带扩散项四阶抛物方程的一类本性并行差分格式

给出逼近带扩散项四阶抛物方程一组非对称差分格式,对此组非对称格式重新组合,得到了一类新的具有并行本性的算法.随后,利用矩阵法证明了算法的绝对稳定性.最后给出数值实验.     

三阶非线性KdV方程的交替分段显-隐差分格式

对三阶非线性KdV方程给出了一组非对称的差分公式,用这些差分公式与显、隐差分公式组合,构造了一类具有本性并行的交替分段显-隐格式A·D2证明了格式的线性绝对稳定性．对1个孤立波解、2个孤立波解的情况分别进行了数值试验．数值结果显示,交替分段显-隐格式稳定,有较高的精确度．     

对流扩散方程的数值计算

本文研究了对流扩散方程的一种并行格式.利用一组saul'yev型非对称格式进行二次构造,分别得到了一类并行GE格式和GEL、GER格式;进一步推广,得到绝对稳定的交替分组显式AGE格式,并用数值例子检验AGE格式的数值计算效果.     

一类三阶非对称实矩阵合同的充要条件

从两个非对称实矩阵合同的定义出发,给出了两个二阶非对称实矩阵合同的判定条件.利用矩阵的计算技巧和待定系数法,将一类三阶非对称实矩阵合同的判定归结于二阶非对称实矩阵的情形,并刻画了两类非对称实矩阵合同的等价关系,最后得出了一类三阶非对称实矩阵合同判定的一个充要条件.     

KdV方程的一类本性并行差分格式

对三阶KdV方程给出了—组非对称的差分公式,并用这些差分公式和对称的Crank-Nicolson型公式构造了一类具有本性并行的交替差分格式．证明了格式的线性绝对稳定性．对—个孤立波解、二个孤立波解和三个孤立波解的情况分别进行了数值试验,并对—个孤立波解的数值解的收敛阶和精确性进行了试验和比较．     

色散方程的一类新的并行交替分段隐格式

本文给出了一组逼近色散方程的非对称差分格式，并用这组格式和对称的Crank-Nicolson型格式构造了求解色散方程的并行交替分段差分隐格式．这个格式是无条件稳定的，能直接在并行计算机上使用．数值试验表明，这个格式有很好的精度．     

四阶抛物方程一类变步长本性并行格式的稳定性分析

本文给出了四阶抛物方程一类变步长的本性并行差分格式,并用发展的能量法给出了该格式的绝对稳定性证明,得到了绝对稳定性估计.     

一类基于非对称偏差的过程能力指数

以基本尺寸为基准,研究非对称偏差下总体质量特性值的分布及过程离散程度,在给出一类非对称分布的基础上,研究基于非对称偏差的过程能力指数,并将其推广到角度质量控制问题。     

一类偏积分微分方程一阶差分全离散格式

本文给出了数值求解一类偏积分微分方程的一阶差分全离散格式。时间方向采用了一阶向后差分格式，空间方向采用二阶差分格式，给出了稳定性的证明，误差估计及收敛性的结果，并给出了数值例子。     

Some Linear Isomorphism Theorems for Certain 2nth-Order Nonsymmetric Differential Operator with Parameter

本文给出了一类带参数２ｎ阶非对称微分算子Ａλ的一些正则性定理，籍此可刻画一类飞行器在其运行过程中的双向平稳行为．     

Abelian and non-abelian Paley type group schemes

In this paper, we present a construction of abelian Paley type group schemes which are inequivalent to Paley group schemes. We then determine the equivalence amongst their configurations, the Hadamard designs or the Paley type strongly regular graphs obtained from these group schemes, up to isomorphism. We also give constructions of several families of non-abelian Paley type group schemes using strong multiplier groups of the abelian Paley type group schemes, and present the first family of p-groups of non-square order and of non-prime exponent that contain Paley type group schemes for all odd primes p.     

