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Characterization of polynomial Systems Satisfying generalized Convolution Differential-Difference Equations

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数学研究与评论 1989年第2期9卷 159-172页

作者： H.W.gould W.Y.Kerr department of mathematics’ West Virginia Vniversity

I. Introduction. The present paper has been motivated by the desire to find all polynomial solutions of the convolution type differential -difference equation （1.1） Dxgn（x）=sum from i=1 to n-1 (gi（x）gn-i（x）,n≥2,) where g1（x） is assumed to be a constant. This problem arose in work by one of the authors （Kerr） with a differential equation arising in a coal research project

关键词： Characterization of polynomial Systems Satisfying generalized Convolution Differential-Difference Equations

On Characterization of Monoids by properties of generators

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Journal of Mathematical research with Applications 2020年第4期40卷 367-380页

作者： Morteza JAFARI Akbar gOLCHIN Hossein MOHAMMADZADEH SAANY department of mathematics University of Sistan and Baluchestan

Kilp and Knauer in(Comm. Algebra, 1992, 20(7), 1841–1856) gave characterizations of monoids when all generators in category of right S-acts(S is a monoid) satisfy properties such as freeness, projectivity, strong flatness, Condition(p), principal weak flatness, principal weak injectivity, weak injectivity, injectivity, divisibility, strong faithfulness and torsion *** in(Semigroup Forum, 2013, 87: 653–662) characterized monoids by some other properties of generators including weak flatness, Condition(E) and regularity. To our knowledge,the problem has not been studied for properties mentioned above of(finitely generated, cyclic,monocyclic, Rees factor) right acts. In this article we answer the question corresponding to these properties and also f g-weak injectivity.

关键词： generator finitely generated Subannihilator congruence injective

The Representation Theorems of Conjugate Spaces of Some l0（{Xi}） Type F-Normed Spaces

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Journal of Mathematical research with Applications 2017年第5期37卷 591-602页

作者： Jianyong WANg department of mathematics Changshu Institute of Technology

In a paper published in Acta Mathematica Sinica(2016, 59（4）) we obtained some representation theorems for the conjugate spaces of some ltype F-normed spaces. In this par per, for a sequence of normed spaces {X}, we study the representation problems of conjugate spaces of some l（{X}） type F-normed spaces, obtain the algebraic representation continued equalities(l（{X）)*A=(c（{X}）)*A=c（{Xi*}）,(L（X）)*A=(c（X）)*A=(c（X）)*A=(c（X）)*A=C（X*）,and the topological representation((c（{X}）)*,sw*) = c（{X*}）,where sw* is the sequential weak star topology. For the sequences of inner product spaces and number fields with the usual topology, the concrete forms of the basic representation theorems are obtained at last.

关键词： l~0({X_i}) type F-normed space locally convex space locally bounded space sequential weak star topology representation theorem

Anticancer activity test of ethyl acetate extract of endophytic fungi isolated from soursop leaf(Annona muricata L.)

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Asian pacific Journal of Tropical Medicine 2017年第6期10卷 635-640页

作者： Minarni I Made Artika Heddy Julistiono Nurliani Bermawie Eny Ida Riyanti Hasim Akhmad Endang Zainal Hasan department of Biochemistry Faculty of Mathematics and SciencesBogor Agricultural UniversityDarmaga CampusBogor 16680Indonesia research Center for Biology The Indonesian Institute of Sciences(LIPI)Cibinong-Bogor Indonesia research Institute of Medicinal and Aromatic plants Agricultural Research AgencyBogor-Indonesia Center for Biotechnology and genetic Resources of Agriculture Agricultural Research AgencyBogor-Indonesia

