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THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

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Acta Mathematica Scientia 2023年第1期43卷 324-348页

作者：狄华斐容伟杰 School of mathematics and Information Science Guangzhou UniversityGuangzhou510006China key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou UniversityGuangzhou510006China

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final *** the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random ***,we propose the Fourier truncation method for stabilizing the above ill-posed *** derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

关键词： regularized solution approximation forward/backward problems fractional Laplacian Gaussian white noise Fourier truncation method

Global Optimization Method for Linear Multiplicative Programming

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Acta Mathematicae Applicatae Sinica 2015年第2期31卷 325-334页

作者： Xue-gang ZHOU Bing-yuan CAO Kun WU School of mathematics and Information Science Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Department of Applied mathematics Guangdong University of Finance School of Mathematical Science and Computing Technology Center South University

In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming（LMP）. The problem（LMP） is firstly converted into an equivalent programming problem（LMP（H））by introducing p auxiliary variables. Then by exploiting structure of（LMP（H））, a linear relaxation programming（LP（H）） of（LMP（H）） is obtained with a problem（LMP） reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems（LP（H））. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

关键词： linear multiplicative programming global optimization linear programming branch and bound

A local version of Hardy spaces associated with operators on metric spaces

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Science China mathematics 2013年第2期56卷 315-330页

作者： GONG RuMing LI Ji YAN LiXin School of mathematics and Information Science Guangzhou University key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou University Department of mathematics Sun Yat-sen University

Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.

关键词： local Hardy space non-negative self-adjoint operator semigroups local (1 p)-atoms Moser typelocal boundedness condition space of homogeneous type

Chaos and null systems

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Science China mathematics 2013年第3期56卷 607-618页

作者： WANG HuoYun LIU Xin FU HeMan School of mathematics and Information Science Guangzhou University key laboratory of mathematics and interdisciplinary Science Guangdong Higher Education Institutes Guangzhou University College of mathematics and Information sciences Zhaoqing University

A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Let 0≦p≦q≦1. A dynamical system is Dqp chaotic, if there is an uncountable subset in which any two different points have trajectory approaching time set with lower density p and upper density q. In this paper, we show that there is a null system which is also D3/41/4 chaotic.

关键词： null system Dpq chaos topological sequence entropy

The Complexity and Randomness of Linear Multi-secret Sharing Schemes with Non-threshold Structures

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 1073-1084页

作者： Chun-ming Tang Shu-guang DAI School of mathematics and Information Science Guangzhou University key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou University State key laboratory of Information Security School of Information Science and Technology Sun Yat-Sen University

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.

关键词： secret sharing multi-secret sharing scheme non-threshold multi-access structure linear code complexity randomness

New Non-TravellingWave Solutions of Calogero Equation

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Advances in Applied mathematics and Mechanics 2016年第6期8卷 1036-1049页

作者： Xiaoming Peng Yadong Shang Xiaoxiao Zheng School of mathematics and Information Science Guangzhou UniversityGuangzhou 510006China key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou UniversityGuangzhou 510006China

In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero *** equation is reduced to some(1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test *** on this idea and with the aid of symbolic computation,some new explicit solutions can be obtained.

关键词： Variable separation approach extended homoclinic test approach non-travelling wave solution.

Periods of polynomials over a Galois ring

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Science China mathematics 2013年第9期56卷 1761-1772页

作者： ZHANG XiaoLei HU Lei State key laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences School of mathematics sciences Univeristy of Chinese Academy of Sciences School of mathematics and Information sciences Guangzhou University key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou University

The period of a monic polynomial over an arbitrary Galois ring GR(pe,d) is theoretically determined by using its classical factorization and Galois extensions of rings. For a polynomial f(x) the modulo p remainder of which is a power of an irreducible polynomial over the residue field of the Galois ring, the period of f(x) is characterized by the periods of the irreducible polynomial and an associated polynomial of the form (x-1)m+pg(x). Further results on the periods of such associated polynomials are obtained, in particular, their periods are proved to achieve an upper bound value in most cases. As a consequence, the period of a monic polynomial over GR(pe,d) is equal to pe-1 times the period of its modulo p remainder polynomial with a probability close to 1, and an expression of this probability is given.

关键词： period of polynomial Galois ring sequence

The twoscale asymptotic error analysis for piezoelectric problems in the quasi-periodic structure

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Science China(Physics,Mechanics & Astronomy) 2013年第10期56卷 1844-1853页

作者： FENG YongPing DENG MingXiang GUAN XiaoFei School of mathematics and Information sciences Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Guangzhou 510006 China Department of mathematics University of California San Diego 92093 USA Department of mathematics Tongji University Shanghai 200092 China

Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.

关键词： twoscale method piezoelectricity quasi-periodic structure homogenization constants

Radically distributed value and normal families of meromorphic functions

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Frontiers of mathematics in China 2014年第2期9卷 355-376页

作者： Jianming QI Guowei ZHANG Weniun YUAN Department of mathematics and Physics Shanghai Dianji University Shanghai 200240 China School of mathematics and Information sciences Guangzhou UniversityGuangzhou 510006 China Department of mathematics Anyang Normal University Anyang 455000 China key laboratory of mathematics and interdisciplinary sciences of guangdong Higher education institutes Guangzhou University Guangzhou 510006 China

We establish several upper-bound estimates for the growth of meromorphic functions with radially distributed value. We also obtain a normality criterion for a class of meromorphic functions, where any two of whose dif... 详细信息

关键词： Meromorphic function Nevanlinna theory normal family angular characteristic function radially distributed value