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A Note of the Interpolating Sequence in Qp∩H~∞

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Wuhan University Journal of Natural sciences 2024年第1期29卷 1-6页

作者： ZHOU Jizhen SUN Hejie school of mathematics and Big data Anhui University of science and Technology

In this paper,{zn}n=1~∞ acts as an interpolating sequence for Qp∩H~∞.An analytic function f is constructed,and f(zn)=∑jλjfzj(zn)=λn,n=1,2,…for any {λn}∈l~∞,wheref and ■ belong to Qp∩H~∞.As a result,the st... 详细信息

关键词： Q_p space H∞ space F (p,p - 2,s) ∩H~∞ interpolating sequence

On the convergence of tracking differentiator with multiple stochastic disturbances

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science China(Information sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG school of mathematics and Big data Foshan University school of mathematics and Statistics Central South University Academy of mathematics and Systems science Chinese Academy of Sciences Systems Engineering Institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China school of mathematics and Computational science Xiangtan UniversityXiangtan 411105China school of Statistics and data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

A verifiable essential secret image sharing scheme based on HLRs(VESIS-(t,s,k,n))

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CAAI Transactions on Intelligence Technology 2024年第2期9卷 388-410页

作者： Massoud Hadian Dehkordi Seyed Taghi Farahi Samaneh Mashhadi Cryptography and data Security Laboratory School of MathematicsIran University of Science and TechnologyNarmakTehranIran

In traditional secret image sharing schemes,a secret image is shared among shareholders who have the same *** if the shareholders have two different positions,essential and non‐essential,it is necessary to use essential secret image sharing *** this article,a verifiable essential secret image sharing scheme based on HLRs is ***'s share consists of two *** first part is produced by the shareholders,which prevents the fraud of *** second part is a shadow image that is produced by using HLRs and the first part of *** verification of the first part of the shares is done for the first time by using multilinear and bilinear ***,for verifying shadow images,Bloom Filters are used for the first *** proposed scheme is more efficient than similar schemes,and for the first part of the shares,has formal security.

关键词： Bloom Filter cryptography Essential Secret Image Sharing Verifiability

Computing Persistent Homology by Spanning Trees and Critical Simplices

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Research 2024年第2期2023卷 519-527页

作者： Dinghua Shi Zhifeng Chen Chuang Ma Guanrong Chen Department of mathematics Cllege of ScienceShanghai UniversityShanghaiChina school of Big data Fuzhou University of International Studies and TradeFuzhouChina Department of data science and Big data Technology School of InternetAnhui UniversityHefeiChina Department of Electrical Engineering City University of Hong KongHong KongChina

Topological data analysis can extract effective information from higher-dimensional *** mathematical basis is persistent *** persistent homology can calculate topological features at different spatiotemporal scales of the dataset,that is,establishing the integrated taxonomic relation among points,lines,and ***,the simplicial network composed of all-order simplices in a simplicial complex is *** the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values,a method based on the concept of critical simplices can be developed by searching all-order spanning *** this new method,not only the Morse function values with the theoretical minimum number of critical simplices can be obtained,but also the Betti numbers and composition of all-order cavities in the simplicial network can be calculated ***,this method is used to analyze some examples and compared with other methods,showing its effectiveness and feasibility.

关键词： Morse establishing topological

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

Construction of Optimal Mixed-Level Uniform Designs

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Journal of Systems science & Complexity 2024年第2期37卷 841-862页

作者： CHATTERJEE Kashinath LIU Min-Qian QIN Hong YANG Liuqing Department of Population Health sciences Division of Biostatistics and Data ScienceAugusta UniversityGA 30912USA NITFID LPMC&KLMDASRSchool of Statistics and Data ScienceNankai UniversityTianjin 300071China school of Statistics and mathematics Zhongnan University of Economics and LawWuhan 430073China

The theory of uniform design has received increasing interest because of its wide application in the field of computer *** generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial *** this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower *** methods are all deterministic construction methods which can avoid the complexity of stochastic *** saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these ***,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.

关键词： Generalized discrete discrepancy Hadamard matrix mixed-level design orthogonal array supersaturated design

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

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science China(Information sciences) 2024年第2期67卷 144-156页

作者： Ran LIU Hui WANG Wuquan LI school of mathematics and Statistics science Ludong University

This paper investigates the prescribed-time state-feedback stabilization and prescribed-time inverse optimality problems for stochastic high-order nonlinear systems. First, a time-varying controller is designed by developing scaled quartic Lyapunov functions, which can guarantee that the system has a unique strong solution almost surely on the prescribed interval for any system initial conditions and that the states and the control converge to the origin in a mean-square form within the prescribed time. Then, the controller is redesigned to address the problem of prescribed-time inverse optimal mean-square stabilization. Finally,a concrete example is provided to confirm the efficiency of the proposed design schemes.

关键词： stochastic high-order nonlinear systems prescribed-time stabilization the scaled design inverse optimality

On equivalence of state-based potential games

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science China(Information sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG Institute of mathematics School of ScienceHebei University of Technology

In this paper, we explore state-based potential games using the semi-tensor product of ***, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

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