QUAFITIZED HALL EFFECT IM VERY STRONG MAGEETIC FIELD

The experimentally observed quantized Hall plateau of P_xy=3h/e² in two-dimensional electron gas, when the lowest Landau level is 1/3 filled, is discussed. The consistency of the cxtremal condition for the Hartree-Fock potential in the possible charge-density-wave state with, opening an energy gap at the Fermi level is indicated. The exactness of Such 1/3 "fractional" quantization might be justified by a modified version of Laughlin's argument based on gauge invariance.     

Some new constructions of bivariate Weibull models

In this article, several approaches are advanced towards the construction of bivariate Weibull models from the consideration of failure behaviors of the components of a two-component system. First, a general method of construction of bivariate life models is developed in the setting of random environmental effects. Some new bivariate Weibull models are derived as special cases and added insights are provided for some of the existing ones. In the course of model formulation in terms of the dependence structure, a new bivariate family of life distributions is constructed so as to incorporate both positive and negative quadrant dependence in the same parametric setting, and a bivariate Weibull model is obtained as a special case. Finally, some distributional properties are presented for a bivariate Weibull model derived from the consideration of random hazards.     

Fe、Co、Ni混合团簇磁性的密度泛函研究

基于13原子二十面体结构,采用密度泛函方法系统计算研究了Fe、Co及Ni单质及二元混合团簇的磁性.发现有限温度下团簇磁性随结构畸变的敏感性随Fe、Co、Ni顺序逐渐减弱,同时发现二十面体结构Fe_(13)及Co_(13)均具有不同磁矩的近简并低能态.对FeNi及CoNi混合团簇、其磁矩随组分的变化不存在反常现象,但对于FeCo混合团簇、其磁矩随组分的演化行为存在个别反常现象.我们认为:这种反常现象能够对FeCo非晶合金中的实验观测结果提供一种可能的理论解释.     

Lp (?m × ?n) boundedness for the Marcinkiewicz integral on product spaces

L^p(R^m × Rⁿ) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the L^p(R^m × Rⁿ) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained.     

Lipschitz estimates for generalized commutators of fractional integrals with rough kernel

Let (0 < α < n) be the generalized commutator generated by fractional integral with rough kernel and the m–th order remainder of the Taylor formula of a function A. In this paper, the (L^p, L^r) (r > 1) boundedness, the weak (L¹, L^{n/(n–α–β)}) boundedness and the (L^p, ?^{β, ∞}_p) boundedness of are discussed, when D^γA belongs to the Lipschitz function spaces.     

THE SUM OF DEFICIENCIES OF ENTIRE FUNCTION ON C~n

This paper proves that: Let / be an entire function of finite order λon Cn. Then(1) , where k(X) is a nonnegative constant depending only on A;(2) If (a, f) = 1, then A is a positive integer and equals the lower order of /.     

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.     

Additive Jordan isomorphisms of nest algebras on normed spaces

Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A²)=φ(A)² for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT⁻¹ for every or φ(A)=TA∗T−1 for every .     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.