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Journal of Systems Science & Complexity 2010年第1期23卷 153-176页

作者： Satoshi TSUJIMOTO Department of applied mathematics and Physics Graduate School of InformaticsKyoto University

It is shown that the nonautonomous discrete Toda equation and its Backlund transformation can be derived from the reduction of the hierarchy of the discrete KP equation and the discrete two-dimensional Toda equation. Some explicit examples of the determinant solutions of the nonautonomous discrete Toda equation including the Askey-Wilson polynomial are presented. Finally we discuss the relationship between the nonautonomous discrete Toda system and the nonautonomous discrete Lotka- Volterra equation.

关键词： Askey-Wilson polynomial Darboux transformation discrete KP hierarchy nonautonomous discrete Lotka-Volterra equation nonautonomous discrete Toda equation.

New Results on System of Generalized Quasi-Ky Fan Inequalities with Set-Valued Mappings in Topological Semilattice Spaces

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Journal of Systems Science & Complexity 2016年第6期29卷 1585-1595页

作者： NGUYEN The Vinh PHAM Thi Hoai Department of mathematics University of Transport and Communications school of applied mathematics and informatics University of Science and Technology

Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological *** obtained results are new and different from the corresponding known results in the *** special cases of the main result are also *** examples are given to illustrate the results.

关键词： C△-quasiconvex (quasiconcave) Fan-Browder fixed point theorem set-valued Ky Faninequality topological semilattice upper (lower) C-continuous.

A novel method for clustering cellular data to improve classification

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Neural Regeneration Research 2025年第9期20卷 2697-2705页

作者： Diek W.Wheeler Giorgio A.Ascoli Center for Neural informatics Structures&PlasticityKrasnow Institute for Advanced Study Bioengineering Department Volgenau School of Engineering George Mason University FairfaxVAUSA

Many fields,such as neuroscience,are experiencing the vast prolife ration of cellular data,underscoring the need fo r organizing and interpreting large datasets.A popular approach partitions data into manageable subsets via hierarchical clustering,but objective methods to determine the appropriate classification granularity are *** recently introduced a technique to systematically identify when to stop subdividing clusters based on the fundamental principle that cells must differ more between than within *** we present the corresponding protocol to classify cellular datasets by combining datadriven unsupervised hierarchical clustering with statistical *** general-purpose functions are applicable to any cellular dataset that can be organized as two-dimensional matrices of numerical values,including molecula r,physiological,and anatomical *** demonstrate the protocol using cellular data from the Janelia MouseLight project to chara cterize morphological aspects of neurons.

关键词： cellular data clustering dendrogram data classification Levene's one-tailed statistical test unsupervised hierarchical clustering

A COMBINATORIAL ASPECT OF A DISCRETE-TIME SEMI-INFINITE LOTKA-VOLTERRA EQUATION

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Journal of Systems Science & Complexity 2010年第1期23卷 71-80页

作者： Shuhei KAMIOKA Satoru MIZUTANI Department of applied mathematics and Physics Graduate School of InformaticsKyoto University KDDI Corporation Garden Air Tower

A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) *** particular,Hankel determinants used in a determinantsolution to the dLV equation are evaluated,via the Gessel-Viennot method,in terms of ***,the recurrence of the dLV equation describing its time-evolution is equivalentlyexpressed as a time-evolution of weight of specific subgraphs.

关键词： Combinatorial proofs discrete integrable systems dynamics on graphs Gessel-Viennot method Hankel determinants non-intersecting paths weighted paths on labeled graphs.

