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.     

强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何

本文给出了强正则$(\alpha,\beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立.     

算子强不可约的充要条件

本文证明了Cowen-Douglas 算子是强不可约的充要条件,是它的换位代数模去其Jacobson 根同构于$H^{\infty}(D)$中的一个闭子代数,这里$D$表示开单位圆盘, $H^{\infty}(D)$表示$D$上的有界解析函数的全体.     

Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities

We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.     

Toric Rigid Spaces

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.