二类广义Vandermonde行列式的计算

给出了二类广义Vandermonde行列式计算的显式表示式.     

Selection theorems and treeability

We show that domains of non-trivial trees have members. Using this, we show that smooth treeable equivalence relations have Borel transversals, and essentially countable treeable equivalence relations have Borel complete countable sections. We show also that treeable equivalence relations which are ccc idealistic, measured, or generated by a Borel action of a Polish group have Borel complete countable sections.

     

一般线性模型基于最大特征根的相对效率

定义了一般线性模型参数的最小二乘估计(LS估计)与BLU估计的一种新的相对效率,给出了当设计矩阵满秩,协方差阵非负定时这种相对效率的下界,最后讨论了其与广义相关系数(zρ3)之间的关系.     

Mapping properties of analytic functions on the unit disk

Let be analytic on the unit disk with . In 1989, D. Marshall conjectured the existence of the universal constant such that whenever the area, counting multiplicity, of a portion of over is . Recently, P. Poggi-Corradini (2007) proved this conjecture with an unspecified constant by the method of extremal metrics. In this note we show that such a universal constant exists for a much larger class consisting of analytic functions omitting two values of a certain doubly-sheeted Riemann surface. We also find a numerical value, , which is sharp for the problem in this larger class but is not sharp for Marshall's problem.

     

Groups which do not admit ghosts

A ghost in the stable module category of a group is a map between representations of that is invisible to Tate cohomology. We show that the only non-trivial finite -groups whose stable module categories have no non-trivial ghosts are the cyclic groups and . We compare this to the situation in the derived category of a commutative ring. We also determine for which groups the second power of the Jacobson radical of is stably isomorphic to a suspension of .

     

Resplendent models and $${\Sigma_1^1}$$ -definability with an oracle

In this article we find some sufficient and some necessary -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view of a model of arithmetic. These internal arguments are used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model.      

On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

New properties of r-Stirling series

The summation of some series involving the Stirling numbers of the first kind can be found in several works but there is no such a computation for Stirling numbers of the second kind let alone the r-Stirlings. We offer a comprehensive survey and prove new results.      

Spectral analysis of eigenparameter dependent boundary value transmission problems

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces.