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The twisted conical Kahler-Ricci solitons on Fano manifolds

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science China mathematics 2024年第5期67卷 1085-1102页

作者： Xishen Jin Jiawei Liu school of mathematics Renmin University of ChinaBeijing 100872China school of mathematics and Statistics Nanjing University of Science&TechnologyNanjing 210094China

In this paper,we show the relation between the existence of twisted conical K?hler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano *** is based on our proofs of some openness theorems on the existence of twisted conical Kahler-Ricci solitons,which generalize Donaldson’s existence conjecture and the openness theorem of the conical K?hler-Einstein metrics to the conical soliton case.

关键词： greatest log Bakry-Emery-Ricci lower bound twisted conical Kahler-Ricci soliton twisted Kahler-Ricci soliton

Accumulated-state-error-based event-triggered sampling scheme and its application to H∞ control of sampled-data systems

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science China(Information sciences) 2024年第6期67卷 328-341页

作者： Xian-Ming ZHANG Qing-Long HAN Bao-Lin ZHANG Xiaohua GE Dawei ZHANG school of science Computingand Engineering TechnologiesSwinburne University of Technology College of Automation and Electronic Engineering Qingdao University of Science & Technology school of mathematics Shandong University

This paper is concerned with event-triggered H∞control of sampled-data systems. Its novelties lie in three aspects:（i） A novel accumulated-state-error-based event-triggered scheme is introduced by comparing the integral of the state error from tk to t with the system state sampled at tk. This condition works well due to the fact that the so-called Zeno behaviour does not occur.（ii） A novel Lyapunov functional is constructed to establish a criterion to ensure some certain H∞performance of the closed-loop system. This Lyapunov functional is dependent on the integral of the state error involved in the event-triggered scheme.（iii） Under the event-triggered sampling scheme, suitable state-feedback controllers can be designed rather than be given a priori. Moreover, a self-triggered implementation of the proposed event-triggered sampling scheme is presented as well. Finally, a batch reactor model and an inverted pendulum system are given to demonstrate the effectiveness of the proposed method.

关键词： event-triggered sampling self-triggered implementation $H_\infty$ control looped-functional

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

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

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Acta Mathematica Scientia 2024年第2期44卷 650-670页

作者：司智勇 school of mathematics and Information science Henan Polytechnic UniversityJiaozuo454003China

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau *** backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau *** this method,the system is decoupled and linearized to avoid solving the non-linear equation at each *** theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

关键词： time-dependent Ginzburg-Landau equation generalized scalar auxiliary variable algorithm maximum bound principle energy stability

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

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Acta Mathematica Scientia 2024年第5期44卷 1707-1720页

作者： Lixia FENG Yan LI Zhiyu WANG Liankuo ZHAO school of mathematics and Computer science Shanxi Normal UniversityTaiyuan030031China

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

关键词： weighted Bergman spaces Békolléweights Carleson measure Toeplitz operators

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

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Acta Mathematica Scientia 2024年第5期44卷 1735-1746页

作者： Gonglin YUAN Xiong ZHAO Jiajia YU school of mathematics and Information science Center for Applied Mathematics of Guangxi(Guangxi University)Guangxi UniversityNanning530004China

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization *** global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS *** some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection ***,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

关键词： cautious BFGS nonconvex problems Lipschitz continuity projection technique global convergence

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1229-1243页

作者： Xiaohui LI Meiqi LIU Chunyuan DENG school of mathematics science South China Normal UniversityGuangzhou 510631China

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are *** use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert ***,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

关键词： norm orthogonal projection positive operator spectral block operator valued matrix

DPK:Deep Neural Network Approximation of the First Piola-Kirchhoff Stress

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Advances in Applied mathematics and Mechanics 2024年第1期16卷 75-100页

作者： Tianyi Hu Jerry Zhijian Yang Cheng Yuan Institute of Artificial Intelligence School of Computer ScienceWuhan UniversityWuhanHubei 430072China school of mathematics and Statistics Wuhan UniversityWuhanHubei 430072China Hubei Key Laboratory of computational science Wuhan UniversityWuhanHubei 430072China

This paper presents a specific network architecture for approximation of the first Piola-Kirchhoff *** neural network enables us to construct the constitutive relation based on both macroscopic observations and atomistic simulation *** contrast to traditional deep learning models,this architecture is intrinsic symmetric,guarantees the frame-indifference and material-symmetry of ***,we build the approximation network inspired by the Cauchy-Born rule and virial stress *** numerical results and theory analyses are presented to illustrate the learnability and effectiveness of our network.

关键词： Piola-Kirchhoff stress deep neural networks Cauchy-Born rule

The Perturbed Compound Poisson Risk Model with Proportional Investment

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 109-128页

作者： Nai-dan Deng Chun-wei Wang Jia-en Xu school of mathematics and Statistics Henan University of Science and TechnologyLuoyang471023China

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.

关键词： expected discounted dividend payments lognormal distribution proportional investment perturbed risk model sinc numerical method