The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Ganna Kudryavtseva - One of the best experts on this subject based on the ideXlab platform.
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Semitransitive subsemigroups of the Singular Part of the finite symmetric inverse semigroup
Acta Mathematica Hungarica, 2011Co-Authors: Karin Cvetko-vah, Damjana Kokol Bukovšek, Tomaž Košir, Ganna KudryavtsevaAbstract:We prove that the minimal cardinality of a semitransitive subsemigroup in the Singular Part $\mathcal{I}_{n}\setminus \mathcal{S}_{n}$ of the symmetric inverse semigroup $\mathcal{I}_{n}$ is 2 n − p +1, where p is the greatest proper divisor of n , and classify all semitransitive subsemigroups of this minimal cardinality.
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Semitransitive subsemigroups of the Singular Part of the finite symmetric inverse semigroup
Acta Mathematica Hungarica, 2011Co-Authors: Karin Cvetko-vah, Tomaž Košir, Damjana Kokol Bukovšek, Ganna KudryavtsevaAbstract:We prove that the minimal cardinality of a semitransitive sub- semigroup in the Singular Part In \S n of the symmetric inverse semigroup In is 2n − p +1 , wherep is the greatest proper divisor of n, and classify all semitran- sitive subsemigroups of this minimal cardinality.
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Semitransitive subsemigroups of the Singular Part of the finite symmetric inverse semigroup
arXiv: Group Theory, 2009Co-Authors: Karin Cvetko-vah, Tomaž Košir, Damjana Kokol Bukovšek, Ganna KudryavtsevaAbstract:We prove that the minimal cardinality of the semitransitive subsemigroup in the Singular Part $\IS_n\setminus \S_n$ of the symmetric inverse semigroup $\IS_n$ is $2n-p+1$, where $p$ is the greatest proper divisor of $n$, and classify all semitransitive subsemigroups of this minimal cardinality.
Andreas Steenpaß - One of the best experts on this subject based on the ideXlab platform.
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The classification of real Singularities using Singular Part III: Unimodal Singularities of corank 2
Journal of Symbolic Computation, 2020Co-Authors: Janko Böhm, Magdaleen S. Marais, Andreas SteenpaßAbstract:Abstract We present a classification algorithm for isolated hypersurface Singularities of corank 2 and modality 1 over the real numbers. For a Singularity given by a polynomial over the rationals, the algorithm determines its stable equivalence class by specifying all representatives in Arnold's list of normal forms ( Arnold et al., 1985 ) belonging to this class, and the corresponding values of the moduli parameter. By specifying, in addition, the inertia index, the right equivalence class of the Singularity is determined. We discuss how to computationally realize the individual steps of the algorithm for all Singularities under consideration, and give explicit examples. The algorithm is implemented in the Singular library realclassify.lib .
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The classification of real Singularities using Singular Part I: Splitting Lemma and simple Singularities
Journal of Symbolic Computation, 2015Co-Authors: Magdaleen S. Marais, Andreas SteenpaßAbstract:We present algorithms to classify isolated hypersurface Singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first Part covers the splitting lemma and the simple Singularities; a second and a third Part will be devoted to the unimodal Singularities up to corank 2. All algorithms are implemented in the Singular library realclassify.lib (Marais and Steenpaß, 2012).http://www.elsevier.com/locate/jsc2016-05-31hb201
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The classification of real Singularities using Singular Part I: Splitting Lemma and simple Singularities
Journal of Symbolic Computation, 2015Co-Authors: Magdaleen S. Marais, Andreas SteenpaßAbstract:We present algorithms to classify isolated hypersurface Singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first Part covers the splitting lemma and the simple Singularities; a second and a third Part will be devoted to the unimodal Singularities up to corank 2. All algorithms are implemented in the Singular library realclassify.lib (Marais and Steenpass, 2012).Comment: 12 pages, 1 tabl
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The classification of real Singularities using Singular. Part II
Journal of Symbolic Computation, 2014Co-Authors: Magdaleen S. Marais, Andreas SteenpaßAbstract:In the classification of real Singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence classes of the unimodal real Singularities of corank 2. In other words, we explicitly answer the question which normal forms of different type are equivalent, and how a normal form can be transformed within the same equivalence class by changing the value of the parameter. This provides new theoretical insights into these Singularities and has important consequences for their algorithmic classification.
