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Stabilities of delay stochastic McKean-Vlasov equations in the G-framework

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Science China(Information Sciences) 2025年第1期68卷 255-277页

作者： Haiyan YUAN Quanxin ZHU department of mathematics Heilongjiang Institute of Technology Key Laboratory of Computing and Stochastic mathematics (Ministry of Education) School of Mathematics and Statistics Hunan Normal University

This article focuses on a type of stochastic Mc Kean-Vlasov equation in the G-framework(G-SMVE) and addresses the stability issue for delay stochastic Mc Kean-Vlasov equations in the G-framework(G-SMVDEs). Distribution dependence and uncertainty prevent us from directly applying the stochastic analysis method for stochastic Mc Kean-Vlasov equations(SMVEs)to G-SMVEs directly. To overcome this difficulty, we introduce definitions, including the derivative of a function with a law under the G-expectation and the Lions derivatives. Then we construct a new G-It? formula for G-SMVEs according to the G-It? formula for stochastic differential equations in the G-framework(G-SDEs) and the It? formula for SMVEs. Using the new G-It? formula and the Lyapunov functional method, we investigate the moment exponential stability and almost sure asymptotic stability of G-SMVDEs. To overcome the difficulty in obtaining the distribution dependence of the exact solution to the G-SMVDE, we introduce the empirical measure and the corresponding interacting particle system, and then prove the stability equivalence between the underlying G-SMVDE and the corresponding interacting particle system. Two examples are used to confirm our theoretical results.

关键词： delay stochastic McKean-Vlasov equations Wasserstein distance G-Brownian motion Lions derivative stability

Role of copper chelating agents: between old applications and new perspectives in neuroscience

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Neural Regeneration Research 2025年第3期20卷 751-762页

作者： Rosalba Leuci Leonardo Brunetti Vincenzo Tufarelli Marco Cerini Marco Paparella Nikola Puvača Luca Piemontese department of Pharmacy-Pharmaceutical Science University of Bari Aldo MoroBariItaly department of Precision and Regenerative Medicine and Jonian Area(DiMePRe-J) Section of Veterinary Science and Animal ProductionUniversity of Bari Aldo MoroBariItaly department of Engineering Management in Biotechnology Faculty of Economics and Engineering Management in Novi SadUniversity Business Academy in Novi SadNovi SadSerbia

The role of copper element has been an increasingly relevant topic in recent years in the fields of human and animal health, for both the study of new drugs and innovative food and feed supplements. This metal plays an important role in the central nervous system, where it is associated with glutamatergic signaling, and it is widely involved in inflammatory processes. Thus, diseases involving copper(Ⅱ) dyshomeostasis often have neurological symptoms, as exemplified by Alzheimer's and other diseases(such as Parkinson's and Wilson's diseases). Moreover, imbalanced copper ion concentrations have also been associated with diabetes and certain types of cancer, including glioma. In this paper, we propose a comprehensive overview of recent results that show the importance of these metal ions in several pathologies, mainly Alzheimer's disease, through the lens of the development and use of copper chelators as research compounds and potential therapeutics if included in multi-target hybrid drugs. Seeing how copper homeostasis is important for the well-being of animals as well as humans, we shortly describe the state of the art regarding the effects of copper and its chelators in agriculture, livestock rearing, and aquaculture, as ingredients for the formulation of feed supplements as well as to prevent the effects of pollution on animal productions.

关键词： agriculture Alzheimer's disease chelators copper feed supplements multi-target

An Almost Sure Result on Approximation of Homogeneous Random Field from Local Averages

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Chinese Journal of Electronics 2019年第1期28卷 93-99页

作者： SONG Zhanjie ZHANG Shuo School of mathematics Tianjin University department of mathematics Tianjin University of Finance and Economics

The problem of approximation of homogeneous random field from asymmetric local average sampling is considered in this paper. As a general sampling result, a sufficient condition is obtained to ensure the homogeneous random field be approximated from local averages with probability 1, which extended the result for weak sense stochastic process from local averages to homogeneous random field.

关键词： Sampling theorem Homogeneous random field Local averages sampling

A complexity measure approach based on forbidden patterns and correlation degree

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Chinese Physics B 2010年第6期19卷 177-183页

作者：王福来 department of mathematics and Statistics Zhejiang University of Finance and Economics

Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic （usually chaotic） series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the Henon map with multi-parameters.

关键词： complexity theory forbidden words symbolic dynamics correlation dimensions

An improvement on measure methods of the complexity theory and its applications

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Chinese Physics B 2009年第9期18卷 4042-4048页

作者：王福来杨辉煌 department of mathematics and Statistics Zhejiang University of Finance and Economics

A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henon map are studied and the results are satisfactory.

关键词： complexity theory complexity dynamic system chaos

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

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Chinese Physics B 2010年第9期19卷 244-249页

作者：王福来 department of mathematics and Statistics Zhejiang University of Finance and Economics

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

关键词： pseudo random numbers uniform map chaos

REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

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Acta Mathematica Scientia 2011年第5期31卷 1877-1888页

作者：谢华朝訾瑞昭 department of mathematics Henan University of Economics and Law department of mathematics Zhejiang University

In this paper, we consider the nonlinear instability of incompressible Euler equations. If a steady density is non-monotonic, then the smooth steady state is a nonlinear instability. First, we use variational method to find a dominant eigenvalue which is important in the construction of approximate solutions, then by energy technique and analytic method, we obtain the dynamical instability result.

关键词： Euler equations incompressible nonlinear instability

The constructive technique and its application in solving a nonlinear reaction diffusion equation

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Chinese Physics B 2009年第2期18卷 405-410页

作者：赖绍永郭云喜青音吴永宏 department of Applied mathematics Southwestern University of Finance and Economics department of mathematics and Statistics Curtin University of Technology

A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.

关键词： additional generating condition method exact solutions nonlinear reaction-diffusion equation

Homological Dimensions of the Extension Algebras of Monomial Algebras

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Acta Mathematica Sinica,English Series 2015年第4期31卷 675-694页

作者： Hong Bo SHI department of mathematics Nanjing University of Finance and Economics

The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using the two combinatorial algorithms -- Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.

关键词： Topdown bottomup dimension tree syzygy finitistic dimensions