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Parametric“non-nested”discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang Department of mathematics North Carolina State UniversityRaleighNC 27695USA SMS-HCIC-School of mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006China

We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex *** is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the *** polynomials in the coefficients are called discriminants for *** is also known that discriminants can be obtained using repeated parametric greatest common *** resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so *** this paper,we give a new type of discriminant that is not based on repeated greatest common *** new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

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Opto-Electronic Advances 2024年第2期7卷 14-21页

作者： Pengcheng Huo Ruixuan Yu Mingze Liu Hui Zhang Yan-qing Lu Ting Xu National Laboratory of Solid-State Microstructures and Collaborative Innovation center of Advanced Microstructures Nanjing UniversityNanjing 210093China College of Engineering and applied Sciences Key Laboratory of Intelligent Optical Sensing and Manipulation and Jiangsu Key Laboratory of Artificial Functional MaterialsNanjing UniversityNanjing 210093China

An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

关键词： electron vortex beam orbital angular momentum diffraction holography

Lattice water fuels acidic water oxidation

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Science China Chemistry 2024年第7期67卷 2132-2133页

作者： Minyue Zhao Jianyong Feng Zhaosheng Li Zhigang Zou Collaborative Innovation center of Advanced Microstructures National Laboratory of Solid State MicrostructuresCollege of Engineering and Applied SciencesNanjing UniversityNanjing 210093China Jiangsu Key Laboratory for Nano Technology Nanjing UniversityNanjing 210093China

In comparison to commercial alkaline water electrolysis technologies,proton-exchange membrane water electrolyzers(PEMWEs)offer intriguing advantages for hydrogen production,such as high current density,compact system ... 详细信息

关键词： Lattice alkaline system

Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

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Science China mathematics 2024年第8期67卷 1865-1880页

作者： Xiequan Fan Haijuan Hu Lihu Xu center for applied mathematics Tianjin UniversityTianjin 300072China School of mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao 066004China Department of mathematics Faculty of Science and TechnologyUniversity of MacaoMacaoChina

In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for *** to our results,Berry-Esseen's bounds and moderate deviation principles are also *** norm... 详细信息

关键词： Euler-Maruyama scheme Cram´er-type moderate deviations self-normalized sequences BerryEsseen’s bounds

Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations

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Communications in Theoretical Physics 2024年第5期76卷 1-15页

作者： Alemu Yilma Tefera Shangshuai Li Da-jun Zhang Department of mathematics Shanghai UniversityShanghai 200444China Newtouch center for mathematics of Shanghai University Shanghai 200444China Department of applied mathematics Faculty of Science and EngineeringWaseda UniversityTokyo 169-8555Japan

This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable *** the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated *** this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit *** equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral *** solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex *** solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

关键词： Cauchy matrix approach Sylvester equation nonlinear Schrödinger equation non-isospectral integrable system explicit solution

Weak type(1, 1) of the Riesz transform on some direct product manifolds with exponential volume growth

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Science China mathematics 2024年第7期67卷 1599-1622页

作者： Hong-Quan Li Jie-Xiang Zhu School of Mathematical Sciences Fudan UniversityShanghai200433China center for applied mathematics Tianjin UniversityTianjin300072China

In this paper, we are concerned with the Riesz transform on the direct product manifold H^(n)× M,where H^(n) is the n-dimensional real hyperbolic space, and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type(1, 1) property. In addition, we obtain the weak type(1, 1) of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume growth. Particularly, we provide a simpler proof of weak type(1, 1) boundedness of some operators considered in the work of Li et al.(2016).

关键词： Riesz transform heat kernel direct product real hyperbolic space

Gradient-based algorithms for multi-objective bi-level optimization

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Science China mathematics 2024年第6期67卷 1419-1438页

作者： Xinmin Yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang National center for applied mathematics in Chongqing Chongqing401331China School of Mathematical Sciences Chongqing Normal UniversityChongqing401331China Department of mathematics Southern University of Science and TechnologyShenzhen518055China National center for applied mathematics Shenzhen Shenzhen518000China Department of mathematics and Statistics University of VictoriaVictoriaBCV8W 2Y2Canada

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of ***,its multi-objective and hierarchical bi-level nature makes it notably ***-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement ***,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical *** address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and ***,we demonstrate the theoretical validity by accomplishing the desirable Pareto *** experiments confirm the practical efficiency of the proposed method and verify the theoretical *** accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA *** results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

关键词： multi-objective bi-level optimization convergence analysis Pareto stationary learning to optimize

Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises

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Acta Mathematica Sinica,English Series 2024年

作者： Chang-Song DENG Xing HUANG School of mathematics and Statistics Wuhan University center for applied mathematics Tianjin University

We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetricα-stable L′evy process(1/2 < α ≤ 1), where the drift coefficient is Ho¨lder continuous in space variable,while the noise coefficient is Lipscitz continuous in space variable, and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance. If the drift coefficient does not depend on distribution variable, our methodology developed in this paper applies to the case α ∈(0, 1].The main tool relies on heat kernel estimates for(distribution independent) stable SDEs and Banach's fixed point theorem.

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Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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Science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes School of mathematics Southwestern University of Finance and EconomicsChengdu611130China School of mathematics Shandong UniversityJinan250100China applied and Computational mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme