A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

Wandering vector multipliers for unitary groups

A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself. A special case of unitary system is a discrete unitary group. We prove that for many (and perhaps all) discrete unitary groups, the set of wandering vector multipliers is itself a group. We completely characterize the wandering vector multipliers for abelian and ICC unitary groups. Some characterizations of special wandering vector multipliers are obtained for other cases. In particular, there are simple characterizations for diagonal and permutation wandering vector multipliers. Similar results remain valid for irrational rotation unitary systems. We also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups. There are applications to wavelet systems.

     

Inhomogeneous discrete calderón reproducing formulas for spaces of homogeneous type

In this article a Littlewood-Paley theorem for a new kind of Littlewood-Paley g-functions over spaces of homogeneous type is presented. Based on it the authors establish inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous type, making use of Calderón-Zygmund operators.     

Exact Penalty Functions for Convex Bilevel Programming Problems

In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given.     

Error estimates for the finite element approximation of linear elastic equations in an unbounded domain

In this paper we present error estimates for the finite element approximation of linear elastic equations in an unbounded domain. The finite element approximation is formulated on a bounded computational domain using a nonlocal approximate artificial boundary condition or a local one. In fact there are a family of nonlocal approximate boundary conditions with increasing accuracy (and computational cost) and a family of local ones for a given artificial boundary. Our error estimates show how the errors of the finite element approximations depend on the mesh size, the terms used in the approximate artificial boundary condition, and the location of the artificial boundary. A numerical example for Navier equations outside a circle in the plane is presented. Numerical results demonstrate the performance of our error estimates.

     

关于Z4-线性码C4(m，D)的一点注记

本文首先给出了Z4-线性码C4(m,D)的一个大的自同构子群.然后,利用该自同构子群得到了C4(m,6)当m为奇数时的Lee重量分布的一个约化公式.最后,利用该约化公式及计算机搜索得到C4(7,6)的Lee重量分布.C4(7,6)经Gray映射后得的二元非线性码与最优二元线性码[256,37,92]有相同的参数.     

Goldstein, Levitin-Polyak投影法中的一个可行步长准则

１引　言设Ω是Ｒｎ空间的一个非空的凸闭紧子集,Ｆ是Ｒｎ→Ｒｎ的算子．我们考虑变分不等式问题： 变分不等式问题在数学规划中起着很重要的作用,因此,长期以来一直受到广泛的重视．求解变分不等式问题的方法中,有一类投影迭代方法,例如［１,４,６,９］．在所有的投影迭代方法中,Ｇｏｌｄｓｔｅｉｎ［６］,Ｌｅｖｉｔｉｎ－Ｐｏｌｙａｋ［９］所提出的方法;是最简单的．这里,ＰΩ（ｘ）是ｘ在　上的投影,即　的唯一解． 我们称算子Ｆ在集合Ω上是单调的,若在用Ｇｏｌｄｓｔｅｉｎ,Ｌｅｖｉｔｉｎ－Ｐｏｌｙａｋ方法（２）求…     

A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L^∞(L²) for velocity and concentration and the super convergence in L^∞(H¹) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.