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Science China mathematics 2024年第9期67卷 2171-2194页

作者： Chuanjun Chen Xiaofeng Yang school of mathematics and Information sciences Yantai UniversityYantai 264005China Department of mathematics University of South CarolinaColumbiaSC 29208USA

In this paper,an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow *** scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches,including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization(explicit-IEQ)approach for dealing with coupled nonlinear *** obtained scheme is very efficient since it only needs to solve several decoupled,linear elliptic equations with constant coefficients at each time *** also strictly prove the solvability and unconditional energy stability of the scheme,and verify the accuracy and stability of the scheme through plenty of numerical examples.

关键词： finite element method decoupled scheme two-phase fow Cahn-Hilliard equation Navier-Stokes equations energystability

MULTIPLICATION OPERATORS ON WEIGHTED DIRICHLET SPACES

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Acta Mathematica Scientia 2024年第6期44卷 2225-2248页

作者：韩凯凯李玉成王茂发 school of Statistics and mathematics Hebei University of Economics and Business school of Mathematical sciences Hebei Normal University school of mathematics and Statistics Wuhan University

In this paper,we study multiplication operators on weighted Dirichlet spaces Dβ（β∈R）.Let n be a positive integer and β∈R,we show that the multiplication operator Mz~non Dβis similar to the operator ⊕1~nMzon the space ⊕1~nDβ.Moreover,we prove that Mz~n（≥2） on Dβis unitarily equivalent to ⊕1~nMzon ⊕1~nDβif and only if β=*** addition,we completely characterize the unitary equivalence of the restrictions of Mz~nto different invariant subspaces zkDβ（k≥1）,and the unitary equivalence of the restrictions of Mz~nto different invariant subspaces Sj（0≤jz~n) of Mz~non a family of analytic function spaces Aα2（α ∈ R） on D(in fact,the family of spaces Aα2（α∈R） is the same with the family of spaces Dβ（β∈R）) in terms of the multiplier algebra of the underlying function *** this paper,we give a new characterization of the commutant A'(Mz~n) of Mz~non Dβ,and characterize the self-adjoint operators and unitary operators in A'(Mz~n).We find that the class of self-adjoint operators（unitary operators） in A'(Mz~n) when β≠0 is different from the class of self-adjoint operators（unitary operators） in A'(Mz~n) when β=0.

关键词： 47B35 commutant multiplication operator similarity unitary equivalence weighted Dirichlet space

Weak Graph Map Homotopy and Its Applications

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Chinese Annals of mathematics,Series B 2024年第2期45卷 235-252页

作者： Conglei ZHANG Yanying WANG Zhiguo ZHANG Yan ZHAO school of Mathematical sciences Hebei Normal UniversityShijiazhuang 050024China Department of Basic Science Shanxi Agricultural UniversityJinzhang 030801ShanxiChina Center for Topology and Geometry based Technology School of Mathematical SciencesHebei Normal UniversityShijiazhuang 050024China school of Mathematical sciences Hebei Normal UniversityTaiyuan 030031China school of mathematics and computer Science Shanxi Normal UniversityShijiazhuang 050024China school of mathematics and Science Hebei GEO UniversityShijiazhuang 050031China

The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and *** prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in *** difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial *** discuss its advantages over the graph homotopy *** its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple ***,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.

关键词： Weak graph map homotopy Trivial vertex Strong deformation retract Mapping class group MP-Homotopy group

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 695-707页

作者： Song-bai GUO Yu-ling XUE Xi-liang LI Zuo-huan ZHENG school of Science Beijing University of Civil Engineering and ArchitectureBeijing 102616China school of mathematics and Statistics Hainan Normal UniversityHaikou 571158China Academy of mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China school of mathematics and Information Science Shandong Technology and Business UniversityYantai 264005China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>*** approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using *** addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)1.

关键词： uniform persistence epidemic model control reproduction number quarantine standard incidence rate

The Optimization of Binary Randomized Response Based on Lanke Privacy and Utility Analysis

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Chinese Journal of Electronics 2024年

作者： Yihui ZHOU Wenli WANG Jun YAN Zhenqiang WU Laifeng LU school of computer Science Shaanxi Normal University school of mathematics and Statistics Shaanxi Normal University school of mathematics and computer Applications Shangluo College

Currently, it has become a consensus to enhance privacy protection. Randomized response(RR) technique, as the mainstream perturbation mechanism for local differential privacy, has been widely studied. However,most of the research in literature managed to modify existing RR schemes and propose new mechanisms with better privacy protection and utility, which are illustrated only by numerical experiments. We study the properties of generalized binary randomized response mechanisms from the perspectives of Lanke privacy and utility. The mathematical expressions of privacy and utility for the binary RR mechanism are given respectively. Moreover, the comparison principle for privacy and utility of any two mechanisms is proved. Finally, the optimization problem of the binary RR mechanism is discussed. Our work is based on a rigorous mathematical proof of privacy and utility for the general binary RR mechanism, and numerical verification illustrates the correctness of the conclusions. It can provide theoretical support for the design of binary RR mechanism and can be applied in data collection, analysis and publishing.

