关于NA情况下重对数律收敛速度的一般形式

研究了NA序列重对数律收敛速度的一般形式，把Davis和Gut的结果推广到了NA的情形，并使梁汉营等人关于对数律一个结果成为特例；作为推论，得到了关于NA序列重对数律收敛速度的充分条件．     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed.     

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.     

Ribaucour Transformations for Hypersurfaces in Space Forms

The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20.     

Some conformally flat spin manifolds, Dirac operators and automorphic forms

In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Γ where U is a subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S¹×Sn−1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of Γ are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.     

Rankin-Cohen brackets on pseudodifferential operators

Pseudodifferential operators that are invariant under the action of a discrete subgroup Γ of SL(2,R) correspond to certain sequences of modular forms for Γ. Rankin-Cohen brackets are noncommutative products of modular forms expressed in terms of derivatives of modular forms. We introduce an analog of the heat operator on the space of pseudodifferential operators and use this to construct bilinear operators on that space which may be considered as Rankin-Cohen brackets. We also discuss generalized Rankin-Cohen brackets on modular forms and use these to construct certain types of modular forms.     

Structure of minimizers in linear-quadratic Bolza problems of optimal control

In this paper, we study intersections of extremals in a linear-quadratic Bolza problem of optimal control. The structure of the inter-sections is described. We show that this structure implies the semipositive definiteness of the quadratic cost functional. In addition, we derive necessary and sufficient conditions for the existence of minimizers.