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HAUSDORFF DIMENSION OF RECURRENCE SETS FOR MATRIX TRANSFORMATIONS OF TORI 认领 引用
1
作者 Zhangnan HU Bing LI 《Acta Mathematica Scientia》 SCIE CSCD 2025年第4期1659-1673,共15页
Let T:Td→Td,defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ1|≤|λ2|≤…≤|λd|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈Td:Tn... Let T:Td→Td,defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ1|≤|λ2|≤…≤|λd|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈Td:Tnx∈B(x,ψ(n))for infinitely many n}forα≥log|λd/λ1|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim infn→∞-logψ(n).In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula. 展开更多
关键词 quantitative recurrence properties Hausdorff dimension matrix transformations
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Matrix transformations of l^q(X) to l^p(Y ) 认领 引用
2
作者 GUO Hao LI Rong-lu WU Jun-de 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第1期78-86,共9页
Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.
关键词 matrix transformation, sequence space demi-linear mapping.
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Determination of Transmission Routing of OXC Nodes Based on AWG Multiplexer by Matrix Transformation 认领 引用 被引量：1
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作者 GUOAi-huang FUJun-mei 《Semiconductor Photonics and Technology》 2004年第1期1-4,7,共4页
The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relatio... The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relation between the input and output wavelengths of the AWG multiplexer, the wavelength transmission routings of the space switching and wavelength switching OXC nodes are determined. 展开更多
关键词 AWG multiplexer OXC nodes Matrix transformation Wavelength transmission routing
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Research on the Applications of Probability Model and Matrix Transformation in Data Analysis and Management under the Environment of Information Time 认领 引用
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作者 Ying Cao 《International Journal of Technology Management》 2015年第7期152-154,共3页
In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the import... In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic. 展开更多
关键词 Probability Model Matrix Transformation Data Analysis and Management.
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Virtual polarization elements for spatially programmable Jones matrix transformations on a free-space plane 认领 引用
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作者 MINGYUE WANG JIAYUAN WANG 《Photonics Research》 SCIE EI CAS CSCD 2025年第11期I0020-I0031,共12页
Precise control over light's spatial and polarization characteristics is essential for advanced photonic systems,yet most conventional approaches are constrained to local, contact-based manipulation at physical in... Precise control over light's spatial and polarization characteristics is essential for advanced photonic systems,yet most conventional approaches are constrained to local, contact-based manipulation at physical interfaces.To overcome these constraints, here we introduce a fundamentally new framework for action-at-a-distance polarization control using virtual polarization elements(VPEs). VPEs apply prescribed local Jones matrix transformations between an input field at the modulation plane and an output field at a remote, contactless free-space plane,enabling programmable polarization operations without local material interaction. We demonstrate this concept using metasurface-based VPEs that realize diverse functionalities: single-function VPEs implementing circular polarizer, linear polarizer, half-wave plate, and quarter-wave plate operations;a multi-function VPE simultaneously encoding spatially distinct Jones matrices with arbitrary relative phase differences;and vortex wave plate configurations for generating vector vortex beams. Furthermore, we extend the VPE platform to synthesize Stokes skyrmions-topologically nontrivial vectorial fields-on a remote plane, including multi-skyrmion integration and polarization-controlled switching. By decoupling the modulation and target planes, VPEs open new opportunities for remote polarization shaping, non-invasive beam engineering, and topological light field synthesis. 展开更多
关键词 spatially programmable Jones matrix transformations advanced photonic systemsyet input field virtual polarization elements vpes vpes free space plane metasurface based vpes virtual polarization elements prescribed local jones matrix transforma tions
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The Dual Spaces of Sets of Difference Sequences of Order m and Matrix Transformations 认领 引用 被引量：4
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作者 Eberhard MALKOWSKY M.MURSALEEN Suthep SUANTAI 《Acta Mathematica Sinica,English Series》 SCIE 2007年第3期521-532,共12页
Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order dif... Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X. 展开更多
关键词 difference sequences dual spaces matrix transformations
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Error modeling of 3-RSR parallel robot based on D-H transformation matrix 认领 引用 被引量：4
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作者 李瑞琴 杨斌 《Journal of Measurement Science and Instrumentation》 CAS 2014年第3期53-59,2,共7页
By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （... By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation. 展开更多
