On Weitzenböck curvature operators

The Weitzenböck curvature operators are the curvature terms of order zero that appear in the well‐known classical Weitzenböck formula. In this paper, we use the formalism of double forms to prove a simple formula for these operators and to study their geometric properties.     

Moments of L-Functions Attached to the Twist of Modular Form by Dirichlet Characters

Let f(z) be a holomorphic cusp form of weight κ with respect to the full modular group SL2(Z). Let L(s, f) be the automorphic L-function associated with f(z) and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,and the result also holds for any real number 0 k 1 under the GRH for L(s, f ■χ).The authors also prove that under the GRH for L(s, f ■χ),for any real number k 0 and any large prime q.     

Radial symmetry and regularity of solutions for poly-harmonic Dirichlet problems

Let B=B₁(0) be the unit ball in Rn and r=|x|. We study the poly-harmonic Dirichlet problem

     

On the asymptotic behavior of nonoscillatory solutions of second order quasilinear ordinary differential equations

In this paper second order quasilinear ordinary differential equations are considered, and a necessary and sufficient condition for the existence of a slowly growing positive solution is established. Moreover, the precise asymptotic forms as t→∞ of slowly growing positive solutions and slowly decaying positive solutions are obtained.     

A system of integral equations on half space

Let be the n-dimensional upper half Euclidean space, and let α be any real number satisfying 0<α<n, we study positive solutions of the following system of integral equations in :

     

Stack structures on GIT quotients parametrizing hypersurfaces

We suggest to endow Mumford's GIT quotient scheme with a stack structure, by replacing Proj(?) of the invariant ring with its stack theoretic analogue. We analyse the stacks resulting in this way from classically studied invariant rings, and in particular for binary forms of low degree. Our viewpoint is that the stack structure carries interesting geometric information that is intrinsically present in the invariant ring, but lost when passing to its Proj(?). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

有理对称矩阵的准正交相似

对一个有理对称矩阵A,用线性代数的理论直接证明了存在准正交矩阵P使得P~(-1)AP成为A的有理标准形,并给出了P的算法.     

Cartan geometries and multiplicative forms

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures.     

Le Système d'Euler de Kato en Famillie(Ⅱ)

This article is the second article on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems over the cuspidal eigencurve, which interpolate the Kato's Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato's Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve; this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.     

Spectrophotometric Determination of Ternary Mixtures by the Derivative Ratio Spectrum-Zero Crossing Method

Abstract

A new spectrophotometric method is introduced for the assay of ternary mixtures with overlapping spectra. The method is based on the use of the first derivative of the ratio spectra and measurements of zero-crossing wavelengths. The ratio spectra were obtained by dividing the absorption spectrum of the mixture by that of one of the components. The concentration of the other components are then determined from their respective calibration graphs treated similarly. The method has been applied for the resolution of two ternary mixtures, namely, dipyridamole, aspirin and salicylic acid (I) and dipyridamole, oxazepam and 2-amino-5-chlorobenzophenone (II). Salicylic acid and benzo-phenone derivative are the degradation products of aspirin and oxazepam, respectively. The proposed method was applied for the assay of these combinations in synthetic mixtures and in commercial dosage forms. The results obtained were precise and accurate.