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Assouad dimensions of Moran sets and Cantor-like sets

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Frontiers of mathematics in China 2016年第3期11卷 705-722页

作者： Wenwen LI Wenxia LI Junjie MIAO Lifeng XI Department of mathematics Ningbo University Ningbo 315211 China School of mathematics and Statistics Fuyang Normal University Fuyang 236037 China Department of mathematics East China Normal University Shanghai 200241 China Shanghai Key lab of PMMP East China Normal University Shanghai 200241 China

We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set introduced in [J. Math. Anal. Appl., 2015, 432：888 917], we also study the Assouad dimensions of Cantor-like sets.

关键词： Fractal Assouad dimension Moran set Cantor-like set

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

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维普期刊数据库

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Acta Mathematica Scientia 2013年第4期33卷 1024-1030页

作者：吴秀兰高文杰 Institute of mathematics Jilin University College of mathematics Jilin Normal University

This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on... 详细信息

关键词： porous medium equation blow-up positive initial energy

Abstract principal component analysis

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Science China mathematics 2013年第12期56卷 2783-2798页

作者： LI TianJiang DU Qiang Department of mathematics The Pennsylvania State University University ParkPA 16802 USA CGG Houston TX 77072 USA lab of Applied mathematics Beijing Computational Science Research Center

We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and *** describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial *** illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.

关键词： abstract principal component analysis pattern recognition mode extraction reduced order mod-eling traveling waves

A peep at knowledge science in a categorical prospect

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Frontiers of Computer Science 2016年第5期10卷 767-768页

作者： Ruqian LU MADIS Key lab Research Center of Network Science Academy of Mathematics and Systems Scince Chinese Academy of Sciences Beijing 100190 China

mathematics and structuralism Since a long time ago, scientists have pursued the idea of assigning each object of science with a structure. In the long run of history, this idea got a loud name of ＂structuralism＂ which received most attention from the mathematicians. The best known early work in ＂structural mathematics＂ was done by the Bourbaki School [1]. However, their work was not fully formal, par- tially because they used a semi-formal natural language to explain mathematical structuralism [1]. The invention of cat- egory theory in the forties provides a rigorous framework for structuring the mathematics [2]. It also provides an alterna- tive foundation for mathematics other than the set theory, in particular after the many setbacks the latter has suffered.

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Anti-amyloid antibodies in Alzheimer’s disease: what did clinical trials teach us?

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Neural Regeneration Research 2025年第4期20卷 1092-1093页

作者： Danko Jeremic Lydia Jiménez-Díaz Juan D.Navarro-López NeuroPhysiology&Behavior lab University of Castilla-La ManchaBiomedical Research Center(CRIB)School of Medicine of Ciudad RealCiudad RealSpain

Although many causes of Alzheimer’s disease(AD)may exist,both the original amyloid cascade and tau hypotheses posit that abnormal misfolding and accumulation of amyloid-β(Aβ)and tau protein is the central event causing the ***,that conclusion could be only partly true,and there is conflicting evidence about the role of both proteins in AD,being able to precede and influence one *** researchers argue that these proteins are mere executors rather than primary causes of ***,there have been continuing refinements of both hypotheses,with alternative explanations proposed.Aβand tau proteins may be independently involved in specific neurotoxic pathways;yet there may be other crucial processes going on in early ***,accumulating evidence suggests that Aβand tau act synergistically,rather than additively in disease onset(Jeremic et al.,2021,2023a).

关键词： amyloid Alzheimer additive

Linear Time Algorithms for Parallel Machine Scheduling

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Acta Mathematica Sinica,English Series 2007年第1期23卷 137-146页

作者： Zhi Yi TAN Yong HE Department of mathematics State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 P. R. China Department of mathematics Zhejiang University Hangzhou 310027 P. R. China

This paper addresses linear time algorithms for parallel machine scheduling problems. We introduce a kind of threshold algorithms and discuss their main features. Three linear time threshold algorithm classes DT, PT and DTm are studied thoroughly. For all classes, we study their best possible algorithms among each class. We also present their application to several scheduling problems, The new algorithms are better than classical algorithms in time complexity and/or worst-case ratio. Computer-aided proof technique is used in the proof of main results, which greatly simplifies the proof and decreases case by case analysis.

关键词： scheduling design and analysis of algorithm worst-case ratio computer-aided proof

The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1804-1824页

作者： Qi Rong DENG Xing Gang HE Ming Tian LI Yuan Ling YE School of mathematics and Statistics Center for Applied Mathematics of Fujian Province&Key Laboratory of Analytical Mathematics and Applications(Ministry of Education)Fujian Normal UniversityFuzhou350117P.R.China School of mathematics and Statistics Key Lab NAA-MOE and Hubei Key Lab-Math.Sci.Central China Normal UniversityWuhan430079P.R.China School of Mathematical Sciences&South China Research Center for Applied mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou510631P.R.China

Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski *** prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).

关键词： Moran-Sierpinski measures orthonormal basis of exponential functions self-affine measures spectral measures

Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma

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Chinese Physics B 2017年第9期26卷 301-309页

作者： M S Alam M G Hafez M R Talukder M Hossain Ali Department of Applied mathematics University of RajshahiRajshahi-6205Bangladesh Plasma Science and Technology lab Department of Applied Physics and Electronic EngineeringUniversity of RajshahiRajshahi-6205Bangladesh Department of mathematics Chittagong University of Engineering and TechnologyChittagong-4349Bangladesh

This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo（PLK） method is employed to derive the two-sided Korteweg–de Vries（KdV） equations with their corresponding phase shifts. The nonlinear Schrodinger equation（NLSE） is obtained from the modified Kd V（mKdV） equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.

关键词： wave-wave interaction rogue waves degenerate plasmas Bohm potential

Biquadratic tensors,biquadratic decompositions,and norms of biquadratic tensors

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Frontiers of mathematics in China 2021年第1期16卷 171-185页

作者： Liqun QI Shenglong HU Xinzhen ZHANG Yanwei XU Huawei Theory Research lab Hong KongChina Department of mathematics School of ScienceHangzhou Dianzi UniversityHangzhou310018China Department of Applied mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina School of mathematics Tianjin UniversityTianjin300354China

Biquadratic tensors play a central role in many areas of *** include elastic tensor and Eshelby tensor in solid mechanics,and Riemannian curvature tensor in relativity *** singular values and spectral norm of a general third order tensor are the square roots of the M-eigenvalues and spectral norm of a biquadratic tensor,*** tensor product operation is closed for biquadratic *** of these motivate us to study biquadratic tensors,biquadratic decomposition,and norms of biquadratic *** show that the spectral norm and nuclear norm for a biquadratic tensor may be computed by using its biquadratic ***,either the number of variables is reduced,or the feasible region can be *** show constructively that for a biquadratic tensor,a biquadratic rank-one decomposition always exists,and show that the biquadratic rank of a biquadratic tensor is preserved under an independent biquadratic Tucker *** present a lower bound and an upper bound of the nuclear norm of a biquadratic ***,we define invertible biquadratic tensors,and present a lower bound for the product of the nuclear norms of an invertible biquadratic tensor and its inverse,and a lower bound for the product of the nuclear norm of an invertible biquadratic tensor,and the spectral norm of its inverse.

关键词： Biquadratic tensor nuclear norm tensor product biquadratic rank-one decomposition biquadratic Tucker decomposition