Degree distribution of the greatest common divisor of polynomials over 𝔽q

We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field ??_q. We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

广义凸集的支撑函数

本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。     

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G.     

Harmonic Analysis on the Compact Homogeneous Spaces──about Fourier Multiplier ofH~P（M） Space

ＨａｒｍｏｎｉｃＡｎａｌｙｓｉｓｏｎｔｈｅＣｏｍｐａｃｔＨｏｍｏｇｅｎｅｏｕｓＳｐａｃｅｓ──ａｂｏｕｔＦｏｕｒｉｅｒＭｕｌｔｉｐｌｉｅｒｏｆＨ~Ｐ（Ｍ）Ｓｐａｃｅ￥ＤｏｎｇＤａｏｚｈｅｎ；ＺｈｅｎｇＸｕｅａｎ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉ?..     

幂函数的一些密码学性质

二元域上n数组空间上的非线性置换在分组码，杂凑函数与流密码等密码学领域中有重要应用.域GF（2n）上的幂函数提供了二元域上n数组空间上的一类非线性置换．本文着重研究幂函数的强完全性、完全性与非线性度等密码学性质．作为结果，本文证明了幂函数具有完全性；证明了具有强完全性的函数必有较高的拓扑非线性度；木文找到一类具有强完全性的幂函数；周时也定出了幂函数的代数非线性度．     

Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space

We treat m-dimensional real submanifolds M of complex space forms ̿M when the maximal holomorphic tangent subspace is (m−1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX,Y)−h(X,FY) = g(FX,Y)η, η∊ T⊥(M), on the structure F and on the second fundamental form h of these submanifolds. Especially when the ambient space ̿M is a complex Euclidean space, we obtain a complete classification of submanifolds M which satisfy these conditions.Mathematics Subject Classifications (2000): 53C15, 53C40, 53B20.     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

几乎齐次函数的刻划定理

给出了几乎齐次函数的一个新的刻划定理，这一刻划是齐次函数欧拉定理的拓广。     

Backlund transformation and variable separation solutions for the generalized Nozhnik—Novikov—Veselov equation

Using the extended homogeneous balance method, the B?cklund transformation for a (2+1)-dimensional integrable model, the generalized Nizhnik－Novikov－Veselov (GNNV) equation, is first obtained. Also, making use of the B?cklund transformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form equations. Starting from these three equations, a rather general variable separation solution of the model is constructed. The abundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitrary functions.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.