Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)...Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.展开更多
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
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
Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage...Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage transformer errors, particularly minor variations in multi-channel setups, remains challenging. This paper proposes a method for online error tracking of multi-channel capacitive voltage transformers using a Co-Prediction Matrix. The approach leverages the strong correlation between in-phase channels, particularly the invariance of the signal proportions among them. By establishing a co-prediction matrix based on these proportional relationships, The influence of voltage changes on the primary measurements is mitigated. Analyzing the relationships between the co-prediction matrices over time allows for inferring true measurement errors. Experimental validation with real-world data confirms the effectiveness of the method, demonstrating its capability to continuously track capacitive voltage transformer measurement errors online with precision over extended durations.展开更多
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
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
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
A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical...A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.展开更多
A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical im...A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.展开更多
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
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
The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twent...The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twenty-six rats were randomly divided into control group (C, n=8), diabetic group (D, n=9), and diabetes+heparin group (DH, n=9). After 8-week therapy of heparin (200 U once daily by abdominal injection), TGF-β 1, LN and FN expression in glomeruli was detected by immunohistochemical method. The results showed that the expression levels of TGF-β 1, LN and FN were higher in group D than in group C. It was found that heparin could reduce 24-h urinary albumin excretion and inhibit overexpression of TGF-β 1, LN and FN in glomeruli of diabetic rats. It suggested that the inhibitory effect of heparin on diabetic glomerular sclerosis was at least partly related with the inhibition of TGF-β 1 expression.展开更多
Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the ...Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))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 l_(p)-norm of the matrix A^(ru)and 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 l_(p)(A^(ru)).展开更多
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
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
文摘Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
基金NationalKeyLabofBroadBandFiberTransmissionandCommunicatonSystemTechnology ElectronicUniversityofScienceandTechnology China
文摘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.
基金Supported by Natural Science Foundations of China (11101108, 11171301, 10771191 and 10471124)Natural Science Foundation of Zhejiang Province of China (Y6090105)
文摘Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.
文摘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.
文摘Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage transformer errors, particularly minor variations in multi-channel setups, remains challenging. This paper proposes a method for online error tracking of multi-channel capacitive voltage transformers using a Co-Prediction Matrix. The approach leverages the strong correlation between in-phase channels, particularly the invariance of the signal proportions among them. By establishing a co-prediction matrix based on these proportional relationships, The influence of voltage changes on the primary measurements is mitigated. Analyzing the relationships between the co-prediction matrices over time allows for inferring true measurement errors. Experimental validation with real-world data confirms the effectiveness of the method, demonstrating its capability to continuously track capacitive voltage transformer measurement errors online with precision over extended durations.
基金the German DAAD Foundation(German Academic Exchange Service)Grant No.911 103 012 8the Research Project #1232 of the Serbian Ministry of Science,Technology and Development
文摘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.
基金National Natural Science Foundation of China(No.51275486)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20111420110005)
文摘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.
基金supported by the Key Natural Science Research of Guangdong Province,China P.R(Grant No.05Z003)the Project of Tackling Key Problem of Guangdong Province,China P.R(Grant No.2006B12401008)the National Natural Science Foundation of China(Grant No.10672067).
文摘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.
文摘A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.
文摘A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.
文摘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.
基金Supported by National Science Foundation of China(No.60904070,61272032)the Natural Science Foundation of Zhejiang Province(No.LY12F02002,Y1111101)
文摘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.
文摘The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twenty-six rats were randomly divided into control group (C, n=8), diabetic group (D, n=9), and diabetes+heparin group (DH, n=9). After 8-week therapy of heparin (200 U once daily by abdominal injection), TGF-β 1, LN and FN expression in glomeruli was detected by immunohistochemical method. The results showed that the expression levels of TGF-β 1, LN and FN were higher in group D than in group C. It was found that heparin could reduce 24-h urinary albumin excretion and inhibit overexpression of TGF-β 1, LN and FN in glomeruli of diabetic rats. It suggested that the inhibitory effect of heparin on diabetic glomerular sclerosis was at least partly related with the inhibition of TGF-β 1 expression.
文摘Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))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 l_(p)-norm of the matrix A^(ru)and 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 l_(p)(A^(ru)).
文摘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.
