CSpace中国科学院数学与系统科学研究院http://ir.amss.ac.cn:802022-01-28T23:20:52Z2022-01-28T23:20:52ZA NOTE ON TRANSMISSION EIGENVALUES INCakoni, FioralbaMeng, ShixuXiao, Jingnihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591172021-10-26T00:27:19Z2021-10-26T00:27:19ZTitle: A NOTE ON TRANSMISSION EIGENVALUES IN
Authors: Cakoni, Fioralba; Meng, Shixu; Xiao, Jingni
Description: This short note was motivated by our efforts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justification of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21, 23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our findings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically stratified media. We hope that these results can provide reasonable conjectures for general electromagnetic media.2021-10-26T00:27:19ZBounds on antipodal spherical designs with few anglesXu, ZhiqiangXu, ZiliYu, Wei-Hsuanhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591142021-10-26T00:27:19Z2021-10-26T00:27:19ZTitle: Bounds on antipodal spherical designs with few angles
Authors: Xu, Zhiqiang; Xu, Zili; Yu, Wei-Hsuan
Description: A finite subset X on the unit sphere S-d is called an s-distance set with strength t if its angle set A(X) := {< x, y > : x, y is an element of X, x not equal y} has size s, and X is a spherical t-design but not a spherical (t + 1)-design. In this paper, we consider to estimate the maximum size of such antipodal set X for small s. Motivated by the method developed by Nozaki and Suda, for each even integer s is an element of [ t+5/2, t + 1] with t >= 3, we improve the best known upper bound of Delsarte, Goethals and Seidel. We next focus on two special cases: s = 3, t = 3 and s = 4, t = 5. Estimating the size of X for these two cases is equivalent to estimating the size of real equiangular tight frames (ETFs) and Levenstein-equality packings, respectively. We improve the previous estimate on the size of real ETFs and Levenstein-equality packings. This in turn gives an upper bound on vertical bar X vertical bar when s = 3, t = 3 and s = 4, t = 5, respectively.2021-10-26T00:27:19ZOptimal Minimax Variable Selection for Large-Scale Matrix Linear Regression ModelHao, MeilingQu, LianqiangKong, DehanSun, LiuquanZhu, Hongtuhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591202021-10-26T00:27:19Z2021-10-26T00:27:19ZTitle: Optimal Minimax Variable Selection for Large-Scale Matrix Linear Regression Model
Authors: Hao, Meiling; Qu, Lianqiang; Kong, Dehan; Sun, Liuquan; Zhu, Hongtu
Description: Large-scale matrix linear regression models with high-dimensional responses and high dimensional variables have been widely employed in various large-scale biomedical studies. In this article, we propose an optimal minimax variable selection approach for the matrix linear regression model when the dimensions of both the response matrix and predictors diverge at the exponential rate of the sample size. We develop an iterative hard-thresholding algorithm for fast computation and establish an optimal minimax theory for the parameter estimates. The finite sample performance of the method is examined via extensive simulation studies and a real data application from the Alzheimer's Disease Neuroimaging Initiative study is provided.2021-10-26T00:27:19ZSpalling fracture of Ni/Al nanolaminates influenced by chemical reactionTian, XiaXiang, MeizhenCui, JunzhiJi, GuangyuFu, Zhuojiahttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591082021-10-26T00:27:18Z2021-10-26T00:27:18ZTitle: Spalling fracture of Ni/Al nanolaminates influenced by chemical reaction
Authors: Tian, Xia; Xiang, Meizhen; Cui, Junzhi; Ji, Guangyu; Fu, Zhuojia
Description: We investigate spalling behaviors of Ni/Al nanolaminates by molecular dynamics simulations. First, we discuss spalling damage distributions in shocked Ni/Al nanolaminates. Voids nucleate in Al layers, while no voids are located in Ni layers or along the Ni/Al interfaces. This is because the spall strength of single-crystalline Ni is higher than that of single-crystalline Al. We reveal influences of a shock-induced chemical reaction on dynamic spalling damage and fracture processes. An abnormal "decrease -> increase -> decrease" zigzag variation tendency of the spall strength of Ni/Al nanolaminates as the impact velocity increase is observed in our simulations, which resulted from combining effects of micro-structures, chemical reactions, and temperature softening. When the impacting intensity is relatively low, the spall strength of Ni/Al nanolaminates decreases as the impact velocity increases due to micro-structure effects. However, when the loading velocity increases to a certain magnitude (2.5 km/s), the intimate contact of liquid Al with amorphous Ni near the interface makes the chemical reaction rate increase rapidly to form a large amount of Ni/Al alloys and enhances the spall strength. Published under an exclusive license by AIP Publishing.2021-10-26T00:27:18ZYoung's seminormal basis vectors and their denominatorsFang, MingLim, Kay JinTan, Kai Menghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591112021-10-26T00:27:18Z2021-10-26T00:27:18ZTitle: Young's seminormal basis vectors and their denominators
Authors: Fang, Ming; Lim, Kay Jin; Tan, Kai Meng
