$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 19 Issue 1

January 2021

Issue of Open Mathematics

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Contents
Journal Overview

In this paper, we study Bernstein-Walsh type estimates for the higher-order derivatives of an arbitrary algebraic polynomial on quasidisks.

Review Article

Open Access August 16, 2021

Semiprimeness of semigroup algebras

Junying Guo, Xiaojiang Guo

Page range: 803-832

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Abstract

Abundant semigroups originate from p.p. rings and are generalizations of regular semigroups. The main aim of this paper is to study the primeness and the primitivity of abundant semigroup algebras. We introduce and study D ∗ {{\mathcal{D}}}^{\ast } -graphs and Fountain matrices of a semigroup. Based on D ∗ {{\mathcal{D}}}^{\ast } -graphs and Fountain matrices, we determine when a contracted semigroup algebra of a primitive abundant semigroup is prime (respectively, semiprime, semiprimitive, or primitive). It is well known that for any algebra A {\mathcal{A}} with unity, A {\mathcal{A}} is primitive (prime) if and only if so is M n ( A ) {M}_{n}\left({\mathcal{A}}) . Our results can be viewed as some kind of generalizations of such a known result. In addition, it is proved that any contracted semigroup algebra of a locally ample semigroup whose set of idempotents is locally finite (respectively, locally pseudofinite and satisfying the regularity condition) is isomorphic to some contracted semigroup algebra of primitive abundant semigroups. Moreover, we obtain sufficient and necessary conditions for these classes of contracted semigroup algebras to be prime (respectively, semiprime, semiprimitive, or primitive). Finally, the structure of simple contracted semigroup algebras of idempotent-connected abundant semigroups is established. Our results enrich and extend the related results on regular semigroup algebras.

In this paper, we provide existence and uniqueness of entropy solutions to a general nonlinear parabolic problem on a general convex set with merely integrable data and in the setting of Orlicz spaces.

We get the strong and Δ \Delta -convergence of the Picard-Krasnoselskii hybrid iteration scheme to a fixed point of a self-map endowed with the condition ( B γ , μ ) \left({B}_{\gamma ,\mu }) . We use the nonlinear context of CAT(0) spaces for establishing these results. We present a new example of a self-map endowed with ( B γ , μ ) \left({B}_{\gamma ,\mu }) condition and prove that its Picard-Krasnoselskii hybrid iterative process is more effective than the Picard and Krasnoselskii hybrid iterative processes. This improves and extends some recently announced results of the current literature.

The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other things, we show that the rising factorial moments of the degenerate Poisson random variable with parameter α \alpha are given by the degenerate Lah-Bell polynomials evaluated at α \alpha . We also show that the probability-generating function of the degenerate Poisson random variable is equal to the generating function of the degenerate Lah-Bell polynomials. Also, we show similar results for the Poisson random variables. Here the n n th Lah-Bell number counts the number of ways a set of n n elements can be partitioned into non-empty linearly ordered subsets, the Lah-Bell polynomials are natural extensions of the Lah-Bell numbers and the degenerate Lah-Bell polynomials are degenerate versions of the Lah-Bell polynomials.

Special Issue on Fractional Problems with Variable-Order or Variable Exponents (Part I)

Open Access December 31, 2021

On the mixed fractional quantum and Hadamard derivatives for impulsive boundary value problems

Somboon Niyoom, Sotiris K. Ntouyas, Chayapat Sudprasert, Jessada Tariboon

Page range: 1598-1611

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Abstract

In this work, we initiate the study of a new class of impulsive boundary value problems consisting of mixed type fractional quantum and Hadamard derivatives. We will establish existence and uniqueness results by using tools from the functional analysis. We prove the uniqueness result via Banach’s contraction mapping principle, while we will use the Leray-Schauder nonlinear alternative to establish an existence result. We also present examples to illustrate the obtained results.

Open Access December 31, 2021

The L_p dual Minkowski problem about 0 < p < 1 and q > 0

Fangxia Lu, Zhaonian Pu

Page range: 1648-1663

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Abstract

The ( p , q p,q )-th dual curvature measures and the L p {L}_{p} dual Minkowski problem were recently introduced by Lutwak, Yang, and Zhang. In this paper, we give a solution to the existence part of the L p {L}_{p} dual Minkowski problem about 0 < p < 1 0\lt p\lt 1 and q > 0 q\gt 0 for arbitrary measures. This fills up previously obtained results.

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes original and relevant works on topics across the full span of mathematics. The journal's primary goal is to maintain the high quality of its published content and to provide free, instant, and continued access to all content worldwide.

AIMS AND SCOPE
Open Mathematics aims to promote knowledge directly relevant to all fields of mathematics. Subject areas suitable for publication include, but are not limited to, the following:

Algebra, Algebraic Geometry, Category Theory, Complex Analysis, Control Theory and Optimization, Differential Equations, Differential Geometry, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Functional Analysis, Geometry, Mathematical Logic and Foundations, Mathematical Physics, Number Theory, Numerical Analysis, Operator Theory, Probability Theory and Statistics, Real Analysis, and Topology.

The journal accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.

Volume 19 Issue 1

Issue of Open Mathematics

Sharp conditions for the convergence of greedy expansions with prescribed coefficients

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Range-kernel weak orthogonality of some elementary operators

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Stability analysis for Selkov-Schnakenberg reaction-diffusion system

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On non-normal cyclic subgroups of prime order or order 4 of finite groups

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Some results on semigroups of transformations with restricted range

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Quasi-ideal Ehresmann transversals: The spined product structure

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On the regulator problem for linear systems over rings and algebras

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Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights

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Resolving resolution dimensions in triangulated categories

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Entire functions that share two pairs of small functions

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On stochastic inverse problem of construction of stable program motion

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Pentagonal quasigroups, their translatability and parastrophes

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Counting certain quadratic partitions of zero modulo a prime number

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Global attractors for a class of semilinear degenerate parabolic equations

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A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation

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On sub-class sizes of mutually permutable products

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Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity

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Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity

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On kernels by rainbow paths in arc-coloured digraphs

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Fully degenerate Bell polynomials associated with degenerate Poisson random variables

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Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation

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A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces

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Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group

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Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

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Hodge-Deligne polynomials of character varieties of free abelian groups

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Diophantine approximation with one prime, two squares of primes and one kth power of a prime

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The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications

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Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

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On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions

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Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

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Asymptotic measure-expansiveness for generic diffeomorphisms

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Infinitesimals via Cauchy sequences: Refining the classical equivalence

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The (1, 2)-step competition graph of a hypertournament

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Properties of multiplication operators on the space of functions of bounded φ-variation

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Disproving a conjecture of Thornton on Bohemian matrices

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Some estimates for the commutators of multilinear maximal function on Morrey-type space

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Inviscid, zero Froude number limit of the viscous shallow water system

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Inequalities between height and deviation of polynomials

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New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms

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Solvability of the abstract evolution equations in L^s-spaces with critical temporal weights

The B-topology on S^∗-doubly quasicontinuous posets

On primitive solutions of the Diophantine equation x² + y² = M

Finite groups with 4p²q elements of maximal order

Power moments of automorphic L-functions related to Maass forms for SL₃(ℤ)