Objective: To analyze anticancer activity of an ethyl acetate extract of endophytic fungi isolated from soursop leaf(Annona muricata L.). Methods: Anticancer activity of fungal extracts was determined by observing its toxicity against MCF-7(Michigan Cancer Foundation-7) cells in vitro by using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MTT) assay method. At an extract concentration of 100 μg/m L, 4 isolates out of 12 showed high activity against the cancer cell growth. The four isolates were then selected for further IC50 determination, by measuring the inhibition of cancer cell proliferation at extract concentration of 25 μg/m L, 50 μg/m L, 100 μg/m L, 200 μg/m L and 400 μg/m L. Results: Results showed that isolate Sir-g5 had the highest anticancer activity with an IC50 of 19.20 μg/m L. The best isolates were screened again using a normal cell(Chang cells) to determine its toxicity against normal cells. Results indicated that the extracts do not affect the proliferation of normal cells. Molecular identification showed that the fungal isolate Sir-g5 has a close relationship with phomopsis sp. Conclusions: The endophytic fungi isolated from soursop leaf has the potential to be used as a source of anticancer agents.

关键词： Annona muricata L Anticancer MCF-7 Endophytic fungi Soursop leaf

Augmented Lagrangian Alternating Direction Method for Tensor RpCA

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Journal of Mathematical research with Applications 2017年第3期37卷 367-378页

作者： Ruru HAO Zhixun SU department of mathematics Dalian University of Technology

Tensor robust principal component analysis(TRpCA) problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRpCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.

关键词： tensor RpCA alternating direction method augmented Lagrangian function high-order SVD

generalized Lagrangian Duality in Set-valued Vector Optimization via Abstract Subdifferential

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Acta Mathematicae Applicatae Sinica 2022年第2期38卷 337-351页

作者： Yan-fei CHAI San-yang LIU Si-qi WANg department of mathematics Xi'an Polytechnic UniversityXi'an 710048China School of mathematics and Statistics Xidian UniversityXi'an 710071China College of Transportation Engineering Chang'an UniversityXi'an 710064China

In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract *** first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency,which used by the concepts of supremum and infimum of a *** then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object ***,we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization *** addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.

关键词： Nonconvex set-valued vector optimization abstract subdifferential generalized augmented Lagrangian duality exact penalization sub-optimal path

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The Nilpotent-Centralizer Methods

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Journal of Mathematical research with Applications 2014年第5期34卷 597-607页

作者： Yubin gAO Yanling SHAO department of mathematics North University of China

An nxn complex sign pattern(ray pattern) S is said to be spectrally arbitrary if for every monic nth degree polynomial f(λ) with coefficients from C,there is a complex matrix in the complex sign pattern class(ray pattern class) of S such that its characteristic polynomial is f(λ).We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns,*** find that the Nilpotent-Centralizer methods for three kinds of patterns(sign pattern,complex sign pattern,ray pattern) are the same in form.

关键词： complex sign pattern ray pattern spectrally arbitrary pattern nilpotence.

On Transcendental Entire Solutions of Systems of Complex Differential-Difference Equations

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Journal of Mathematical research with Applications 2017年第3期37卷 299-306页

作者： Manli LIU Lingyun gAO department of mathematics Ji'nan University

By using the Nevanlinna value distribution theory, we will mainly investigate the form of entire solutions with finite order on a type of system of differential-difference equations and a type of differential-difference equations, two interesting results are obtained. And it extends some results concerning complex differential(difference) equations to the systems of differential-difference equations.

关键词： differential-difference equation transcendental entire solutions meromorphic functions

Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment

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International Journal of Biomathematics 2016年第5期9卷 277-294页

作者： Jianjun Jiao Shaohong Cai Yujuan Zhang Limei Li School of mathematics and Statistics guizhou Key Laboratory of Economic System Simulation guizhou University of Finance and Economics guiyang Guizhou 550004 P R. China College of mathematics and Information Science Anshan Normal University Anshan Liaoning 114007 P. R. China School of Continuous Education guizhou University of Finance and Economics guiyang Guizhou 550004 P. R. China

In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population- extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.

关键词： Stage-structured single population system winter hibernation impulsive effect population-extinction permanence.