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Impact of vaccination on the dynamics of COVID-19:A mathematical study using fractional derivatives

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International Journal of Biomathematics 2024年第2期17卷 201-232页

作者： Shraddha Ramdas Bandekar Mini Ghosh C.Rajivganthi Division of mathematics School of Advanced Sciences Vellore Institute of TechnologyChennaiIndia

Arrival of a new disease marks a yearlong destruction of human lives and economy in general,and if the disease turns out to be a pandemic the loss is ***-19 is one such pandemic that has claimed millions of lives till *** is a suffering throughout the world due to various factors associated with the pandemic,be it loss of livelihoods because of sudden shutdown of companies and lockdown,or loss of lives due to lack of medical aid and inadequate vaccination *** this study,we develop a six-compartmental epidemiological model incorporating *** motivation behind the study is to analyze the significance of higher vaccination efficacy and higher rate of population getting vaccinated in controlling the rise in infectives and thereby the untimely demise of various *** work begins with an ordinary differential equation model followed by stability analysis of the same,after which a fractional-order derivative model of the same is formulated and the existence of uniformly stable solution for the system is *** addition to this,we present the stability of the equilibria in general for the fractional model *** sensitivity analysis of the basic reproduction number along with its correlation with various parameters is *** addition to this,sensitivity of certain state variables in the fractional model with respect to *** orders as well with respect to different infection rate is exhibited in this *** related to lockdown and usage of face shields are incorporated in the entire study,and importance of these is highlighted in the study as *** major takeaway from the study is that mere vaccination will not sufice in eradication of the *** vaccine efficacy plays a major role along with other intervention included in the *** numerical simulations are carried out in MATLAB software using ode45 and fdel2.

关键词： Caputo fractional derivative basic reproduction number stability analysis sensitivityanalysis vaccination

Some Modified Equations of the Sine-Hilbert Type

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Chinese Physics Letters 2024年第4期41卷 1-6页

作者：闫铃娟刘亚杰胡星标 LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are *** on these b... 详细信息

关键词： bilinear equations equation

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

Distributed generalized Nash equilibrium seeking:event-triggered coding-decoding-based secure communication

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Science China(Information sciences) 2024年第7期67卷 271-284页

作者： Shaofu YANG Wenying XU Wangli HE Jinde CAO school of computer Science and Engineering Southeast University school of mathematics Southeast University Key Laboratory of Advanced Control and Optimization for Chemical Processes East China University of Science and Technology

In this paper, we consider the distributed generalized Nash equilibrium(GNE) seeking problem in strongly monotone games. The transmission among players is implemented through a digital communication network with limited bandwidth. For improving communication efficiency or/and security, an event-triggered coding-decoding-based communication is first proposed, where the data(decision variable) are first mapped to a series of finite-level codewords and, only when an event condition is satisfied, then sent to the neighboring agents. Moreover, a distributed communication-efficient GNE seeking algorithm is constructed accordingly,and the overrelaxation scheme is further taken into consideration. Through primal-dual analysis, the proposed algorithm is proven to converge to a variational GNE with fixed step-sizes by recasting it as an inexact forward-backward iteration. Finally, numerical simulations illustrate the benefit of the proposed algorithms in terms of saving communication resources.

关键词： noncooperative games event-triggered communication coding-decoding quantization

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A unified pre-training and adaptation framework for combinatorial optimization on graphs

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Science China mathematics 2024年第6期67卷 1439-1456页

作者： Ruibin Zeng Minglong Lei Lingfeng Niu Lan Cheng school of computer Science and Technology University of Chinese Academy of SciencesBeijing100049China Faculty of Information Technology Beijing University of TechnologyBeijing100124China school of Economics and Management University of Chinese Academy of SciencesBeijing100190China school of mathematics and Statistics Central South UniversityChangsha410075China

Combinatorial optimization(CO)on graphs is a classic topic that has been extensively studied across many scientific and industrial ***,solving CO problems on graphs through learning methods has attracted great *** deep learning methods,e.g.,graph neural networks(GNNs),have been used to effectively assist the process of solving ***,current frameworks based on GNNs are mainly designed for certain CO problems,thereby failing to consider their transferable and generalizable abilities among different COs on ***,simply using original graphs to model COs only captures the direct correlations among objects,which does not consider the mathematical logicality and properties of *** this paper,we propose a unified pre-training and adaptation framework for COs on graphs with the help of the maximum satisfiability(Max-SAT)*** first use Max-SAT to bridge different COs on graphs since they can be converted to Max-SAT problems represented by standard formulas and clauses with logical *** we further design a pre-training and domain adaptation framework to extract the transferable and generalizable features so that different COs can benefit from *** the pre-training stage,Max-SAT instances are generated to initialize the parameters of the *** the fine-tuning stage,instances from CO and Max-SAT problems are used for adaptation so that the transferable ability can be further *** experiments on several datasets show that features extracted by our framework exhibit superior transferability and Max-SAT can boost the ability to solve COs on graphs.

关键词： combinatorial optimization graph neural networks domain adaptation maximum satisfiability problem

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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

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

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

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