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A SIMPLE ITERATIVE ALGORITHM FOR MAXCUT

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Journal of Computational Mathematics 2024年第5期42卷 1277-1304页

作者： Sihong Shao Dong Zhang Weixi Zhang CAPT LMAM and School of Mathematical SciencesPeking UniversityBeijing 100871China lmam and school of mathematical sciences Peking UniversityBeijing 100871China

We propose a simple iterative(SI)algorithm for the maxcut problem through fully using an equivalent continuous *** does not need rounding at all and has advantages that all subproblems have explicit analytic solutions,the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient *** experiments on G-set demonstrate the *** particular,the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in[***.,248(2017),365-403]are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.

关键词： Maxcut Iterative algorithm Exact solution Subgradient selection Fractional programming

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data science Peking University Zuse Institute Berlin Department of Mathematics and Computer science Freie Universit?t Berlin Laboratory of Mathematics and Applied Mathematics(lmam)and school of mathematical sciences Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

Essentially Commuting Truncated Toeplitz Operators

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2453-2480页

作者： Xi ZHAO Tao YU school of Mathematics and science Hebei GEO University school of mathematical sciences Dalian University of Technology

A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space. In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.

关键词： 47B32 47B35 commutator compact operator maximal ideal space model space Truncated Toeplitz operator

FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY

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Acta Mathematica Scientia 2024年第2期44卷 405-419页

作者：付昂李明金杨迪 school of mathematical sciences University of Science and Technology of ChinaHefei230026China

For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent *** this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave *** an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.

关键词： volterra lattice hierarchy matrix-resolvent method wave functions even GUE correlators

ALTERNATING OPTIMIZATION METHOD FOR ISOGEOMETRIC TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS

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Journal of Computational Mathematics 2024年第1期42卷 134-155页

作者： Xiaoya Zhai school of mathematical sciences University of Science and Technology of ChinaHefei 230071China

Topology optimization (TO) has developed rapidly recently. However, topology optimization with stress constraints still faces many challenges due to its highly non-linear properties which will cause inefficient computation, iterative oscillation, and convergence guarantee problems. At the same time, isogeometric analysis (IGA) is accepted by more and more researchers, and it has become one important tool in the field of topology optimization because of its high fidelity. In this paper, we focus on topology optimization with stress constraints based on isogeometric analysis to improve computation efficiency and stability. A new hybrid solver combining the alternating direction method of multipliers and the method of moving asymptotes (ADMM-MMA) is proposed to solve this problem. We first generate an initial feasible point by alternating direction method of multipliers (ADMM) in virtue of the rapid initial descent property. After that, we adopt the method of moving asymptotes (MMA) to get the final results. Several benchmark examples are used to verify the proposed method, and the results show its feasibility and effectiveness.

关键词： Isogeometric topology optimization Stress constraints The ADMM-MMA solver

On the Difference Between the Skew-rank of an Oriented Graph and the Rank of Its Underlying Graph

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 129-136页

作者： Jia-min Zhu Bo-jun Yuan Yi Wang school of mathematical sciences Anhui UniversityHefei230601China school of science Zhejiang University of Science and TechnologyHangzhou310023China

Let G be a simple graph and G~σ be the oriented graph with G as its underlying graph and orientation σ.The rank of the adjacency matrix of G is called the rank of G and is denoted by r(G).The rank of the skew-adjacency matrix of G~σ is called the skew-rank of G~σ and is denoted by sr(G~σ).Let V(G)be the vertex set and E(G) be the edge set of *** cyclomatic number of G,denoted by c(G),is equal to |E(G)|-|V(G)|+ω(G),where ω(G) is the number of the components of *** is proved for any oriented graph G~σ that-2c(G)≤sr(G~σ)-r(G)≤2c(G).In this paper,we prove that there is no oriented graph G~σwith sr(G~σ)-r(G)=2c(G)-1,and in addition,there are infinitely many oriented graphs G~σ with connected underlying graphs such that c(G)=k and sr(G~σ)-r(G)=2c(G)-l for every integers k,l satisfying 0 ≤l≤4k and l≠1.

关键词： cyclomatic number rank skew-rank

Continuous Orbit Equivalence of Semigroup Actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1581-1598页

作者： Xiang Qi QIANG Cheng Jun HOU school of mathematical science Yangzhou UniversityYangzhou 225002P.R.China

We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corresponding transformation groupoids and their operator *** particular,we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C^(∗)-isomorphism between the associated transformation groupoid C^(∗)-*** also give some examples of orbit equivalence,consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.

关键词： Semigroup action continuous one-sided orbit equivalence continuous orbit equivalence groupoid C^(∗)-algebras

MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

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Acta Mathematica Scientia 2024年第4期44卷 1200-1228页

作者： Quanquan YAO Peiyong ZHU school of mathematical sciences University of Electronic Science and Technology of ChinaChengdu 611731China

Let(X,T)be a linear dynamical system,where X is a Banach space and T:X→X is a bounded linear *** paper obtains that(X,T)is sensitive(Li-Yorke sensitive,mean sensitive,syndetically mean sensitive,respectively)if and only if(X,T)is Banach mean sensitive(Banach mean Li-Yorke sensitive,thickly multi-mean sensitive,thickly syndetically mean sensitive,respectively).Several examples are provided to distinguish between different notions of mean sensitivity,syndetic mean sensitivi`ty and mean Li-Yorke sensitivity.

关键词： mean sensitive Banach mean sensitive syndetically mean sensitive Li-Yorke sensitive mean Li-Yorke sensitive

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 TechnologyXi'an 710021China school of Physical and mathematical sciences Nanyang Technological UniversitySingapore 637371Singapore

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^(-1) at 0.1 A·g^(-1)after 100 cycles),which is much better than that of pure CF electrode(57 mAh·g^(-1) at 0.1 A·g^(-1) after 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·g^(-1).The 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 Freestanding anodes Sodium-ion batteries