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A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS

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Acta Mathematica Scientia 2024年第5期44卷 2019-2040页

作者： Li HU Zhiyuan LI Xiaona YANG school of mathematics and Statistics Ningbo UniversityNingbo315211China school of Mathematical sciences Xiamen UniversityXiamen361005China

In this article,we consider the diffusion equation with multi-term time-fractional *** first derive,by a subordination principle for the solution,that the solution is positive when the initial value is *** an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a ***,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

关键词： fractional diffusion equation inverse source problem nonlocal observation observation uniqueness Tikhonov regularization

Ramsey Numbers of Trees Versus Multiple Copies of Books

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 600-612页

作者： Xiao-bing GUO Si-nan HU Yue-jian PENG school of Mathematical sciences Luoyang Normal UniversityLuoyang 471934China school of mathematics Hunan UniversityChangsha 410082China

Given two graphs G and H,the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_(N) in red or blue yields a red G or a blue *** v(G) be the number of vertices of G and χ(G) be the chromatic number of *** s(G) denote the chromatic surplus of G,the number of vertices in a minimum color class among all proper χ(G)-colorings of *** showed that R(G,H)≥(v(G)-1)(χ(H)-1)+s(H) if G is connected and v(G)≥s(H).A connected graph G is H-good if R(G,H)=(v(G)-1)(χ(H)-1)+s(H).Let tH denote the disjoint union of t copies of graph H,and let G∨H denote the join of G and *** a complete graph on n vertices by K_(n),and a tree on n vertices by T_(n).Denote a book with n pages by B_(n),i.e.,the join K_(2) ∨■.Erd?s,Faudree,Rousseau and Schelp proved that T_(n) is B_(m)-good if n≥*** this paper,we obtain the exact Ramsey number of T_(n) versus 2B_(2).Our result implies that T_(n) is 2B_(2)-good if n≥5.

关键词： ramsey number ramsey goodness tree book

Tighter sum uncertainty relations via(α,β,γ)weighted Wigner–Yanase–Dyson skew information

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Communications in Theoretical Physics 2024年第3期76卷 91-99页

作者： Cong Xu Zhaoqi Wu Shao-Ming Fei school of Mathematical sciences Capital Normal UniversityBeijing 100048China Department of mathematics Nanchang UniversityNanchang 330031China Max-Planck-Institute for mathematics in the sciences 04103 LeipzigGermany

We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew *** results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew *** also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew *** examples are provided to illustrate the tightness of our uncertainty relations.

关键词： quantum channels (α,β,γ)WWYD skew information (α,β,γ)MWWYD skew information uncertainty relations

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

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Chinese Physics B 2024年第7期33卷 137-145页

作者：张晓娇吴祥 school of mathematics and Information Science Nanchang Normal UniversityNanchang 330032China school of Mathematical sciences Guizhou Normal UniversityGuiyang 550001China

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

关键词： contraction theory virtual system bipartite consensus Lurie multi-agent systems

On the Security of Homomorphic Encryption Schemes with Restricted Decryption Oracles

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Journal of Systems Science & Complexity 2024年第5期37卷 2240-2261页

作者： MA Guangsheng LI Hongbo school of mathematics and Physics North China Electric Power UniversityBeijing 100096China Academy of mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of sciences Beijing 100049China

Fully homomorphic encryption(FHE)can be used for privacy-preserving aggregation of medical *** this typical application,the security against passive attacks has been well studied by Li and Micciancio(2021).In this paper,the authors further consider a“nearly passive”kind of attack,where the attacker may behave like a passive attacker in the view of the third-party *** capture the security against this hard-to-detect attack,the authors propose a new notion of IND-CPA^(rD)*** authors show that the standard LWE encryption and its related FHE schemes can not defend against IND-CPA^(rD)attack,even under a stricter rule limiting the content and number of queries made by the *** make the application of FHE schemes more secure,the authors discuss some possible modifications that may serve as countermeasures to IND-CPA^(rD)attack.

关键词： Homomorphic encryption privacy secure cloud computing security