关键词 error modeling 3-RSR parallel robot Denavit-Hartenberg （D-H） transformation matrix
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Orthogonalization of unified and extended Bézier basis and its transformation matrix 认领 引用
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作者 FANG Meie JI Zhongping WANG Guozhao 《Computer Aided Drafting,Design and Manufacturing》 2013年第1期41-46,共6页
UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brz... UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved. 展开更多
关键词 UE-B6zier basis orthogonalization legendre basis transformation matrix
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Transformation Matrix for Combined Loads Applied to Thin-Walled Structures 认领 引用 被引量：1
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作者 Abdelraouf M. Sami Alsheikh David William Alan Rees 《World Journal of Mechanics》 2022年第6期65-78,共14页
This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with... This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load. 展开更多
关键词 Thin-Walled Structure Open Sections Transformation Matrix Load Transformation Combined Load Transformation Shear Centre Warping Bimoment Sectorial Area Properties
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Generalized Euler-Riesz difference sequence space with a paranormed fractional ordered µ 认领 引用
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作者 Munevver Tuz Cigdem Asma Bektas 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第1期214-224,共11页
In this study,we introduce the sequence space lμ(p,Δm) with a fractional order μ.Furthermore,we give some topological properties of this space.Also we introduce α-,β-,andγ-duals of lμ(p,Δm) and its... In this study,we introduce the sequence space lμ(p,Δm) with a fractional order μ.Furthermore,we give some topological properties of this space.Also we introduce α-,β-,andγ-duals of lμ(p,Δm) and its some matrix mappings. 展开更多
关键词 Euler-Riesz sequence space difference sequence space paranorm α-β-andγ-duals matrix transformations
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Discrete Fourier Transformation Matrix for Global Sensitivity Analysis in Probabilistic Optimal Power Flow Calculation 认领 引用
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作者 Xingyu Lin Junzhou Wang +3 位作者 Junjie Tang Ferdinanda Ponci Antonello Monti Wenyuan Li 《CSEE Journal of Power and Energy Systems》 SCIE EI CSCD 2026年第3期1194-1207,共14页
The commonly used global sensitivity analysis(GSA)can quantify the influence of random input variables on the variance of target outputs.To avoid the extremely large computational burden of the Monte Carlo simulation ... The commonly used global sensitivity analysis(GSA)can quantify the influence of random input variables on the variance of target outputs.To avoid the extremely large computational burden of the Monte Carlo simulation method(MCSM),a discrete Fourier transformation matrix(DFTM)method is developed for the first time to efficiently tackle the variancebased GSA of transmission systems in the probabilistic optimal power flow(POPF)with correlated random inputs.The proposed DFTM method has a flexible sampling strategy and includes two sub-methods named the discrete sine/cosine transformation matrix(DSTM/DCTM).The superiority of the DFTM in both accuracy and efficiency for the variance-based GSA in POPF is demonstrated by its comparisons with Hong's point estimate method(HPEM),the unscented transformation method(UTM)and the first-order second-moment method(FOSMM).Based on Nataf transformation,it is found through a theoretical derivation in the paper that both HPEM and UTM may lead to a negative variance of output in some cases,which will cause erroneous results of the GSA.In contrast,the proposed DFTM has an immunity to such variance abnormality.The tests and comparisons are implemented on a modified IEEE 118-bus power system,where MCSM is used as a reference for accuracy. 展开更多
关键词 Discrete Fourier transformation matrix global sensitivity analysis Nataf transformation probabilistic optimal power flow variance abnormality
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BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX 认领 引用 被引量：1
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作者 Feyzi BASAR Hadi ROOPAEI 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1518-1536,共19页
Let the triangle matrix Arube a generalization of the Cesàro matrix and U∈{c0,c,l∞}.In this study,we essentially deal with the space U(Aru)defined by the domain of Aruin the space U and give the ... Let the triangle matrix Arube a generalization of the Cesàro matrix and U∈{c0,c,l∞}.In this study,we essentially deal with the space U(Aru)defined by the domain of Aruin the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(Aru).We characterize the classes(l∞(Aru):l∞),(l∞(Aru):c),(c(Aru):c),and(U:V(Aru))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the lp-norm of the matrix Aruand as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain lp(Aru). 展开更多
关键词 matrix domain normed sequence space duals and matrix transformations
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CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS 认领 引用 被引量：1
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作者 陈爱红 李容录 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2285-2294,共10页
In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.