Graded group schemes and graded group varieties

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of a?ne group schemes and are in correspondence with graded Hopf algebras. Graded group varieties take the place of infinitesimal group schemes. We generalize the result that connected graded bialgebras are graded Hopf algebra to our setting and we describe the algebra structure of graded group varieties. We relate these new objects to the classical ones providing a new and broader framework for the study of graded Hopf algebras and a?ne group schemes.     

On a Class of Non-commutative Imprimitive Association Schemes of Rank 6

Many facts about group theory can be generalized to the context of the theory of association schemes. In particular, association schemes with fewer than 6 elements are all commutative. While there is a nonabelian group with 6 elements which is unique up to isomorphism, there are infinitely many isomorphism classes of non-commutative association schemes with 6 elements. All examples previously known to us are imprimitive, and fall into three classes which are reasonably well understood. In this paper, we construct a fourth class of noncommutative, imprimitive association schemes of rank 6.     

Group signature schemes with forward secure properties

A group signature scheme allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signature can be revealed by a designated entity. We introduce a forward secure schemes into group signature schemes. When the group public key remains fixed, a group signing key evolves over time. Because the signing key of a group member is evolving at time, the possibility of the signing key being exposed is decreased. We propose a forward secure group signature scheme based on Ateniese and Camenisch et al.’s group signature scheme. The security is analyzed and the comparisons between our scheme with other group signature schemes are made.     

Fourth order accurate compact scheme with group velocity control (GVC )

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points     

On the Existence of Auslander–Reiten Sequences of Group Representations. I

This is the first part of our study of the existence ofAuslander–Reiten sequences of group representations. In this part weconsider representations of group schemes in characteristic 0; in Part II weconsider representations of group schemes in characteristic p; andin Part III we give applications to representations of groups and Liealgebras.     

On the Normal Structure of NonCommutative Association Schemes of Rank 6

The concept of an association scheme is a far-reaching generalization of the notion of a group. Many group theoretic facts have found a natural generalization in scheme theory. One of these generalizations is the observation that, similar to groups, association schemes of finite order are commutative if they have at most five elements and not necessarily commutative if they have six elements. While there is (up to isomorphism) only one noncommutative group of order 6, there are infinitely many pairwise non-isomorphic noncommutative association schemes of finite order with six elements. (Each finite projective plane provides such a scheme, and non-isomorphic projective planes yield non-isomorphic schemes.) In this note, we investigate noncommutative schemes of finite order with six elements which have a symmetric normal closed subset with three elements. We take advantage of the classification of the finite simple groups.     

On the Existence of Auslander–Reiten Sequences of Group Representations II

This is the second part of our study of the existence ofAuslander–Reiten sequences of group representations. In Part I weconsidered representations of group schemes in characteristic 0; in thispart we consider representations of group schemes in characteristicp; and in Part III we give applications to representations ofabstract groups and Lie algebras.     

Linear Key Predistribution Schemes

In a key predistribution scheme, some secret information is distributed among a set of users. For a given family of privileged groups, this secret information must enable every user in a privileged group to compute a common key associated with that group. Besides, this common key must remain unknown to some specified coalitions of users outside the privileged group. We present in this paper a new model, based on linear algebraic techniques, for the design of key predistribution schemes that unifies all previous proposals. This new model provides a common mathematical formulation and a better understanding of key predistribution schemes. Two new families of key predistribution schemes that are obtained by using this model are presented. Those families provide, for some specification structures, schemes that have better information rates than the ones given in previous proposals or fit in situations that have not been considered before.     

Schur rings and non-symmetric association schemes on 64 vertices

In this paper we enumerate essentially all non-symmetric association schemes with three classes, less than 96 vertices and with a regular group of automorphisms. The enumeration is based on a computer search in Schur rings. The most interesting cases have 64 vertices.In one primitive case and in one imprimitive case where no association scheme was previously known we find several new association schemes. In one other imprimitive case with 64 vertices we find association schemes with an automorphism group of rank 4, which was previously assumed not to be possible.