Description: We study Young's seminormal basis vectors of the dual Specht modules of the symmetric group, indexed by a certain class of standard tableaux, and their denominators. These vectors include those whose denominators control the splitting of the canonical morphism Delta(lambda+mu) -> Delta(lambda)circle times Delta(mu) over Z((p)), where Delta(nu) is the Weyl module of the classical Schur algebra labelled by nu. (C) 2021 Elsevier Inc. All rights reserved.2021-10-26T00:27:18ZAdaptive Tracking Control of FIR Systems Under Binary-Valued Observations and Recursive Projection IdentificationWang, TingHu, MinZhao, Yanlonghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/590992021-10-26T00:27:17Z2021-10-26T00:27:17ZTitle: Adaptive Tracking Control of FIR Systems Under Binary-Valued Observations and Recursive Projection Identification
Authors: Wang, Ting; Hu, Min; Zhao, Yanlong
Description: In this article, adaptive tracking control of finite impulse response (FIR) systems is studied with binary-valued measurements. An adaptive control strategy is proposed based on an online identification algorithm. First, the designed control inputs are proved to be bounded and satisfy a persistent excitation (PE) condition under the assumption of periodic and PE target signals, which ensures the convergence of the identification algorithm. Second, the convergence rate of the identification algorithm is proved to be O(1/t) and it depends on the true parameter instead of a priori information of the parameter, which is more intuitive. Due to the convergence and the convergence rate of the identification algorithm, we finally prove that the adaptive tracking control is asymptotically optimal and the tracking speed is faster than the previous control algorithm. The simulations are given to validate the developed results in this article.2021-10-26T00:27:17ZExistence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equationCao, DaominQin, GuolinZhan, WeichengZou, Changjunhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591022021-10-26T00:27:17Z2021-10-26T00:27:17ZTitle: Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation
Authors: Cao, Daomin; Qin, Guolin; Zhan, Weicheng; Zou, Changjun
Description: By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and traveling-wave vortex solutions for the gSQG equation, which extends the result of Hmidi and Mateu [28] to alpha is an element of [1, 2). Moreover, we obtain the C-infinity regularity of vortices boundary and the convexity of each vortices component. (C) 2021 Elsevier Inc. All rights reserved.2021-10-26T00:27:17ZAlmost sure convergence of randomised-difference descent algorithm for stochastic convex optimisationGeng, XiaoxueHuang, GaoZhao, Wenxiaohttp://ir.amss.ac.cn:80/handle/2S8OKBNM/591052021-10-26T00:27:17Z2021-10-26T00:27:17ZTitle: Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation
Authors: Geng, Xiaoxue; Huang, Gao; Zhao, Wenxiao
Description: Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep neural networks, it essentially relies on obtaining the unbiased estimates of gradients/subgradients of the objective functions. In this paper, by constructing the randomised differences of the objective function, a gradient-free algorithm, named the stochastic randomised-difference descent algorithm, is proposed for stochastic convex optimisation. Under the strongly convex assumption of the objective function, it is proved that the estimates generated from stochastic randomised-difference descent converge to the optimal value with probability one, and the convergence rates of both the mean square error of estimates and the regret functions are established. Finally, some numerical examples are prsented.2021-10-26T00:27:17ZStochastic greedy algorithms for maximizing constrained submodular plus supermodular functionsJi, SaiXu, DachuanLi, MinWang, YishuiZhang, Dongmeihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/590932021-10-26T00:27:16Z2021-10-26T00:27:16ZTitle: Stochastic greedy algorithms for maximizing constrained submodular plus supermodular functions
Authors: Ji, Sai; Xu, Dachuan; Li, Min; Wang, Yishui; Zhang, Dongmei
Description: The problem of maximizing the sum of a constrained submodular and a supermodular function has many applications such as social networks, machine learning, and artificial intelligence. In this article, we study the monotone submodular + supermodular maximization problem under a cardinality constraint and a p-system constraint, respectively. For each problem, we provide a stochastic algorithm and prove the approximation ratio of each algorithm theoretically. Since the algorithm of the latter problem can also solve the former problem, we do some numerical experiments of the two algorithms to compare the time as well as the quality of the two algorithms in solving the former problem.2021-10-26T00:27:16ZWell-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equationsHao, ChengchunLuo, Taohttp://ir.amss.ac.cn:80/handle/2S8OKBNM/590962021-10-26T00:27:16Z2021-10-26T00:27:16ZTitle: Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
Authors: Hao, Chengchun; Luo, Tao
Description: The well-posedness theory is studied for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in Lagrangian coordinates, and substitute it into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, the velocity equation is linearized with respect to the position vector field whose time derivative is the velocity. In this formulation, a key idea is to use the Lie derivative of the magnetic field taking the advantage that the magnetic field is tangential to the free boundary and divergence free. This paper contributes to the program of developing geometric approaches to study the well-posedness of free boundary problems of ideal magnetohydrodynamics equations under the condition of Taylor sign type for general free boundaries not restricted to graphs. (c) 2021 Elsevier Inc. All rights reserved.2021-10-26T00:27:16Z