Group extensions and free actions by finite groups on solvmanifolds

The purpose of this paper is to generalize Yalçin's result [Trans. Amer. Math. Soc. 352 , 2689–2700 (2000)] from tori to solvmanifolds. As a result, we prove that if (?_p)^r acts freely on a solvmanifold M of dimension n, then r ≤ n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

拟线性双曲抛物耦合组强适定非线性初边值问题

本文用叠代方法得到强适定双曲抛物耦合系统非线性初始边值问题局部解的存在唯一性。     

随机变量序列函数的几乎处处中心极限定理

该文证明了随机元序列的一个一般的几乎处处中心极限定理, 并把这一结论应用于随机变量序列的函数.     

Study of the Hubbard model at half filling

Under the conditions of a strong Coulomb repulsion between electrons at a lattice site, we now study the equations for the self-energy part of the electron Green’s function, which we previously obtained using the generating functional method. These equations have a form close to that corresponding to the self-consistent Born approximation in the weak-coupling theory. In these equations, we omit the dependence of the self-energy on the momentum, which corresponds to the infinite-dimensional space limit. We then numerically solve the integral equations, where all the variables depend only on the frequency, and obtain results consistent with the dynamical mean field theory. In particular, we show that as the Coulomb repulsion increases, the three-peak structure of the quasiparticle spectrum changes into a two-peak structure and the metal–insulator phase transition occurs. The proposed method can be used to study other models of the theory of strongly correlated systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 63–76, January, 2008.     

Small Compact Perturbation of Operators in B∞（Ω）

Abstract： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.     

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the solutions of classical problems in option pricing theory in Mathematical Finance. The paper is dedicated to Professor Luigi Albano on the occasion of his 70th birthday.     

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.     

赋序列范数的矢值序列空间ss(E)的强暴露性和暴露性

刻划了赋序列范数的矢值B anach序列空间ss(E)的强暴露性和暴露性,给出了它们的判据.     

算子权移位的换位代数的交换性

令T是以{Wk}∞k=1B(Cn)为权序列的内射算子权移位.设T是强不可约的,而且sup1k<∞‖W-1k‖< ∞.用A′(T)表示T的换位代数,radA′(T)表示A′(T)的Jacobson根.本文刻划了radA′(T)并且证明了商代数A′(T)/radA′(T)是交换的.     

关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.