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Initial Boundary Value Problem of an Equation from Mathematical Finance

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Chinese Annals of Mathematics,Series B 2016年第3期37卷 465-482页

作者： Huashui zhan School of Applied Mathematics Xiamen University of Technology

Consider the initial boundary value problem of the strong degenerate parabolic equation ?_(xx)u + u?_yu-?_tu = f(x, y, t, u),(x, y, t) ∈ Q_T = Ω×(0, T)with a homogeneous boundary condition. By introducing a new kind of entropy solution, according to Oleinik rules, the partial boundary condition is given to assure the well-posedness of the problem. By the parabolic regularization method, the uniform estimate of the gradient is obtained, and by using Kolmogoroff 's theorem, the solvability of the equation is obtained in BV(Q_T) sense. The stability of the solutions is obtained by Kruzkov's double variables method.

关键词： Mathematical finance Oleinik rules Partial boundary condition Entropy solution Kruzkov's double variables method

A PROXIMAL POINT ALGORITHM FOR A SYSTEM OF GENERALIZED MIXED VARIATIONAL INEQUALITIES

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Journal of Systems Science & Complexity 2012年第5期25卷 964-972页

作者： Bo WAN Xuegang zhan Department of Mathematics and Statistics Chongqing Technology and Business University School of Accountancy Chongqing Technology and Business University

This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

关键词： Lipschitz continuity proximal point algorithms relaxed (γ τ)-cocoercivity system ofgeneralized mixed variational inequalities.

Harnack Estimates for Weak Solutions to a Singular Parabolic Equation

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Chinese Annals of Mathematics,Series B 2011年第3期32卷 397-416页

作者： Huashui zhan School of Sciences Jimei University Xiamen 361021 Fujian China

By an interpolation method,an intrinsic Harnack estimate and some supestimates are established for nonnegative solutions to a general singular parabolic equation.

关键词： Harnack estimate Interpolation method Nonnegative solution Singular parabolic equation

Solution to Nonlinear Parabolic Equations Related to P-Laplacian

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Chinese Annals of Mathematics,Series B 2012年第5期33卷 767-782页

作者： Huashui zhan School of Sciences Jimei University Xiamen 361021 Fujian China. E-mail: hszhan@***

Consider the following Cauchy problem：where 1 〈 p 〈 2, 1 〈 m 〈 p_~11, and # is a a-finite measure in N. By the Moser＇s iteration method, the existence of the weak solution is obtained, provided that （M＋1）N 〈 P. In mN＋l contrast, if 〉 p, there is no solution to the Cauchy problem with an initial value δ（X）, where 5（x） is the classical Dirac function.

关键词： Nonlinear parabolic equation Cauchy problem Existence a-Finite measure

Cloud-Edge Collaborative Federated GAN Based Data Processing for IoT-Empowered Multi-Flow Integrated Energy Aggregation Dispatch

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Computers, Materials & Continua 2024年第7期80卷 973-994页

作者： zhan Shi Electric Power Dispatching Control Center Guangdong Power Grid Co.Ltd.Guangzhou510030China

The convergence of Internet of Things(IoT),5G,and cloud collaboration offers tailored solutions to the rigorous demands of multi-flow integrated energy aggregation dispatch data *** generative adversarial networks(GANs)are instrumental in resource scheduling,their application in this domain is impeded by challenges such as convergence speed,inferior optimality searching capability,and the inability to learn from failed decision making ***,a cloud-edge collaborative federated GAN-based communication and computing resource scheduling algorithm with long-term constraint violation sensitiveness is proposed to address these *** proposed algorithm facilitates real-time,energy-efficient data processing by optimizing transmission power control,data migration,and computing resource *** employs federated learning for global parameter aggregation to enhance GAN parameter updating and dynamically adjusts GAN learning rates and global aggregation weights based on energy consumption constraint *** results indicate that the proposed algorithm effectively reduces data processing latency,energy consumption,and convergence time.

关键词： IoT federated learning generative adversarial network data processing multi-flowintegration energy aggregation dispatch

Recent advance on the efficiency at maximum power of heat engines

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Chinese Physics B 2012年第2期21卷 36-45页

作者： Tu zhan-Chun Department of Physics Beijing Normal UniversityBeijing 100875China

This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman＇s ratchet as a heat engine are presented. It is found that： the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.

关键词： effciency at maximum power heat engine universality bounds

Abstract models for heat engines

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Frontiers of physics 2021年第3期16卷 99-110页

作者： zhan-Chun Tu Department of Physics Beijing Normal UniversityBeijing100875China

We retrospect three abstract models for heat engines which include a classic abstract model in textbook of thermal physics,a primary abstract model for finite-time heat engines,and a refined abstract model for finite-time heat *** detailed models of heat engines in literature of finite-time thermodynamics may be mapped into the refined abstract *** future developments based on the refined abstract model are also surveyed.

关键词： abstract model heat engine finite-time thermodynamics

Remarks on the Three-dimensional Lattice Model

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Chinese Physics Letters 1996年第6期13卷 412-415页

作者： HU zhan-ning Institute of Theoretical Physics Chinese Academy of SciencesBeijing 100080

We find the connection between the weight functions of the three-dimensional(3D)Bazhanov-Baxter model and the 3D vertex model proposed by Mangazeev et *** the weight function of the 3D integrable model with the modifi... 详细信息

关键词： form. vertex integrable

Evolutionary p(x)-Laplacian Equation with a Convection Term

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 655-670页

作者： Hua-shui zhan School of Applied Mathematics Xiamen University of Technology

The paper studies an evolutionary p(x)-Laplacian equation with a convection term ut=div(ρα|■u|p(x)-2■u)+∑N i=1■bi(u)/■xi,whereρ(x)=dist(x,■Ω),ess inf p(x)=p^->*** assure the well-posedness of the solutions,the paper shows only a part of the boundary,Σp■■Ω,on which we can impose the boundary value.Σp is determined by the convection term,in particular,when 1<α<(p^--2)/2,Σp={x∈■Ω:bi′(0)ni(x)<0}.So,there is an essential difference between the equation and the usual evolutionary p-Laplacian *** last,the existence and the stability of weak solutions are proved under the additional conditionsα<(p^--2)/2 andΣp=■Ω.

关键词： Evolutionary p(x)-Laplacian equation week solution Fichera-Oleinik theory boundary degeneracy