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Evaluation of Binomial Series with Harmonic Numbers

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Journal of Mathematical research with Applications 2023年第1期43卷 49-58页

作者： Khristo BOYADZHIEV department of mathematics Ohio Northern University

We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.

关键词： digamma function Lerch transcendent binomial coefficient central binomial coefficient harmonic number stirling number of the first kind

Characterizations of Commutators of Singular Integral Operators on Variable Exponent Spaces

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Journal of Mathematical research with Applications 2020年第5期40卷 519-533页

作者： Chenglong FANg department of mathematics Yili Normal University

The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable *** on this main purpose, we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators. Immediately after, applying the characterizations of TriebelLizorkin space with variable exponent, we obtain that b ∈■β if and only if the commutator of Calderón-Zygmund singular integral operator is bounded, respectively, from■ to■,from■ to■ with■. Moreover, we prove that the commutator of Riesz potential operator also has corresponding results.

关键词： commutator Lipschitz space Triebel-Lizorkin space variable exponent singular integral operator

THE gENERALIZED ROpER-SUFFRIDgE OpERATOR ON THE UNIT BALL IN COMpLEX BANACH AND HILBERT SpACES

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Acta Mathematica Scientia 2017年第6期37卷 1817-1829页

作者：崔艳艳王朝君刘浩 College of mathematics and Information Science Hebei Normal University College of mathematics and Statistics Zhoukou Normal University Institute of Contemporary mathematics Henan University

In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.

关键词： spirallike mappings starlike mappings Roper-Suffridge operator

A generalization of Backlund theorem

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Chinese Science Bulletin 1995年第22期40卷 1854-1860页

作者：田畴 department of mathematics University of Science and Technology of China Hefei 230026 China

The famous Backlund theorem presented a method to construct a family of surfaces with K=-m^2 from a known surface with K=-m^2, i. e. the well-known Bcklund transformation. With the research and development of the soliton theory, Bcklund transformation has become an important method to find the solutions of soliton *** the same time, geometricians also pay attention to generalizing and developing the geometrical content of the Bcklund theorem. In refs. [4] and [5], the authors

关键词： Backlund transformation gaussian curvature mean curvature gauss-Codazzi equation.

ON THE CROSSINg NUMBER OF THE COMpLETE TRIpARTITE gRApH K1,8,n

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数学物理学报 2006年第S1期 1115-1122页

作者：黄元秋赵霆雷 department of mathematics Hunan Normal University Changsha 410081 China

The well known Zarankiewicz’ conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). presently, Zarankiewicz’ conjecture is proved true only for the case m≤g. In this article, the authors prove that if Zarankiewicz’ conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) + 12[n/2].

关键词： graphs Drawing Crossing number Complete tripartite graph Complete tripartite graph.

Characterization　of　Inverse　and　Left　Inverse　SemigroupsbyTheirS1┐acts

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Communications in Mathematical research 1996年第4期 16-22页

作者：刘仲奎ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＩｎｖｅｒｓｅａｎｄＬｅｆｔＩｎｖｅｒｓｅＳｅｍｉｇｒｏｕｐｓｂｙＴｈｅｉｒＳ１┐ａｃｔｓ＊）ＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｏ... 详细信息

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＩｎｖｅｒｓｅａｎｄＬｅｆｔＩｎｖｅｒｓｅＳｅｍｉｇｒｏｕｐｓｂｙＴｈｅｉｒＳ１┐ａｃｔｓ＊）ＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖ...

关键词： Inverse Semigroup Left Inverse Semigroup Flat Left S act Inverse Left S act

positive Solutions of Second Order Discrete problem on Infinite Intervals

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Journal of Mathematical research with Applications 2024年第4期44卷 511-520页

作者： Haiyi WU Tianlan CHEN department of mathematics Northwest Normal University

In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where?u(x)=u(x+1)-u(x) is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants,■

关键词： positive solutions second order discrete problems infinite intervals fixed-point theorem in cones

A Matrix Representation of Outer Derivations from gl0|2 to the generalized Witt Lie Superalgebra

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Communications in Mathematical research 2019年第4期35卷 367-376页

作者： ZHENg KE-LI Du Xian-kun department of mathematics Northeast Forestry University

Let gl0|2 be a subalgebra of the general linear Lie *** this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.

关键词： outer derivation inner derivation matrix representation generalized Witt Lie superalgebra

THE gLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE pHAN-THEIN-TANNER MODEL

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Acta Mathematica Scientia 2022年第3期42卷 1058-1080页

作者： Ruiying WEI Yin LI Zheng-an YAO School of mathematics and Statistics Shaoguan UniversityShaoguan 512005China Faculty of Education Shaoguan UniversityShaoguan 512005China department of mathematics Sun Yat-sen UniversityGuangzhou 510275China

In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible phan-Thein-Tanner *** a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be *** the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial ***,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.

关键词： phan-Thein-Tanner model global existence time decay rates