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Distributional Dimension of Fractal Sets in Local Fields

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Acta Mathematica Sinica,English Series 2008年第1期24卷 147-158页

作者： Hua QIU wei yi su Department of Mathematics Nanjing University Nanjing 210093 P. R. China

The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension

关键词： local field B-type space F-type space distributional dimension Hausdorff dimension,Fourier dimension

Fractal Dimensions of Fractional Integral of Continuous Functions

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Acta Mathematica Sinica,English Series 2016年第12期32卷 1494-1508页

作者： Yong Shun LIANG wei yi su Institute of Science Nanjing University of Science and Technology Department of Mathematics Nanjing University

In this paper, we mainly explore fractal dimensions of fractional calculus of continuous functions defined on closed intervals. Riemann-Liouville integral of a continuous function f（x） of order v（v 〉 0） which is written as D-Vf（x） has been proved to still be continuous and bounded. Furthermore, upper box dimension of D-v f（x） is no more than 2 and lower box dimension of D-v f（x） is no less than 1. If f（x） is a Lipshciz function, D-v f（x） also is a Lipshciz function. While f（x） is differentiable on [0, 1], D-v f（x） is differentiable on [0, 1] too. With definition of upper box dimension and further calculation, we get upper bound of upper box dimension of Riemann-Liouville fractional integral of any continuous functions including fractal functions. If a continuous function f（x） satisfying HSlder condition, upper box dimension of Riemann-Liouville fractional integral of f（x） seems no more than upper box dimension of f（x）. Appeal to auxiliary functions, we have proved an important conclusion that upper box dimension of Riemann-Liouville integral of a continuous function satisfying HSlder condition of order v（v 〉 0） is strictly less than 2 - v. Riemann-Liouville fractional derivative of certain continuous functions have been discussed elementary. Fractional dimensions of Weyl-Marchaud fractional derivative of certain continuous functions have been estimated.

关键词： Holder condition fractional calculus fractal dimension bound variation

Two-dimensional Wave Equations with Fractal Boundaries

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Acta Mathematica Sinica,English Series 2013年第12期29卷 2321-2342页

作者： Lin Tao MA wei yi su Department of Mathematics Nanjing University College of Mathematical Sciences Guangxi Normal University

This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, differentiable nowhere in its domain. Next, for specific given initial position and 3 different initial velocities, the graphs of solutions are sketched. By computing the box dimensions of boundaries of cross-sections for solution surfaces, we evaluate the range of box dimension of the vibrating membrane. The second case is the equation with p-type derivative. The corresponding solution is shown and numerical example is given.

关键词： Von Koch type curve p-type derivative two-dimensional wave equation fractal boundary fractal dimension

An Endpoint Estimate for the Commutator of Singular Integrals

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1249-1258页

作者： Yong Zhong suN wei yi su Deptartment of Mathematics Nanjing University Nanfing 210093 P. R. China

It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of s... 详细信息

关键词： BMO LMO Commutator Singular integrals

Hausdorff Measure of Homogeneous Cantor Set

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Acta Mathematica Sinica,English Series 2001年第1期17卷 15-20页

作者： Cheng Qin QU Hui RAO wei yi su Department of Mathematics Zhongshan University Department of Mathematics Wuhan University Department of Mathematics Nanjing University

This paper gives the Hausdorff measure of a class of homogeneous Cantor sets.

关键词： Homogeneous cantor set Hausdorff measure Convexity

The Fractional Derivatives of a Fractal Function

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Acta Mathematica Sinica,English Series 2006年第3期22卷 719-722页

作者： Kui YAO wei yi su Song Ping ZHOU Department of Mathematics Nanjing University and PLA University of Sci-Tech Department of Mathematics Nanjing University Institute of Mathematics Zhejiang Sci-Tech University

The present paper investigates the fractional derivatives of weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of wei... 详细信息

关键词： weierstrass function fractional derivatives dimensions of graphs of functions

superconducting,Topological,and Transport Properties of Kagome Metals CsTi_(3)Bi_(5)and RbTi_(3)Bi_(5)

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Research 2024年第2期2023卷 753-762页

作者： Xin-wei yi Zheng-wei Liao Jing-Yang You Bo Gu Gang su School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Department of Physics Faculty of ScienceNational University of Singapore117551Singapore Kavli Institute for Theoretical Sciences and CAS Center for Excellence in Topological Quantum ComputationUniversity of Chinese Academy of SciencesBeijing 100190China

The recently discovered ATi_(3)Bi_(5)(A=Cs,Rb)exhibit intriguing quantum phenomena including superconductivity,electronic nematicity,and abundant topological ***_(3)Bi_(5)present promising platforms for studying kagome superconductivity,band topology,and charge orders in parallel with *** this work,we comprehensively analyze various properties of ATi_(3)Bi_(5)covering superconductivity under pressure and doping,band topology under pressure,thermal conductivity,heat capacity,electrical resistance,and spin Hall conductivity(SHC)using first-principles *** superconducting transition temperature(Tc)of CsTi_(3)Bi_(5)and RbTi_(3)Bi_(5)at ambient pressure are about 1.85 and 1.92 *** subject to pressure,Tc of CsTi_(3)Bi_(5)exhibits a special valley and dome shape,which arises from quasi-two-dimensional compression to three-dimensional isotropic compression within the context of an overall decreasing ***,Tc of RbTi_(3)Bi_(5)can be effectively enhanced up to 3.09 K by tuning the kagome van Hove singularities(VHSs)and flat band through *** can also induce abundant topological surface states at the Fermi energy(EF)and tune VHSs across ***,our transport calculations are in excellent agreement with recent experiments,confirming the absence of charge density ***,SHC of CsTi_(3)Bi_(5)can reach up to 226h·(e·Ω·cm)^(-1)at *** work provides a timely and detailed analysis of the rich physical properties for ATi_(3)Bi_(5),offering valuable insights for further experimental verifications and investigations in this field.

关键词： doping superconductivity conductivity

Applications of Markov spectra for the weighted partition network by the substitution rule

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Communications in Theoretical Physics 2020年第5期72卷 105-112页

作者： Mei-Feng Dai Ting-Ting Ju Yong-Bo Hou Fang Huang Dong-Lei Tang wei-yi su Institute of Applied System Analysis Jiangsu UniversityZhenjiang212013China School of Mathematics and Statistics Nanjing Audit UniversityNanjing211815China Department of Mathematics Nanjing UniversityNanjing210093China

The weighted self-similar network is introduced in an iterative *** order to understand the topological properties of the self-similar network,we have done a lot of research in this ***,according to the symmetry feature of the self-similar network,we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted ***,we obtain eigenvalues of the Laplacian matrix from these two successive ***,we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.

关键词： weighted self-similar network Laplacian matrix eigentime identity Kirchhoff index substitution rule

Hybrid Block Diagonalization Precoding for Multi-User weighted sum-Rate Maximization

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China Communications 2024年第8期21卷 127-141页

作者： su Xiaofeng Jiang yi Key Laboratory for Information Science of Electromagnetic Waves(MoE) Department of Communication Science and EngineeringFudan UniversityShanghai 200433China

This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with *** develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders *** the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the *** the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent *** results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.

关键词： block-diagonal gradient descent hybrid precoding iterative optimization MIMO-OFDM multi-user water-filling power allocation weighted sum-rate maximization