The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices

In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated. Supported by National Natural Science Foundation of China (No. 10531070), National Basic Research Program of China 973 Program (No. 2006CB805900), National Research Program of China 863 Program (No. 2006AA11Z209) and the Natural Science Foundation of Shanghai (Grant No. 06ZR14049).     

Essentially normal Hilbert modules and Khomology Ⅲ: Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. This work is partially supported by the National Natural Science Foundation of China (Grant No. 10525106), the Young Teacher Fund, the National Key Basic Research Project of China (Grant No. 2006CB805905) and the Specialized Research for the Doctoral Program     

Gaining efficiency via weighted estimators for multivariate failure time data

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 ^th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 ^rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)     

The Paley-Wiener theorem in the non-commutative and non-associative octonions

The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved. This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002)     

The Cauchy Problems and Global Solutions to the Deybe System and Burgers＇ Equations in Pseudomeasure Spaces

In this paper we consider the Cauchy problems of Burgers＇ equations and the Deybe system. Their existence and uniqueness of the time-global solutions for small initial data in some pseudomeasure spaces are obtained. The asymptotic stability of small solutions is proved. As an immediate result the existence and uniqueness of the self-similar solutions are also obtained provided the initial data satisfy the self-similar structures.     

Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise

In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus perturbed by a Lévy process. The existence of invariant measure of the solutions are proved also. This work was supported by National Basic Research Program of China (Grant No. 2006CB8059000), Science Fund for Creative Research Groups (Grant No. 10721101), National Natural Science Foundation of China (Grant Nos. 10671197, 10671168), Science Foundation of Jiangsu Province (Grant Nos. BK2006032, 06-A-038, 07-333) and Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences     

Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carath′eodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.     

Fuzzy Topology Based on Residuated Lattice-Valued Logic

We use a semantical method of complete residuated lattice-valued logic to give a generalization of fuzzy topology as a partial answer to a problem by Roser and Turquette. This work is supported by the National Foundation for Distinguished Young Scholars (Grant No: 69725004), Research and Development Project of High-Technology (Grant No: 863-306-ZT06-04-3) and Foundation of Natural Sciences (Grant No: 69823001) of China and Fok Ying-Tung Education Foundation     

SU(3) limit ofsdgpf interacting boson model

TheSU(3) limit of thesdg-pf interacting boson model is proposed. Applications to the collective states of^236,238U are discussed. It is shown that the spectra can be well described by the model. Project sapported by the National Natural Science Foundation of China (Grant No. 19775025), Science Fund of China Nuclear Industry, Excellent Young University Teachers Fund of China National Education Commitee, Fok YingTung Education Foundation.     

Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops

This paper concerns with the number and distributions of limit cycles of a quintic subject to a seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation, Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown. The results obtained are useful to the study of the weakened 16th Hilbert Problem.     

An overview of representation theorems for static risk measures

In this paper, we give an overview of representation theorems for various static risk measures: coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders. This work was supported by National Natural Science Foundation of China (Grant No. 10571167), National Basic Research Program of China (973 Program) (Grant No. 2007CB814902), and Science Fund for Creative Research Groups (Grant No. 10721101)     

Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ

Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average.     

On Pairs of Linear Equations in Three Prime Variables

In this paper, we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.     

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)     

Necessary and Sufficient Conditions for Weak No-Arbitrage in Securities Markets with Frictions

In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage. Some results on state prices are also provided. The results of this paper can provide at least some theoretical insight to the problem. This research was supported in part by a grant of the National Excellent Ph.D. Thesis Project of China (No. 200267), a grant of the National Natural Science Foundation of China (No. 10171115), a “Tenth Five-Year Plan” project of Ministry of Education of China (No. 01JA630009), a grant of the Natural Science Foundation of Guangdong Province (No. 011193), two grants from the Research Grants Council of Hong Kong (CityU 1081/02E, HKU 7139/01H), and a research grant of the University of Hong Kong.     

Sharp Minima for Multiobjective Optimization in Banach Spaces

We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.This research was supported by a Central Research Grant of The Hong Kong Polytechnic University (Grant No. G-T 507). Research of the first author was also supported by the National Natural Science Foundation of PR China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M).     

A level set method to reconstruct the discontinuity of the conductivity in EIT

In this paper, one level set method is applied to finding the interface of discontinuity of the conductivity in EIT(electrical impedance tomography) problem. By choosing one suitable velocity function, a level set reconstruction algorithm is proposed. The theoretical results for EIT problem and regularization are given. Finally the numerical examples demonstrate that the reconstruction algorithm is efficient and stable. The work was supported by the National Natural Science Foundation of China (Grant Nos. 10431030, 10771138), the Shanghai Natural Science Foundation (Grant No. 07JC14001), the National Basic Research Program (Grant No. 2005CB321701) and Ministry of Education of China and State Administration of Foreign Experts Affairs of China under an 111 project (Grant No. B08018).     

Continuity in weak topology:higher order linear systems of ODE

We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill's equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.     

Solutions for the prescribing mean curvature equation

By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^＋ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.     

Some results for a finite family of uniformly L-Lipschitzian mappings in Banach spaces

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend some recent results in Chang [1], Cho et al. [2] Ofoedu [5], Schu [7] and Zeng [8, 9]. The present studies were supported by “the Natural Science Foundation of China (No. 10771141),” the Natural Science Foundation of Zhejiang Province (Y605191), the Natural Science Foundation of Heilongjiang Province (A0211), the Scientific Research Foundation from Zhejiang Province Education Committee (20051897).