The Rost invariant has trivial kernel for quasi-split groups of low rank

For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map . This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for exceptional Jordan algebras as special cases. We show that R _G has trivial kernel if G is quasi-split of type E ₆ or E ₇. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank. Received: November 1, 2000     

Hypercontractivity of Solutions to Hamilton-Jacobi Equations

We show that solutions to some Hamilton-Jacobi Equations associated to the problem of optimal control of stochastic semilinear equations enjoy the hypercontractivity property.     

A Result on Vector Variational Inequalities with Polyhedral Constraint Sets

In this note, by using some well-known results on properly efficient solutions of vector optimization problems, we show that the Pareto solution set of a vector variational inequality with a polyhedral constraint set can be expressed as the union of the solution sets of a family of (scalar) variational inequalities.     

Elastic Constraint Branching, the Wedelin/Carmen Lagrangian Heuristic and Integer Programming for Personnel Scheduling

The Wedelin algorithm is a Lagrangian based heuristic that is being successfully used by Carmen Systems to solve large crew pairing problems within the airline industry. We extend the Wedelin approach by developing an implementation for personnel scheduling problems (also termed staff rostering problems) that exploits the special structure of these problems. We also introduce elastic constraint branching with the twin aims of improving the performance of our new approach and making it more column generation friendly. Numerical results show that our approach can outperform the commercial solver CPLEX on difficult commercial rostering problems.     

跳过程的不变测度与q对的不变测度

本文讨论了一般状态空间上具有不变测度的q对的对偶q对的构造问题,证明了正则q对的不变测度是它的相应跳过程的不变测度的充要条件是该q对的对偶q对是正则的。     

Affine Invariant and Cyclic Codes over p-adic Numbers and Finite Rings

Affine invariant and cyclic codes over p-adic numbers and over integers modulo p ^d are studied. It has been determined what cyclic codes have an extension that is affine invariant.     

Uniformly Most Powerful Invariant Test and Its Application

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＣｏｎｓｉｄｅｒｔｈｅｍｕｌｔｉｎｏｒｍａｌｄｉｓｔｒｉｂｕｔｉｏｎＮ(μ ,Σ) .Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔ,ｕｎｄｅｒｔｈｅｌｏｓｓｆｕｎｃｔｉｏｎＬ(ｄ ,μ) =(ｄ -μ) (ｄ -μ)′,ｔｈｅｅｓｔｉｍａｔｏｒｓｏｆμｏｆｔｈｅｆｏｒｍａ1 Ｘ ,ｗｈｅｒｅａ1∈ (0 ,1 ) , Ｘｉｓａｓａｍｐｌｅｍｅａｎ ,ａｒｅｂｅｔｔｅｒｔｈａｎｔｈｅｌｉｋｅｌｉｈｏｏｄｅｓｔｉｍａｔｏｒ Ｘｉｆａｎｄｏｎｌｙｉｆｎμ′Σ- 1μ≤Ｃ1(1 )ｗｈｅｒｅＣ1=1 +ａ11 -ａ1ａｎｄｎｉｓｔｈｅｎｕｍ…     

第一类超Cartan域上双全纯不变量的极限

本文讨论了第一类超 Cartan域 YI上的双全纯不变量 JY1(w,z;w,z)以及当 (w,z)趋于边界 YI时JYI的极限     

整数环上矩阵平方和的两个新结论

本文利用 F2 上方阵为平方矩阵的充要条件 ,证明了 :1任一阶数为偶数的整数矩阵可表示成 5个平方次幂整数矩阵之和 ;2任一整数矩阵可表示成 6个平方次幂整数矩阵之和 ,从而改进了文 [2 ,3 ]的主要结论 .     

紧支集分布和可加细向量的整平移的线性相关性

In this paper, the global and local linear independence of any compactly supported distributions by using time domain spaces ,and of refinable vectors by invariant linear spaces are investigated.