We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry.A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed t...We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry.A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed to solve the ensuing nonlinear minimization problem.Γ−convergence of the Specht triangle discretization and the unconditional stability of the gradient flow algorithm are proved.We present several numerical examples to demonstrate that our approach significantly enhances both the computational efficiency and accuracy.展开更多
We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best firs...We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending element.The convergence result is proved under minimal smoothness assumption on the solution.Numerical results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.展开更多
We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate)...We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link bet ween a certain C-basis for the induced Specht module and the notion of pairs of partitions.展开更多
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
In this note, we point out that two generalized conforming triangular plate elements, namely GCⅢ-T9 and GCⅡ-T9, proposed in references [2] and [4], are identical to the familiar Specht element[3]. Moreover, another ...In this note, we point out that two generalized conforming triangular plate elements, namely GCⅢ-T9 and GCⅡ-T9, proposed in references [2] and [4], are identical to the familiar Specht element[3]. Moreover, another generalized conformingelement in reference [6] is proved to be equivalent to VZ1 element in [8].展开更多
This is a continuation of our previous work. We classify all the simple q (Dn) - modulesvia an automorphismh defined on the set t λ ｜ ≠ 0 }. When fn (q) ≠ 0, this yields a classification of all the simple q(Dn)-m...This is a continuation of our previous work. We classify all the simple q (Dn) - modulesvia an automorphismh defined on the set t λ ｜ ≠ 0 }. When fn (q) ≠ 0, this yields a classification of all the simple q(Dn)-modules for arbitrary n. In general (i.e., q arbitrary), ifλ(1) = λ(2), we give a necessary and sufficient condition (in terms of some polynomials) to ensure that the irreducible q.1( Bn)- module Dλ remains irreducible on restriction to .q(Dn).展开更多
基金supported by National Natural Science Foundation of China through Grants No.11971467 and No.12371438.
文摘We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry.A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed to solve the ensuing nonlinear minimization problem.Γ−convergence of the Specht triangle discretization and the unconditional stability of the gradient flow algorithm are proved.We present several numerical examples to demonstrate that our approach significantly enhances both the computational efficiency and accuracy.
基金The work of Li was supported by Science Challenge Project,No.TZ2016003The work of Ming was partially supported by the National Natural Science Foundation of China for Distinguished Young Scholars 11425106+2 种基金National Natural Science Foundation of China grants 91630313by the support of CAS NCMISThe work of Shi was partially supported by the National Natural Science Foundation of China grant 11371359.
文摘We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending element.The convergence result is proved under minimal smoothness assumption on the solution.Numerical results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.
文摘We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link bet ween a certain C-basis for the induced Specht module and the notion of pairs of partitions.
文摘This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
文摘In this note, we point out that two generalized conforming triangular plate elements, namely GCⅢ-T9 and GCⅡ-T9, proposed in references [2] and [4], are identical to the familiar Specht element[3]. Moreover, another generalized conformingelement in reference [6] is proved to be equivalent to VZ1 element in [8].
基金the Tianyuan Math. Foundation of China (Grant No. TY10126011) the China Post-doctoral Science Foundation given to the first author.
文摘This is a continuation of our previous work. We classify all the simple q (Dn) - modulesvia an automorphismh defined on the set t λ ｜ ≠ 0 }. When fn (q) ≠ 0, this yields a classification of all the simple q(Dn)-modules for arbitrary n. In general (i.e., q arbitrary), ifλ(1) = λ(2), we give a necessary and sufficient condition (in terms of some polynomials) to ensure that the irreducible q.1( Bn)- module Dλ remains irreducible on restriction to .q(Dn).