Zhilin Han - One of the best experts on this subject based on the ideXlab platform.
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the semi analytical evaluation for nearly Singular integrals in isogeometric elasticity boundary element method
Engineering Analysis With Boundary Elements, 2018Co-Authors: Zhilin Han, Changzheng Cheng, Zhongrong NiuAbstract:Abstract Benefiting from improvement of accuracy in modeling complex geometry and integrity of discretization and simulation, the isogeometric analysis in the boundary element method (IGABEM) has now been implemented by several groups. However, the difficulty of evaluating the nearly Singular integral in IGABEM for elasticity has not yet been effectively solved, which will hinder the application of IGABEM in engineering structure analysis. Herein, the nearly Singular integrals in IGABEM are separated to the non-Singular Part and Singular Part by the subtraction technique. The integral kernels in Singular Part are approximated by the Taylor series polynomial expressions, in which different orders of derivatives are interpolated by the non-uniform rational B-splines (NURBS). Furthermore, the analytical formulations for the Singular Part with the approximated kernels are derived by a series of integration by Parts, while the non-Singular Part is calculated with Gaussian quadrature. In this way, a semi-analytical method is proposed for the nearly Singular integrals in the IGABEM. Comparing with the conventional IGABEM, the present method can yield accurate displacement and stress for inner points much closer to the boundary. It can obtain effective results with fewer elements than the finite element method because of the precise simulation of geometry and boundary-only discretization.
Xianyun Qin - One of the best experts on this subject based on the ideXlab platform.
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new variable transformations for evaluating nearly Singular integrals in 2d boundary element method
Engineering Analysis With Boundary Elements, 2011Co-Authors: Guizhong Xie, Jianming Zhang, Xianyun QinAbstract:This work presents a further development of the distance transformation technique for accurate evaluation of the nearly Singular integrals arising in the 2D boundary element method (BEM). The traditional technique separates the nearly hyperSingular integral into two Parts: a near strong Singular Part and a nearly hyperSingular Part. The near strong Singular Part with the one-ordered distance transformation is evaluated by the standard Gaussian quadrature and the nearly hyperSingular Part still needs to be transformed into an analytical form. In this paper, the distance transformation is performed by four steps in case the source point coincides with the projection point or five steps otherwise. For each step, new transformation is proposed based on the approximate distance function, so that all steps can finally be unified into a uniform formation. With the new formulation, the nearly hyperSingular integral can be dealt with directly and the near Singularity separation and the cumbersome analytical deductions related to a specific fundamental solution are avoided. Numerical examples and comparisons with the existing methods on straight line elements and curved elements demonstrate that our method is accurate and effective.
Zhongrong Niu - One of the best experts on this subject based on the ideXlab platform.
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the semi analytical evaluation for nearly Singular integrals in isogeometric elasticity boundary element method
Engineering Analysis With Boundary Elements, 2018Co-Authors: Zhilin Han, Changzheng Cheng, Zhongrong NiuAbstract:Abstract Benefiting from improvement of accuracy in modeling complex geometry and integrity of discretization and simulation, the isogeometric analysis in the boundary element method (IGABEM) has now been implemented by several groups. However, the difficulty of evaluating the nearly Singular integral in IGABEM for elasticity has not yet been effectively solved, which will hinder the application of IGABEM in engineering structure analysis. Herein, the nearly Singular integrals in IGABEM are separated to the non-Singular Part and Singular Part by the subtraction technique. The integral kernels in Singular Part are approximated by the Taylor series polynomial expressions, in which different orders of derivatives are interpolated by the non-uniform rational B-splines (NURBS). Furthermore, the analytical formulations for the Singular Part with the approximated kernels are derived by a series of integration by Parts, while the non-Singular Part is calculated with Gaussian quadrature. In this way, a semi-analytical method is proposed for the nearly Singular integrals in the IGABEM. Comparing with the conventional IGABEM, the present method can yield accurate displacement and stress for inner points much closer to the boundary. It can obtain effective results with fewer elements than the finite element method because of the precise simulation of geometry and boundary-only discretization.
