Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.     

Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.

     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

On the Approximation of Functions on Locally Compact Abelian Groups

Questions of approximative nature are considered for a space of functions L ^p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.     

On Some Rings of Arithmetical Functions

In this paper, we consider several constructions which from a given B-product * _B lead to another one We shall be interested in finding what algebraic properties of the ring are shared also by the ring . In particular, for some constructions the rings R _B and will be isomorphic and therefore have the same algebraic properties.     

GaAs：Cr探测器中子辐照改性研究

介绍了一种新型脉冲辐射探测器以及提高其性能的一种方法,并报告了探测器性能与中子积分通量关系的实验结果。     

Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

Analysis of a Class of Parallel Multigrid Smoothers

This paper proposes and analyzes a class of multigrid smoothers called the parallel multiplicative (PM) smoother by subspace decomposition techniques. It shows that the well known additive and multiplicative smoothers and the JSOR smoother are special cases of the PM smoother, and their smoothing properties can be obtained directly from the PM analysis. Moreover, numerical results are presented in this paper to show that the JSOR smoother is more robust and effective than the damped Jacobi smoother on current MIMD parallel computers. AMS subject classification (2000) 65N55, 65Y05.Received May 2004. Revised September 2004. Communicated by Per Lötstedt.Dexuan Xie: This work was partially supported by the National Science Foundation through grant DMS-0241236.     

Parameter Inequalities for Orthogonal Arrays with Mixed Levels

An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Raos bounds. We will also provide a new proof of Raos inequalities for arbitrary orthogonal arrays with mixed levels based on the same method.