• Title/Summary/Keyword: Generalized Inverse

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Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

  • Xiang, Ping;Wu, Minger;Zhou, Rui Q.
    • Structural Engineering and Mechanics
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    • v.54 no.6
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    • pp.1153-1174
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    • 2015
  • Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

Analytical Method for Constrained Mechanical and Structural Systems

  • Eun, Hee-Chang;Park, Sang-Yeol;Lee, Eun-Taik;Chung, Heon-Soo
    • Journal of Mechanical Science and Technology
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    • v.18 no.10
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    • pp.1691-1699
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    • 2004
  • The objective of this study is to present an accurate and simple method to describe the motion of constrained mechanical or structural systems. The proposed method is an elimination method to require less effort in computing Moore-Penrose inverse matrix than the generalized inverse method provided by Udwadia and Kalaba. Considering that the results by numerical integration of the derived second-order differential equation to describe constrained motion veer away the constrained trajectories, this study presents a numerical integration scheme to obtain more accurate results. Applications of holonomically or nonholonomically constrained systems illustrate the validity and effectiveness of the proposed method.

Searching for the Steady State of Unstable Link Structures by using Reduced Dimension Technique (차원 저감화기법을 이용한 불안정 링크구조물의 안정경로 탐색)

  • Kim, Jae-Yeol
    • Journal of Korean Association for Spatial Structures
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    • v.4 no.1 s.11
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    • pp.39-48
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    • 2004
  • Generally, a structural system with large inextensional deformations, or in other words, non-strained deformation is called as 'Unstable Structure', Truss-linked structures, cable structures, membrane structures and movable structures as foldable space structures etc, are included in this category. In this paper, a dynamic analysis method for unstable structural systems is presented. Governing equations for dynamic analysis of unstable truss structures with inextensional displacements are derived. Because of singularity of inverse matrixin in practical analysis of unstable structure, the generalized inverse matrix is Introduced to resolve the singular problem. Also, the RREF technique is used to get the inextensional displacement mode. Two unstable truss structures are analyzed by using presented method. Damping is not considered. From the given results, it is known that proposed method is useful to figure out the dynamic behavior of unstable truss structures.

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A selective review of nonlinear sufficient dimension reduction

  • Sehun Jang;Jun Song
    • Communications for Statistical Applications and Methods
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    • v.31 no.2
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    • pp.247-262
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    • 2024
  • In this paper, we explore nonlinear sufficient dimension reduction (SDR) methods, with a primary focus on establishing a foundational framework that integrates various nonlinear SDR methods. We illustrate the generalized sliced inverse regression (GSIR) and the generalized sliced average variance estimation (GSAVE) which are fitted by the framework. Further, we delve into nonlinear extensions of inverse moments through the kernel trick, specifically examining the kernel sliced inverse regression (KSIR) and kernel canonical correlation analysis (KCCA), and explore their relationships within the established framework. We also briefly explain the nonlinear SDR for functional data. In addition, we present practical aspects such as algorithmic implementations. This paper concludes with remarks on the dimensionality problem of the target function class.

PROPERTIES OF GENERALIZED BIPRODUCT HOPF ALGEBRAS

  • Park, Junseok;Kim, Wansoon
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.323-333
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    • 2010
  • The biproduct bialgebra has been generalized to generalized biproduct bialgebra $B{\times}^L_H\;D$ in [5]. Let (D, B) be an admissible pair and let D be a bialgebra. We show that if generalized biproduct bialgebra $B{\times}^L_H\;D$ is a Hopf algebra with antipode s, then D is a Hopf algebra and the identity $id_B$ has an inverse in the convolution algebra $Hom_k$(B, B). We show that if D is a Hopf algebra with antipode $s_D$ and $s_B$ in $Hom_k$(B, B) is an inverse of $id_B$ then $B{\times}^L_H\;D$ is a Hopf algebra with antipode s described by $s(b{\times}^L_H\;d)={\Sigma}(1_B{\times}^L_H\;s_D(b_{-1}{\cdot}d))(s_B(b_0){\times}^L_H\;1_D)$. We show that the mapping system $B{\leftrightarrows}^{{\Pi}_B}_{j_B}\;B{\times}^L_H\;D{\rightleftarrows}^{{\pi}_D}_{i_D}\;D$ (where $j_B$ and $i_D$ are the canonical inclusions, ${\Pi}_B$ and ${\pi}_D$ are the canonical coalgebra projections) characterizes $B{\times}^L_H\;D$. These generalize the corresponding results in [6].

ON THE GENERALIZED ORNSTEIN-UHLENBECK OPERATORS WITH REGULAR AND SINGULAR POTENTIALS IN WEIGHTED Lp-SPACES

  • Imen Metoui
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.149-160
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    • 2024
  • In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials AΦ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|-2 with a suitable domain generates a quasi-contractive, positive and analytic C0-semigroup in Lp(ℝN , e-Φ(x)dx), 1 < p < ∞. The proofs are based on an Lp-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

THE APPLICATIONS OF ADDITIVE MAP PRESERVING IDEMPOTENCE IN GENERALIZED INVERSE

  • Yao, Hongmei;Fan, Zhaobin;Tang, Jiapei
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.541-547
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    • 2008
  • Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.

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A Study on the Shape Analysis Method of Plane Truss Structures under the Prescribed Displacement (변위제약을 받는 평면트러스 구조물의 형태해석기법에 관한 연구)

  • 문창훈;한상을
    • Computational Structural Engineering
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    • v.11 no.1
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    • pp.217-226
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    • 1998
  • The purpose of this study is to develop a technique for the shape analysis of plane truss structures under prescribed displacement modes. The shape analysis is performed based on the existence theorem of the solution and the Moore-Penrose generalized inverse matrix. In this paper, the homologous deformation of structures was proposed as prescribed displacement modes, the shape of the structure is determined from these various modes and applied loads. In general, the shape analysis is a kind of inverse problem different from stress analysis, and the governing equation becomes nonlinear. In this regard, Newton-Raphson method was used to solve the nonlinear equation. Three different shape models are investigated as numerical examples to show the accuracy and the effectiveness of the proposed method.

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A study on the multivariate sliced inverse regression (다변량 분할 역회귀모형에 관한 연구)

  • 이용구;이덕기
    • The Korean Journal of Applied Statistics
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    • v.10 no.2
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    • pp.293-308
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    • 1997
  • Sliced inverse regression is a method for reducing the dimension of the explanatory variable X without going through any parametric or nonparametric model fitting process. This method explores the simplicity of the inverse view of regression; that is, instead of regressing the univariate output varable y against the multivariate X, we regress X against y. In this article, we propose bivariate sliced inverse regression, whose method regress the multivariate X against the bivariate output variables $y_1, Y_2$. Bivariate sliced inverse regression estimates the e.d.r. directions of satisfying two generalized regression model simultaneously. For the application of bivariate sliced inverse regression, we decompose the output variable y into two variables, one variable y gained by projecting the output variable y onto the column space of X and the other variable r through projecting the output variable y onto the space orthogonal to the column space of X, respectively and then estimate the e.d.r. directions of the generalized regression model by utilize two variables simultaneously. As a result, bivariate sliced inverse regression of considering the variable y and r simultaneously estimates the e.d.r. directions efficiently and steadily when the regression model is linear, quadratic and nonlinear, respectively.

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