关于Camina条件

Ａ．Ｒ．Ｃａｍｉｎａ曾研究过Ｆｒｏｂｅｎｉｕｓ群的一种类似．为此，他提出了两个假设并证明了这两个假设是等价的，在这篇文章中，我们提出比Ｃａｍｉｎａ假设弱且适合特征标表的两个假设，并证明我们的两个假设是等价的，然后，我们建立对这两个新假设而言最基本的情形的若干结果，这个最基本的情形被证明正好是有一个不可约特征标恰在两个共轭类上取非零值的群。     

Nonparametric Estimation of Regression Functions in Point Process Models

We prove that the empirical L ²-risk minimizing estimator over some general type of sieve classes is universally, strongly consistent for the regression function in a class of point process models of Poissonian type (random sampling processes). The universal consistency result needs weak assumptions on the underlying distributions and regression functions. It applies in particular to neural net classes and to radial basis function nets. For the estimation of the intensity functions of a Poisson process a similar technique yields consistency of the sieved maximum likelihood estimator for some general sieve classes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Some decidable classes of formulas of pure hybrid logic

We consider the formulas of pure hybrid logic without occurrences of a satisfaction operator. We describe a couple of formula derivation tactics in sequent calculus and prove the decidability of two classes of formulas. Decidable classes are obtained by setting restrictions on nominal occurrences in the formulas. Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 563–572, October–December, 2007.     

关于完全三部图K(m,n,r)的色唯一性

本文研究完全三部图K(m,n,r)的色唯一性问题，通过比较两个色等价图的色划分数的方法，得出两个关于K(m,n,r)为色唯一图的一般形式数值条件，基本上解决了K(m,n,r)为色唯一图的判定问题．     

Relative integral bases over a Hilbert class field

Let K be a number field, H its Hilbert class field and L a Galois extension of K containing H. In this paper, we prove that L|H has a relative integral basis (RIB) if the order of G=Gal(L|H) is odd or if the 2-Sylow subgroups of G are not cyclic. If the order of G is even and the 2-Sylow subgroups are cyclic we reduce the problem of the existence of a RIB to a quadratic extension of H.     

Univalent Interpolation in Besov Spaces and Superposition into Bergman Spaces

We establish the best possible condition for point singularities to be removable for nonlinear elliptic equations in divergent form with lower order terms from the non-linear Kato classes.      

Obtaining fast error rates in nonconvex situations

We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.     

Parabolic conjugacy in general linear groups

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL _n (q). We show that the number of P(q)-conjugacy classes in GL _n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006)     

具有混合光滑性的Holder-Nikolskii-Wiener类在Lq(Rd)中的平均宽度（英文）

本文研究了具有混合光滑性的Holder-Nikolskii-Wiener类SrpqH在Lq(Rd)中的平均σ-K宽度(2≤q≤p<∞),得到了该量的弱渐近估计.     

Stiefel-Whitney classes and toral actions

Certain Stiefel-Whitney classes of manifolds with smooth, effective toral actions are shown to be computable in terms of Poincare duals of fixed point sets of isotropy subgroups. As an application the toral degrees of symmetry of certain Dold manifolds are determined.