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Impacts of gravitational-wave background from supermassive black hole binaries on the detection of compact binaries by LISA

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Chinese Physics C 2024年第6期48卷 198-203页

作者：黄帆毕研晨曹周键黄庆国 CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China school of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China institute of Applied mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced StudyUCASHangzhou 310024China

In the frequency band of the Laser Interferometer Space Antenna(LISA),extensive research has been conducted on the impact of foreground confusion noise generated by galactic binaries within the Milky Way ***,recent evidence of a stochastic signal,announced by the NANOGrav,EPTA,PPTA,CPTA,and InPTA,indicates that the stochastic gravitational-wave background(SGWB)generated by supermassive black hole binaries(SMBHBs)can contribute strong background noise within the LISA *** the presence of such strong noise,it is expected to have significant impacts on LISA's scientific *** this study,we investigate the impacts of the SGWB generated by SMBHBs on the detection of individual massive black hole binaries,verified galactic binaries,and extreme mass ratio inspirals in the context of *** find it essential to resolve and eliminate the excess noise from the SGWB to guarantee the success of LISA's missions.

关键词： gravitational-wave background supermassive black hole binaries LISA

Learning to select the recombination operator for derivative-free optimization

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Science China mathematics 2024年第6期67卷 1457-1480页

作者： Haotian Zhang Jianyong Sun Thomas Back Zongben Xu school of mathematics and Statistics Xi’an Jiaotong UniversityXi’an710049China Leiden institute of Advanced Computer Science Leiden UniversityLeiden2333 CANetherlands

Extensive studies on selecting recombination operators adaptively,namely,adaptive operator selection(AOS),during the search process of an evolutionary algorithm(EA),have shown that AOS is promising for improving EA's performance.A variety of heuristic mechanisms for AOS have been proposed in recent decades,which usually contain two main components:the feature extraction and the policy *** feature extraction refers to as extracting relevant features from the information collected during the search *** policy setting means to set a strategy(or policy)on how to select an operator from a pool of operators based on the extracted *** components are designed by hand in existing studies,which may not be efficient for adapting optimization *** this paper,a generalized framework is proposed for learning the components of AOS for one of the main streams of EAs,namely,differential evolution(DE).In the framework,the feature extraction is parameterized as a deep neural network(DNN),while a Dirichlet distribution is considered to be the policy.A reinforcement learning method,named policy gradient,is used to train the *** case studies,the proposed framework is applied to two DEs including the classic DE and a recently-proposed DE,which result in two new algorithms named PG-DE and PG-MPEDE,*** on the Congress of Evolutionary Computation(CEC)2018 test suite show that the proposed new algorithms perform significantly better than their ***,we prove theoretically that the considered classic methods are the special cases of the proposed framework.

关键词： evolutionary algorithm differential evolution adaptive operator selection reinforcement learning deep learning

Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size

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Journal of the Operations Research Society of China 2024年第1期12卷 77-92页

作者： Julia Chirkova Vladimir Mazalov institute of Applied Mathematical Research Karelian Research Centre of RASPetrozavodsk185910Russia school of mathematics and Statistics Qingdao UniversityQingdao266071ShandongChina

A single-server queueing system with preemptive access is *** customer has one attempt to enter the system at its working interval[0,T].As soon as the customer request enters the system,the server immediately starts the *** when the next request arrives in the system,the previous one leaves the system even he has not finished his service *** study a non-cooperative game in which the customers wish to maximize their probability of obtaining service within a certain period of *** characterize the Nash equilibrium and the price of anarchy,which is defined as the ratio between the optimal and equilibrium social *** models are *** the first model the number of players is fixed,while in the second it is random and obeys the Poisson *** demonstrate that there exists a unique symmetric equilibrium for both ***,we calculate the price of anarchy for both models and show that the price of anarchy is not monotone with respect to the number of customers.

关键词： Service system Preemptive priorities Strategic users Random number of players Optimal arrivals Kolmogorov backward equations Nash equilibrium Price of anarchy

Global output feedback control of feedforward nonlinear time-delay systems with unknown growth rate and unknown measurement sensitivity

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Control Theory and Technology 2024年第1期22卷 122-134页

作者： Weiyong Yu Keao Gao Hongbing Zhou Qiang Liu Academy of Artificial Intelligence Beijing Institute of Petrochemical TechnologyBeijing102617China school of mathematics and Statistics Nanyang Normal UniversityNanyang473061HenanChina

This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinear terms are dominated by upper triangular linear unmeasured (delayed) states multiplied by unknown growth rate. The unknown growth rate is composed of an unknown constant, a power function of output, and an input function. Furthermore, due to the measurement uncertainty of the system output, it is more difficult to solve this problem. It is proved that the presented output feedback controller can globally regulate all states of the nonlinear systems using the dynamic gain scaling technique and choosing the appropriate Lyapunov–Krasovskii functionals.

关键词： Adaptive control Dynamic gain controllers Feedforward time-delay systems Measurement sensitivity Output feedback

On Ideal-Derived-Set Mappings in Uniform Spaces

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Journal of Mathematical Research with Applications 2024年第4期44卷 502-510页

作者： Lihua LIN Xiangeng ZHOU school of Information Engineering Sanming University institute of mathematics Ningde Normal University

In this paper, we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings. Meanwhile, we introduce a concept of I-Hurewicz boundedness, study some basic topological ope... 详细信息

关键词： uniform spaces mappings I-cluster points I-Hurewicz boundedness

Distributed order estimation for continuous-time stochastic systems

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Control Theory and Technology 2024年第3期22卷 406-418页

作者： Xinghua Zhu Zhixin Liu Xiaoming Hu Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceBeijing 100190China school of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China Department of mathematics KTH Royal Institute of TechnologyStockholm 10044Sweden

In this paper,we investigate the distributed estimation problem of continuous-time stochastic dynamic systems over sensor networks when both the system order and parameters are *** propose a local information criterion(LIC)based on the L_(0)penalty *** minimizing LIC at the diffusion time instant and utilizing the continuous-time diffusion least squares algorithm,we obtain a distributed estimation algorithm to simultaneously estimate the unknown order and the parameters of the *** dealing with the effect of the system noises and the coupling relationship between estimation of system orders and parameters,we establish the almost sure convergence results of the proposed distributed estimation ***,we give a simulation example to verify the effectiveness of the distributed algorithm in estimating the system order and parameters.

关键词： Stochastic differential equations Sensor networks Distributed order estimation Cooperative excitation condition.Convergence

On the Geometry of the Anti-canonical Bundle of the Bott–Samelson–Demazure–Hansen Varieties

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Acta Mathematica Sinica,English Series 2024年第8期40卷 1920-1940页

作者： Indranil BISWAS S.Senthamarai KANNAN Pinakinath SAHA school of mathematics Tata Institute of Fundamental Research1 Homi Bhabha RoadMumbai 400005India Chennai Mathematical institute Plot H1SIPCOT IT ParkSiruseriKelambakkam603103India

Let G be a semi-simple simply connected algebraic group over the field C of complex *** T be a maximal torus of G,and let W be the Weyl group of G with respect to *** Z(w,i)be the Bott–Samelson–Demazure–Hansen variety corresponding to a tuple i associated to a reduced expression of an element w∈*** prove that for the tuple i associated to any reduced expression of a minuscule Weyl group element w,the anti-canonical line bundle on Z(w,i)is globally *** consequence,we prove that Z(w,i)is weak *** that G is a simple algebraic group whose type is different from *** S={α1,...,αn}be the set of simple *** w be such that support of w is equal to *** prove that Z(w,i)is Fano for the tuple i associated to any reduced expression of w if and only if w is a Coxeter element and w^(−1)(Σ_(t=1)^(n)α_(t))∈−S.

关键词： Bott-Samelson-Demazure-Hansen variety Coxeter element anti-canonical line bundle Fano weak Fano

Weighted Probability Density Estimator with Updated Bandwidths

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Journal of Systems Science & Complexity 2024年第2期37卷 886-906页

作者： WU Yi YU Wei WANG Xuejun PRAKASA RAO B L S school of Big Data and Artificial Intelligence Chizhou UniversityChizhou 247000China school of Big Data and Statistics Anhui UniversityHefei 230601China CR Rao Advanced institute of mathematics Statistics and Computer ScienceHyderabad 500046India

In this paper,the authors study a class of weighted version of probability density *** is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or *** statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild ***,the random weighted estimator is also *** numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.

关键词： Asymptotic normality consistency numerical simulation probability density real data analysis updated bandwidths weighted estimator

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou school of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels