{\sum \varepsilon_ia_i: a_i\in A, \varepsilon_i=0\text{ or }1, \sum \varepsilon_i<\infty\right\}$. Burr posed the following question: Determine conditions on integers sequence $B$ that imply either the existence or the non-existence of $A$ for which $P(A)$ is the set of all non-negative integers not in $B$. In this paper, we focus on some problems of subset sum related to Burr's question.
Abstract : This paper establishes the {Baum--Katz} type theorem and the {Marcinkiewicz--Zymund} type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors $\{X,X_n,n\ge1\}$ taking values in a Hilbert space $H$ with general normalizing constants $b_n=n^{\alpha}\widetilde L(n^{\alpha})$, where $\widetilde L(\cdot)$ is the de Bruijn conjugate of a slowly varying function $L(\cdot).$ The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.
Abstract : We prove sharp bounds for Hankel determinants for starlike functions $f$ with respect to symmetrical points, i.e., $f$ given by $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ for $z\in \mathbb{D}$ satisfying $$ Re\dfrac{zf'(z)}{f(z)-f(-z)}>0, \quad z\in \mathbb{D}. $$ We also give sharp upper and lower bounds when the coefficients of $f$ are real.
Abstract : The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of $\alpha$-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.
Abstract : In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space $X$, a syndetically transitive semiflow $(T,X,\pi)$ having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a $T_3$ space $X$, a transitive, nonminimal semiflow $(T,X,\pi)$ having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.
Abstract : The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of $s$ parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of $s$ parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan $s$ parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null $s$ parameter curve.
Abstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
Yong Lin, Yuanyuan Xie
Bull. Korean Math. Soc. 2022; 59(3): 745-756
https://doi.org/10.4134/BKMS.b210445
Yu Wang
Bull. Korean Math. Soc. 2023; 60(4): 1025-1034
https://doi.org/10.4134/BKMS.b220460
St\'ephane R. Louboutin
Bull. Korean Math. Soc. 2023; 60(1): 1-22
https://doi.org/10.4134/BKMS.b210464
Guangzhou Chen , Wen Li, Bangying Xin, Ming Zhong
Bull. Korean Math. Soc. 2022; 59(3): 617-642
https://doi.org/10.4134/BKMS.b210281
Gurpreet Kaur, Sumit Nagpal
Bull. Korean Math. Soc. 2023; 60(6): 1477-1496
https://doi.org/10.4134/BKMS.b220582
Donghoon Jang
Bull. Korean Math. Soc. 2023; 60(5): 1295-1298
https://doi.org/10.4134/BKMS.b220657
Mustafa Altın, Ahmet Kazan, Dae Won Yoon
Bull. Korean Math. Soc. 2023; 60(5): 1299-1320
https://doi.org/10.4134/BKMS.b220680
Jong Yoon Hyun
Bull. Korean Math. Soc. 2023; 60(3): 561-574
https://doi.org/10.4134/BKMS.b210374
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