Structures and electronic properties of Mo_(2n)N_n(n=1-5):a density functional study

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Chinese Physics B 2010年第12期19卷 212-222页

作者：陈杭雷雪玲刘立仁刘志锋祝恒江 school of mathematics Physics and InformaticsXinjiang Normal University

The lowest-energy structures and the electronic properties of Mo2nNn （n=1-5） clusters have been studied by using the density functional theory （DFT） simulating package DMol3 in the generalized gradient approximation （GGA）. The resulting equilibrium geometries show that the lowest-energy structures are dominated by central cores which correspond to the ground states of Mon （n = 2, 4, 6, 8, 10） clusters and nitrogen atoms which surround these cores. The average binding energy, the adiabatic electron affinity （AEA）, the vertical electron affinity （VEA）, the adiabatic ionization potential （AIP） and the vertical ionization potential （VIP） of Mo2nNn （n=1-5） clusters have been estimated. The HOMO LUMO gaps reveal that the clusters have strong chemical activities. An analysis of Mulliken charge distribution shows that charge-transfer moves from Mo atoms to N atoms and increases with cluster size.

关键词： Mo2nNn clusters density functional theory equilibrium structures electronic properties

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

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Acta Mathematica Scientia 2010年第5期30卷 1469-1480页

作者：原保全 school of mathematics and informatics Henan Polytechnic University

In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.

关键词： magneto-micropolar fluid equations regularity criteria blow-up criteria

A Dwindling Filter Line Search Algorithm for Nonlinear Equality Constrained Optimization

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Journal of Systems Science & Complexity 2015年第3期28卷 623-637页

作者： GU Chao ZHU Detong school of mathematics and informatics Shanghai Lixin University of Commerce Department of mathematics Shanghai Normal University

This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.

关键词： Convergence dwindling filter line search nonlinear optimization secant update.

Text Encryption Using Pell Sequence and Elliptic Curves with Provable Security

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Computers, Materials & Continua 2022年第6期71卷 4971-4988页

作者： Sumaira Azhar Naveed Ahmed Azam Umar Hayat Department of mathematics Quaid-i-Azam UniversityIslamabad45320Pakistan Department of applied mathematics and Physics Graduate School of InformaticsKyoto UniversityKyoto606-8501Japan

The demand for data security schemes has increased with the significant advancement in the field of computation and communication *** propose a novel three-step text encryption scheme that has provable security against computation attacks such as key attack and statistical *** proposed scheme is based on the Pell sequence and elliptic curves,where at the first step the plain text is diffused to get a meaningless plain text by applying a cyclic shift on the symbol *** the second step,we hide the elements of the diffused plain text from the *** this purpose,we use the Pell sequence,a weight function,and a binary sequence to encode each element of the diffused plain text into real *** encoded diffused plain text is then confused by generating permutations over elliptic curves in the third *** show that the proposed scheme has provable security against key sensitivity attack and statistical ***,the proposed scheme is secure against key spacing attack,ciphertext only attack,and known-plaintext *** to some of the existing text encryption schemes,the proposed scheme is highly secure against modern cryptanalysis.

关键词： Text encryption pell numbers elliptic curves key sensitivity statistical cryptanalysis

Continuous adjoint-based error estimation and its application to adaptive discontinuous Galerkin method

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applied mathematics and Mechanics(English Edition) 2016年第11期37卷 1419-1430页

作者： Huiqiang YUE Tiegang LIU V.SHAYDUROV Key Laboratory of mathematics Informatics and Behavioral Semantics Ministry of EducationSchool of Mathematics and Systems Science Beihang University

An adaptive mesh refinement algorithm based on a continuous adjoint ap- proach is developed. Both the primal equation and the adjoint equation are approximated with the discontinuous Galerkin （DG） method. The proposed adaptive algorithm is used in compressible Euler equations. Numerical tests are made to show the superiority of the proposed adaptive algorithm.

关键词： adaptivity discontinuous Galerkin (DG) adjoint

ON THE SHARING VALUES OF ALGEBROID FUNCTIONS AND THEIR DERIVATIVES

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Acta Mathematica Scientia 2013年第1期33卷 268-278页

作者：刘惠芳孙道椿 Institute of mathematics and informatics Jiangxi Normal University school of mathematics South China Normal University

In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.

关键词： algebroid function function element shared value uniqueness