关键词 matrix transformation quasi-homogeneous operator gliding hump property
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CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX 认领 引用 被引量：1
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作者 Weiwei Zhang Zhihua Wang Hongwei Ma 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第4期360-368,共9页
This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the pea... This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible. 展开更多
关键词 crack cantilever beam wavelet transform matrix
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DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r,s) ON SOME MADDOX'S SPACES 认领 引用
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作者 Faruk OZGER Feyzi BASAR 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期394-408,共15页
The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spa... The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spaces L∞（B,p）, c（B,p）, and co（B,p）, which are more general and comprehensive than the corresponding consequences of the matrix domain of B（r, s）, as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces L∞ （B, p）, c（B, p）, and co （B, p） are computed and the bases of the spaces c（B, p） and co （B, p） are constructed. The final section of this article is devoted to the characterization of the classes （λ（B, p）： μ） and （μ：λ（B, p））, where λ ∈ {c, co, L∞ } and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of Mmost convergent sequences is obtained by means of a given lemma. 展开更多
关键词 Matrix domain double sequential band matrices almost convergence para-normed spaces matrix transformations
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ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX 认领 引用
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作者 Murat CANDAN 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期354-366,共13页
The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（... The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space. 展开更多
关键词 Almost convergence matrix domain of a sequence space generalized differencematrix,β- and γ-duals and matrix transformations
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A GROUP REPRESENTATION OF CANONICAL TRANSFORMATION 认领 引用
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作者 侯碧辉 杨洪波 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第4期345-350,共6页
The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got ... The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got with linear transformations from seven basic formulae. All of them are Legendre's transformation, which are implemented by 32 matrices of 8 x 8 which are homomorphic to D-4 point group of 8 elements with correspondence of 4:1. Transformations and relationships of four state functions G(P, T), H(P, S), U(V, S), F(V, T) and four variables P, V, T, S in thermodynamics, are just the same Lagendre's transformations with the relationships of canonical transformations. The state functions of thermodynamics are summarily founded on experimental results of macroscope measurements, and Hamilton's canonical transformations are theoretical generalization of classical mechanics. Both group represents are the same, and it is to say, their mathematical frames are the same. This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation. 展开更多
关键词 canonical transformations group theory group represent transformation matrix
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A Geometric View on Inner Transformation between the Variables of a Linear Regression Model 认领 引用 被引量：1
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作者 Zhaoyang Li Bostjan Antoncic 《Applied Mathematics》 2021年第10期931-938,共8页
In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from... In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating. 展开更多
关键词 Matrix Singular Value Decomposition Moore-Penrose Generalized Inverse Matrix Inner Transformation Regression Analysis
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Two-Point Resistance of a Cobweb Network with a 2r Boundary 认领 引用 被引量：19
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作者 谭志中 方靖淮 《Communications in Theoretical Physics》 SCIE CAS CSCD 2015年第1期36-44,共9页
We consider the problem of the two-point resistance on an m ×n cobweb network with a 2r boundary, which has never been solved before. Up to now researchers just only solved the cases with free boundary or null re... We consider the problem of the two-point resistance on an m ×n cobweb network with a 2r boundary, which has never been solved before. Up to now researchers just only solved the cases with free boundary or null resistor boundary. This paper gives the general formulae of the resistance between any two nodes in both tinite and infinite cases using a method of direct summation pioneered by Tan [Z. Z. Tan, et al., J. Phys. A 46 （2013） 195202], which is simpler and can be easier to use in practice. This method contrasts the Green＇s function technique and the Laplacian matrix approach, which is difllcult to apply to the geometry of a cobweb with a 2r boundary. We deduce several interesting results according to our genera/formula. In the end we compare and illuminate our formulae with two examples. Our analysis gives the result directly as a single summation, and the result is mainly composed of the characteristic roots. 展开更多
关键词 equivalent resistance cobweb model matrix transformation boundary conditions
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On a New Summability Result for Operator Matrices 认领 引用
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作者 崔成日 文松龙 《Northeastern Mathematical Journal》 2006年第2期173-180,共8页
For matrices of quasi-homogeneous operators we establish a summability result which is a useful complement of a recent summability result.
关键词 matrix transformation braked space uniform convergence principle
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