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Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation

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Journal of the Operations Research Society of China 2024年第1期12卷 215-241页

作者： Sergey N.Smirnov faculty of computational mathematics and cybernetics Lomonosov Moscow State UniversityMoscow119991Russian Federation

The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial *** the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s *** formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural *** demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.

关键词： Uncertainty Structural stability No arbitrage Continuity of superhedging price Compact-valued multifunction Financial market model approximation Trading constraints

The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

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Chinese Physics B 2013年第5期22卷 96-103页

作者：赵国忠蔚喜军郭鹏云 faculty of mathematics Baotou Teachers' College Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics

In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.

关键词： compressible Euler equations Runge-Kutta control volume discontinuous finite element method,Lagrangian coordinate

Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

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Advances in Applied mathematics and Mechanics 2024年第1期16卷 237-252页

作者： Alexey Shcheglov Jingzhi Li Chao Wang Alexander Ilin Ye Zhang faculty of computational mathematics and cybernetics Shenzhen MSU-BIT UniversityShenzhenGuangdong 518172China faculty of computational mathematics and cybernetics Lomonosov Moscow State UniversityMoscowRussia Department of mathematics&National Center for Applied mathematics Shenzhen&SUSTech International Center for mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear ***,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption *** stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.

关键词： Inverse problem quasi-linear dynamic model uniqueness method of successive approximations stability

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

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Chinese Physics B 2013年第2期22卷 50-63页

作者：赵国忠蔚喜军张荣培 faculty of mathematics Baotou Teachers'College Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics School of Science Liaoning Shihua University

In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian *** equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG *** multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other *** first,a linear Riemann solver is applied to calculate the numerical ？ux at the *** examples show that there is some oscillation in the vicinity of the *** a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation *** single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

关键词： compressible gas dynamic equations RKDG finite element method Lagrangian coordinate multi- medium fluid

Small extrachromosomal circular DNA in amyotrophic lateral sclerosis matter

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Neural Regeneration Research 2025年第5期20卷 1411-1413页

作者： Marcos J.Arauzo-Bravo Daniela Gerovska Matthias Schwab Alexandra Kretz computational Biology and Systems Biomedicine Biodonostia Health Research InstituteSan SebastianSpain Basque Foundation for Science IKERBASQUEBilbaoSpainMax Planck Institute for Molecular BiomedicineComputational Biology and Bioinformatics GroupMünsterNorth Rhine-WestphaliaGermany Department of Cell Biology and Histology Faculty of Medicine and NursingUniversity of Basque Country(UPV/EHU)LeioaSpain Department of Neurology Jena University HospitalJenaThuringiaGermany

Comprehensive studies identify motor neuron spectrum disorders including amyotrophic lateral sclerosis(ALS)as globally rising fatal disorders with the highest prevalence in aging populations,influenced by ethnicity and ancestry(GBD 2016 Motor Neuron Disease Colla borators,2018).While~10% of diagnoses involve a family history(fALS),most cases are considered sporadic(sALS).However,population-based studies suggest that even cases without a common index mutation impart heritability(Ryan et al.,2019),indicating a crucial role of rare and as yet unknown genetic denominators.

关键词： amyotrophic sclerosis

Modified Burgers' equation by the local discontinuous Galerkin method

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Chinese Physics B 2013年第3期22卷 106-110页

作者：张荣培蔚喜军赵国忠 School of Sciences Liaoning Shihua University Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics faculty of mathematics Baotou Normal College

In this paper,we present the local discontinuous Galerkin method for solving Burgers＇ equation and the modified Burgers＇ *** describe the algorithm formulation and practical implementation of the local discontinuous Galerkin method in *** method is applied to the solution of the one-dimensional viscous Burgers＇ equation and two forms of the modified Burgers＇ *** numerical results indicate that the method is very accurate and efficient.

关键词： local discontinuous Galerkin method modified Burgers' equation

Application of integrated simulation environment SIEMNED to the analysis of the MEPHIST-0 tokamak operation

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Plasma Science and Technology 2023年第3期25卷 222-233页

作者： D Yu SYCHUGOV S Yu SOLOVIEV A S ZHILKIN A V MELNIKOV S A KRAT faculty of computational mathematics and cybernetics Lomonosov Moscow State University National Research Centre Kurchatov Institute National Research Nuclear University Moscow Engineering Physics Institute National University Moscow Institute of Physics and Technology

This paper presents the results of numerical simulation of plasma equilibrium and stability in the MEPHIST-0 tokamak with SIEMNED software and comparison of simulation results with *** determined characteristics of the vacuum chamber show that it significantly affects the entire *** various scenarios of the inductor operation,a comparison of experimental data and simulated currents and magnetic fields induced in the chamber was carried *** steady-state tokamak operation,a numerical study of equilibrium plasma configurations was carried out depending on the currents in the poloidal magnetic field coils and plasma *** vertical plasma instability was *** limiting values of plasma ellipticity preventing the vertical plasma instability were numerically *** simulations show that plasma equilibrium is supported by induced *** was shown numerically that magnetic configuration with‘zero of higher order’were obtained before the plasma shot,suggesting consistency between the simulation results and observations.

关键词： mathematical modelling tokamak installation MEPHIST-0

ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION

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Acta Mathematica Scientia 2008年第1期28卷 117-127页

作者：沈彩霞郭柏灵 faculty of Science University of Jiang Su Institute of Applied Physics and computational mathematics

The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.

关键词： The Davey-Stewartson equation the Cauchy problem ill-posedness

Connection between the Principles of Thermodynamics and the Conservation Laws: Physical Meaning of the Principles of Thermodynamics

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Journal of Applied mathematics and Physics 2018年第12期6卷 2697-2704页

作者： L. I. Petrova MSU faculty of computational mathematics and cybernetics Moskva Russia

It has been shown that the first principle of thermodynamics follows from the conservation laws for energy and linear momentum. And the second principle of thermodynamics follows from the first principle of thermodynamics under realization of the integrating factor (namely, temperature) and is a conservation law. The significance of the first principle of thermodynamics consists in the fact that it specifies the thermodynamic system state, which depends on interaction between conservation laws and is non-equilibrium due to a non-commutativity of conservation laws. The realization of the second principle of thermodynamics points to a transition of the thermodynamic system state into a locally-equilibrium state. Phase transitions are examples of such transitions.

关键词： Skew-Symmetric Differential Forms Conservation Laws First Principle of Thermodynamics Realization of Integrating Factor The Second Principle of Thermodynamics The Entropy