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SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES
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作者 刘曼莉 高凌云 房少梅 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期821-838,共18页
In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing sm... In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation. 展开更多
关键词 meromorphic function in several variables Nevanlinna theory partial differ-ential equation total derivative
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Extension of covariant derivative(Ⅱ): From flat space to curved space 被引量:4
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作者 Ya-Jun Yin 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2015年第1期88-95,共8页
This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant fo... This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces. 展开更多
关键词 Tensor analysis on curved surfaces Classicalcovariant derivative and generalized covariant derivative Axiom of the covariant form invariability Covariant differ-ential transformation group Differential invariabilities andintegral invariabilities
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General Integral Formulasof (0, q)(q 〉 0)Differential Forms on the Analytic Varieties 被引量:3
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作者 CHEN Shu-jin 《Chinese Quarterly Journal of Mathematics》 2017年第4期355-370,共16页
In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of (0, q)(q 〉 0) differential forms for the twotypes of the bounded domains in complex sub... In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of (0, q)(q 〉 0) differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of (0, q)(q 〉 0) differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of (0, q)(q 〉 0) differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula. 展开更多
关键词 Complex SUBMANIFOLD ANALYTIC VARIETIES UNIFIED FORMULA Extension differ-ential form Integral representation
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Isotope effect on the stereodynamics for the collision reaction H+LiF(v=0, j=0)→ HF+Li
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作者 岳现房 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第7期268-274,共7页
Stereodynamics for the reaction H+LiF(v = 0, j = 0) → HF+Li and its isotopic variants on the ground-state (12A') potential energy surface (PES) are studied by employing the quasi-classical trajectory (QCT)... Stereodynamics for the reaction H+LiF(v = 0, j = 0) → HF+Li and its isotopic variants on the ground-state (12A') potential energy surface (PES) are studied by employing the quasi-classical trajectory (QCT) method. At a collision energy of 1.0 eV, product rotational angular momentum distributions P(0r), P(~r), and P(Or, Cr), are calculated in the center-of-mass (CM) frame. The results demonstrate that the product rotational angular momentum j' is not only aligned along the direction perpendicular to the reagent relative velocity vector k, but also oriented along the negative y axis. The four generalized polarization-dependent differential cross sections (PDDCSs) are also computed. The PDDCS00 distribution shows a preferential forward scattering for the product angular distribution in each of the three isotopic reactions, which indicates that the title collision reaction is a direct reaction mechanism. The isotope effect on the stereodynamics is revealed and discussed in detail. 展开更多
关键词 STEREODYNAMICS quasi-classical trajectory isotope effect polarization-dependent differ-ential cross-section
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Substrate concentration effect on gene expression in genetic circuits with additional positive feedback 被引量:3
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作者 WU LuLu WANG Pei Lü JinHu 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2018年第8期1175-1183,共9页
In gene regulatory networks, gene regulation loops often occur with multiple positive feedback, multiple negative feedback and coupled positive and negative feedback forms. In above gene regulation loops, auto-activat... In gene regulatory networks, gene regulation loops often occur with multiple positive feedback, multiple negative feedback and coupled positive and negative feedback forms. In above gene regulation loops, auto-activation loops are ubiquitous regulatory motifs. This paper aims to investigate a two-component dual-positive feedback genetic circuit, which consists of a double negative feedback circuit and an additional positive feedback loop(APFL). We study effect of substrate concentration on gene expression in the single and the networked systems with APFLs, respectively. We find that substrate concentration can tune stochastic switch behavior in the signal system and then we explore relationship of substrate concentration with positive feedback strength in aspect of stochastic switch behavior. Furthermore, we also discuss gene expression and stochastic switch behavior in the networked systems with APFLs. Based on analysis in the networked systems, we discover that genes express in some specific cells and do not express in the other cells when the expression achieves its steady state. These results can be used to well explain the character of regionalization in the expression of genes and the phenomenon of gene differentiation. 展开更多
