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VARIABLE STEP-SIZE BDF3 METHOD FOR ALLEN-CAHN EQUATION

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Journal of Computational mathematics 2024年第5期42卷 1380-1406页

作者： Minghua Chen Fan Yu Qingdong Zhang Zhimin Zhang School of mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China department of mathematics Wayne State UniversityDetroitMI 48202USA

In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable *** BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,***.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC *** developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 ***,numerical experiments are performed to illustrate the theoretical *** the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

关键词： Variable step-size BDF3 method Allen-Cahn equation Spectral norm inequality Stability and convergence analysis

Deep bed filtration model for cake filtration and erosion

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applied mathematics and Mechanics(English Edition) 2024年第2期45卷 355-372页

作者： L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV department of applied mathematics HSE UniversityMoscow 101000Russia department of Computer Science and applied mathematics Moscow State University of Civil EngineeringMoscow 129337Russia

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关键词： deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front

Constraining the variable generalized Chaplygin gas model in matter creation cosmology

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Communications in Theoretical Physics 2024年第10期76卷 121-136页

作者： Yogesh Bhardwaj C P Singh department of applied mathematics Delhi Technological University

We explore the variable generalized Chaplygin gas（VGCG） model in the theory of matter creation cosmology within the framework of a spatially homogeneous and isotropic flat Friedmann—Lemai tre—Robertson—Walker space-time. Matter creation cosmology is based on reinterpretation of the energy–momentum tensor in Einstein's field equations. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. The variable Chaplygin gas（VCG） is also studied as a particular solution. We use the Markov chain Monte Carlo method to constrain the free parameters of three models, namely,Lambda-Cold-Dark matter（ΛCDM）, VGCG and VCG models with and without matter creation from the latest observational data from baryon acoustic oscillations, cosmic chronometer, type Ia supernovae（Pantheon） including gamma-ray bursts, quasars and the local measurement of H0from R21 data. Two different combinations of dataset provide a fairly tight constraint on the parameters of the ΛCDM, VGCG and VCG models. The present values of various cosmological parameters are obtained, which are very close to the ΛCDM model. Furthermore, we perform stability analysis, Bayesian evidence analysis and information criteria analysis for these models through studying the sound speed, Bayes factor, and Akaike information criteria（AIC） and Bayesian information criteria（BIC） selection criteria. The values of sound speed for VGCG and VCG models shows that both the models are stable. According to AIC, it is observed that VGCG and VCG models with matter creation are supported considerably less by current observations,while BIC shows that these models are not favoured by observational data.

关键词： Chaplygin gas model cosmological model dark energy matter creation

Bald Eagle Search Optimization Algorithm Combined with Spherical Random Shrinkage Mechanism and Its Application

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Journal of Bionic Engineering 2024年第1期21卷 572-605页

作者： Wenyan Guo Zhuolin Hou Fang Dai Xiaoxia Wang Yufan Qiang department of applied mathematics School of ScienceXi'an University of TechnologyXian 710054ShaanxiChina

Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization *** eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local *** avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is ***,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the ***,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the *** non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the *** results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking *** three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.

关键词： Bald eagle search optimization algorithm Spherical coordinates Chaotic variation Simplex method Encapsulated feature selection

TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS

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Acta Mathematica Scientia 2024年第5期44卷 1931-1944页

作者： Surya GIRI S.Sivaprasad KUMAR department of applied mathematics Delhi Technological UniversityNew Delhi110042India

In this study,we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk ***,these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc inℂ*** obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.

关键词： holomorphic mappings starlike mappings Toeplitz determinants coefficient inequalities

Partially-Observed Maximum Principle for Backward Stochastic Differential Delay Equations

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1524-1526页

作者： Shuang Wu department of applied mathematics China University of PetroleumQingdao 266580China

Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is *** adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional *** backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed *** corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].

关键词： stochastic backward convex

Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System

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Acta Mathematica Sinica,English Series 2024年第8期40卷 2037-2064页

作者： Chang Ming SONG Jian Lin ZHANG Yuan Yuan WANG department of applied mathematics School of Mathematics and Information ScienceZhongyuan University of TechnologyZhengzhou 450007P.R.China

In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible *** prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.

关键词： Diffuse interface model global solutions Navier-Stokes equations Allen-Cahn equation spherically symmetry

Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

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Science China mathematics 2024年第1期67卷 187-210页

作者： Xiao Li Zhonghua Qiao Cheng Wang department of applied mathematics The Hong Kong Polytechnic UniversityHong KongChina department of mathematics The University of MassachusettsNorth DartmouthMA 02747USA

In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard *** scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial *** addition,two stabilization terms in different forms are added for the sake of the numerical *** conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined *** regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error ***,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical ***,the energy stability is also rigorously proved with respect to a modified *** proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.

关键词： nonlocal Cahn-Hilliard equation second-order stabilized scheme higher-order consistency analysis rough and refined error estimate

Mathematical model and optimal control analysis of coffee berry borer with temperature and rainfall variability

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International Journal of Biomathematics 2024年第5期17卷 177-204页

作者： Abdisa Shiferaw Melese department of applied mathematics Adama Science and Technology UniversityAdamaEthiopia

This study focuses on a nonlinear deterministic mathematical model for coffee berry borer(Hypothenemus hampei)with temperature and rainfall *** the model analysis,CBB free and coexistence equilibria are *** basic reproduction numbers at a minimum and maximum temperature and rainfall are *** qualitative analysis of the model revealed the scenario for equilibria together with basic reproduction *** local stability of equilibria is established through the Jacobian matrix and the Routh-Hurwitz criteria,while the global stability of equilibria is demonstrated using an appropriate Lyapunov *** normalized sensitivity analysis has also been performed to observe the impact of different parameters on basic reproduction *** proposed model is extended into an optimal control problem by incorporating two control variables,namely,the preventive measure variable based on the separation of susceptible coffee berries from contacting the pests based on biological control and an increase in the death rate of colonizing females of CBB based on chemical *** disease control analysis is examined using Pontryagin's minimum ***,the numerical simulations are performed based on analytical results and are discussed ***,the cost-effectiveness of control strategies to determine the best approach to minimize the CBB burden was *** study is significant in providing reliable information on how one can use mathematical modeling to improve the roles of control strategies and prevention in CBB transmission in a coffee *** outcome of the study may guide public agriculture policymakers on optimal control strategies to control the *** particular,using chemical pesticides is very effective to combat pests with minimum costs.

关键词： Hypothenemus hampei climate variability optimal control cost-effective analysis numerical simulation