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Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains

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Science China Mathematics 2024年第8期67卷 1827-1864页

作者： Xiaoshu Ge Chunping Zhong school of mathematical sciences Xiamen UniversityXiamen 361005China

In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of typesⅠ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio(1994).These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found in the literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed to admit differential geometry *** are,however,not necessarily Hermitian quadratic as the Bergman *** metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of typesⅠ-Ⅳ,respectively,and they are all proved to be complete K?hler-Berwald *** enjoy very similar curvature properties as those of the Bergman metric on the irreducible classical domains,i.e.,their holomorphic sectional curvatures are bounded between two negative constants and their holomorphic bisectional curvatures are always nonpositive and bounded below by negative constants,*** the viewpoint of complex analysis,these metrics are analogs of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the sense of Chern(1996).

关键词： holomorphic invariant metric Kahler-Berwald metric irreducible classical domains

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The Strategic Analysis of Demand Forecast-Sharing in a Hybrid-Format Online Platform Supply Chain

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Journal of Systems Science and Systems Engineering 2024年第3期33卷 281-310页

作者： Jing Zhao Zijun Yin Guobiao Zhou school of mathematical sciences Tiangong UniversityTianjin300387China

This paper examines the optimal forecast-sharing strategy in a hybrid-format online platform supply chain where a supplier sells a product through agency format and reselling format provided by a platform retailer who possesses demand forecasts from two *** asymmetry and co-opetitive relationship arise between the platform retailer and the supplier,which affect their operational decisions and the supply chain’s *** improve supply chain efficiency,we compare different forecast-sharing strategies(i.e.,no forecast sharing,sharing a single forecast,and sharing two forecasts),and analyze the effects of co-opetitive parameters on the optimal forecast-sharing *** analysis shows that forecast sharing is always beneficial to the supplier,and sharing two forecasts is more beneficial than sharing a single *** for the platform retailer and the whole supply chain,forecast sharing is beneficial only under certain conditions,depending on the co-opetitive *** optimal forecast-sharing strategy is the result of a combination of the negative effect of double marginalization in reselling channel and the positive effect of responding pricing to demand uncertainty in agency *** illustrate the parameter regions of the platform retailer’s voluntary sharing,contract sharing,and no sharing,and also find that higher channel competition intensity,higher market share of agency channel,and higher commission rate can promote the platform retailer’s voluntary *** study extends the research scope of demand forecast-sharing and sheds light on the decision-making processes for managing a hybrid-format online platform supply chain.

关键词： Supply chain management hybrid-format online platform demand forecast-sharing co-opetitive relationship channel competition intensity

Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

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Communications in Theoretical Physics 2024年第1期76卷 1-6页

作者： Engui Fan Yanxi Zhang school of mathematical sciences and Key Laboratory of Mathematics for Nonlinear Science Fudan UniversityShanghai200433China Tianjin Xinhua High school No.99 machang RoadTianjin300204China

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS *** the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关键词： defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents

Data-Driven Direct Adaptive Risk-Sensitive Control of Stochastic Systems

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Journal of Systems Science & Complexity 2024年第4期37卷 1446-1469页

作者： QIAO Nan LI Tao school of mathematical sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and mathematical Practice School of Mathematical SciencesEast China Normal UniversityShanghai 200241China

The authors propose a data-driven direct adaptive control law based on the adaptive dynamic programming(ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive *** authors use online data of the system to iteratively solve the generalized algebraic Riccati equation(GARE) and to learn the optimal control law *** the case with measurable system noises,the authors show that the adaptive control law approximates the optimal control law as time goes *** the case with unmeasurable system noises,the authors use the least-square solution calculated only from the measurable data instead of the real solution of the regression equation to iteratively solve the *** authors also study the influences of the intensity of the system noises,the intensity of the exploration noises,the initial iterative matrix,and the sampling period on the convergence of the ADP ***,the authors present two numerical simulation examples to demonstrate the effectiveness of the proposed algorithms.

关键词： Adaptive dynamic programming direct adaptive control generalized algebraic Riccati equation risk-sensitive control

On entire solutions of some Fermat type differential-difference equations

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 69-88页

作者： LONG Jian-ren QIN Da-zhuan school of mathematical sciences Guizhou Normal UniversityGuiyang 550025China

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference *** the other hand,we also investigate the existence and growth of solutions of nonlinear different... 详细信息

关键词： entire solutions differential-difference equations existence finite order

High-performance sodium storage for cobalt phosphide composite array electrodes

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Rare Metals 2024年第8期43卷 3724-3734页

作者： Man Zhang Xiao-Xu Liu Tian-Yi Ji Yang Li Da-Wei Sheng Shao-Dong Li Pei-Pei Ren Ze-Xiang Shen school of Material Science and Engineering Shaanxi University of Science and Technology school of Physical and mathematical sciences Nanyang Technological University

Transition metal phosphides hold great potential as sodium-ion batteries anode materials owing to their high theoretical capacity and modest ***,volume changes and low intrinsic conductivity seriously largely hinder the further development of metal phosphide *** design of phosphide anode materials with reasonable structure is conducive to solving the problems of volume expansion and slow reaction kinetics during the *** this work,a composite material integrating zeolite imidazolate backbone（ZIF） and carbon materials was synthesized by the original growth ***,by the oxidation-phosphating process,CoP nanoarray composites riveted to carbon fiber（CoP@CF） were *** the CoP@CF,CoP nanoparticles are uniformly distributed on ZIF-derived carbon,reducing agglomeration and volume change during *** also provides a highly conductive network for the active material,improving the electrode ***,when evaluated as an anode for sodium-ion batteries,CoP@CF electrode displays enhanced reversible capacity(262 mAh·g-1at 0.1 A·g-1after 100 cycles),which is much better than that of pure CF electrode(57 mAh·g-1at 0.1 A·g-1after 100 cycles)prepared without the addition of *** rate performance of CoP@CF electrode is also superior to that of pure CF electrode at various current densities from 0.05 to1 A·*** sodium storage behavior of CoP@CF was revealed by ex-situ X-ray photoelectron spectroscopy,X-ray diffraction,and synchrotron radiation absorption *** method provides a reference for the design and synthesis of anode materials in sodium-ion batteries.

关键词： Cobalt phosphide Array structure Free-standing anodes Sodium-ion batteries

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu school of mathematical sciences and Institute of Natural sciences Shanghai Jiao Tong UniversityShanghai 200240China school of mathematical sciences and Fujian Provincial Key Laboratory of mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

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Acta Mathematica Scientia 2024年第3期44卷 947-972页

作者：陈爽郭闪闪许秋菊 school of mathematical sciences Chongqing Normal UniversityChongqing401331China

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic *** some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree *** also prove a uniqueness result via energy estimates.

关键词： compressible nematic liquid crystals time-periodic solution topological degree theory energy estimates

Maximal operators of pseudo-differential operators with rough symbols

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 174-180页

作者： Ramla Benhamoud ZHU Xiang-rong school of mathematical sciences Zhejiang Normal UniversityJinhua 321004China

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal *** theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

关键词： pseudo-differential operator rough Hormander class H-L maximal operator