关键词 substrate concentration additional positive feedback loop stochastic switch behavior gene expression gene differ-entiation
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Implicit Function Theorem and Its Application to a Ulam's Problem for Exact Differential Equations 被引量:1
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作者 Soon-Mo JUNG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第11期2085-2092,共8页
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g(x, y)... We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g(x, y) + h(x, y)y' =0. 展开更多
关键词 Implicit function theorem Ulam's problem Hyers-Ulam-Rassias stability exact differ-ential equation potential function
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Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras (In Memory of Professor Guenter Krause) 被引量:1
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作者 Xiangui Zhao Yang Zhang 《Algebra Colloquium》 SCIE CSCD 2016年第4期701-720,共20页
Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension... Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Grobner-Shirshov basis method. We develop the GrSbner-Shirshov basis theory of differential difference al- gebras, and of finitely generated modules over differential difference algebras, respectively. Then, via GrSbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras. 展开更多
关键词 Gelfand-Kirillov dimension Gr6bner-Shirshov basis Hilbert function differ-ential difference algebra
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Closed-form solutions to fractional-order linear differential equations 被引量:2
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作者 Chunna ZHAO Dingyu XUE 《Frontiers of Electrical and Electronic Engineering in China》 CSCD 2008年第2期214-217,共4页
The definitions and properties of widely used fractional-order derivatives are summarized in this paper.The characteristic polynomials of the fractional-order systems are pseudo-polynomials whose powers of the complex... The definitions and properties of widely used fractional-order derivatives are summarized in this paper.The characteristic polynomials of the fractional-order systems are pseudo-polynomials whose powers of the complex variable are non-integers.This kind of systems can be approximated by high-order integer-order systems,and can be analyzed and designed by the sophisticated integer-order systems methodology.A new closed-form algorithm for fractional-order linear differential equations is proposed based on the definitions of fractional-order derivatives,and the effectiveness of the algorithm is illustrated through examples. 展开更多
关键词 fractional-order differentiator linear sys-tems numerical solutions calculus simulation differ-ential equations integer-order approximations
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Meshfree Approximation for Stochastic Optimal Control Problems
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作者 Hui Sun Feng Bao 《Communications in Mathematical Research》 CSCD 2021年第3期386-418,共33页
In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion ... In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion is to extend the existing gradient projection method to moderate high-dimensional space.The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework,and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach.We also present several numerical experiments to validate the theoretical re-sults of our approach and demonstrate the performance meshfree approxima-tion in solving stochastic optimal control problems. 展开更多
关键词 Stochastic optimal control maximum principle backward stochastic differ-ential equations meshfree approximation
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Mean-variance Portfolio Selections in Continuous-time Model with Stochastic Interest Rate Process
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作者 Zijun Guo Lixin Zhao 《Journal of Systems Science and Information》 2007年第1期61-70,共10页
Under the continuous time (d+1) assets market model with finite time horizon T, and the condition that all coefficients in model are stochastic processes, the decision of investment portfolio selection had been stu... Under the continuous time (d+1) assets market model with finite time horizon T, and the condition that all coefficients in model are stochastic processes, the decision of investment portfolio selection had been studied. By using K.Itǒ formuia and backward stochastic differential equation's theory, on the relation of investment portfolio processes, fortune processes, the backward stochastic differential equation model for stochastic control problem had been established, the relation between the prime fortune process and the end- all fortune process had been proposed, the existence and uniqueness of investment portfolio had been proved, and the formula for investment portfolio had been arrived. On the setting of mean-variance portfolio selection, we obtained the formula of optimal efficient investment portfolio. Furthermore, the mean-variance efficient frontier is too obtained explicitly in the form of parameter. 展开更多
关键词 investment portfolio processes K.Itǒ formula backward stochastic differ-ential equation mean-variance portfolio selection efficient frontier
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