Ultraviolet Finiteness of Chiral Perturbation Theory in Two-Dimensional Quantum Electrodynamics

We consider the perturbation theory in the fermion mass (chiral perturbation theory) in the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction has the exponential form and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.     

多频常微分方程的几何奇异扰动理论

在该文中，作者把常微分方程的几何奇异扰动理论推广到具多个频率的系统，同时给出了一个例子来说明主要理论．     

Field Theory Approach to the Dynamics of a Continuous Medium: A Perturbation Theory

We propose a perturbation theory that allows solving the equations of motion for the displacement vector in the body of the Earth in the framework of the linear theory of elasticity. We show that tectonic processes are primarily determined by tidal actions. We analyze the tidal effects in the Earth–Moon–Sun system.     

A General Resonance Theory Based on Mourre’s Inequality

We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems characterized by Mourre’s inequality and smoothness of the resolvent. Within the framework of perturbation theory it is still possible to give a definite meaning to the notion of complex resonance energies and of corresponding metastable states. The main result is a quasi-exponential decay estimate up to a controlled error of higher order in perturbation theory. submitted 25/07/05, accepted 14/11/05     

Homological Perturbation Theory and Mirror Symmetry

We explain how deformation theories of geometric objects such as complex structures,Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson al-gebras.We use homological perturbation theory to construct A∞ algebra structures on the cohomology,and their canonically defined deformations.Such constructions are used to formulate a version of A∞ algebraic mirror symmetry.     

关于n次积分C半群的扰动

研究了n次积分C半群的可交换扰动问题,得到其扰动定理;并根据n次积分C半群与C半群的关系得到了n次积分C半群的两个乘积扰动定理.     

An application of bilinear integration to quantum scattering

Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature.     

On a perturbed non-local boundary value problem: a multiplicity result

In the present paper, we deal with a non-local boundary value problem with an exponential non-linearity. The existence of one, two or three solutions is investigated under the presence of a suitable perturbation. Our approach is variational and combines results from critical point theory.     

Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory

We study the possibility of expressing the invariant QCD coupling function (i.e., the effective coupling constant) in an explicit analytic form in two- and three-loop approximations as well as in the case of the Padé-transformed -function. Both the timelike and spacelike domains are investigated. Technical aspects of the Shirkov–Solovtsov analytic perturbation theory are considered. Explicit expressions for the two- and three-loop effective coupling functions in the timelike domain are obtained. In the last case, we apply a new method of expanding functions represented in an arbitrary loop order of perturbation theory in powers of the two-loop function. The comparison with numerical data in the infrared region shows that the obtained explicit expressions for the three-loop functions agree fully with the exact numerical results.     

非线性扰动Klein-Gordon方程初值问题的渐近理论

在二维空间中研究一类非线性扰动Klein-Gordon方程初值问题解的渐近理论. 首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein-Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein-Gordon方程初值问题解的渐近近似程度．     

Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film

We obtain formulas for resonances and eigenvalues embedded in the continuous spectrum that are similar to formulas in the standard perturbation theory. We prove that although the imaginary part of the first-order correction to the eigenvalue embedded in the continuous spectrum is zero, the perturbed eigenfunction, as a rule, ceases to be square-summable.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 3, pp. 417–430, June, 2005.     

一类抽象动力系统的C0群性质及其在迁移理论中的应用

本文研究一类抽象动力系统的性质.使用Hilbert空间的分解方法,获得了主算子的谱和相应的群的表示;使用有界线性算子的扰动理论,获得了抽象动力算子的谱分解.作为应用,研究了迁移理论中的一类积-微分方程.     

An Interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory

An interesting positive theory is the GPK theory. The models of this theory include all hyperuniverses (see [5] for a definition of these ones). Here we add a form of the axiom of infinity and a new scheme to obtain GPK_∞⁺. We show that in these conditions, we can interprete the Kelley-Morse theory (KM) in GPK_∞⁺ (Theorem 3.7). This needs a preliminary property which give an interpretation of the Zermelo-Fraenkel set theory (ZF) in GPK_∞⁺. We also see what happens in the original GPK theory. Before doing this, we first need to study the basic properties of the theory. This is done in the first two sections.     

Deformation Theory of Dialgebras

We develop deformation theory of (associative) dialgebras and show that perturbation of algebraic structures of a dialgebra is controlled by the dialgebra cohomology.     

New Identities for Weak KAM Theory

This paper records for the Hamiltonian H =1/2│P│2 + W(x) some old and new identities relevant for the PDE/variational approach to weak KAM theory.     

Traveling wave solutions for Schrödinger equation with distributed delay

The paper is devoted to study of traveling waves of nonlinear Schrödinger equation with distributed delay by applying geometric singular perturbation theory, differential manifold theory and the regular perturbation analysis for a Hamiltonian system. Under the assumptions that the distributed delay kernel is strong general delay kernel and the average delay is small, we first investigate the existence of solitary wave solutions by differential manifold theory. Then by utilizing the regular perturbation analysis for a Hamiltonian system, we explore the periodic traveling wave solutions.     

On the relations between different duals assigned to composed optimization problems

For an optimization problem with a composed objective function and composed constraint functions we determine, by means of the conjugacy approach based on the perturbation theory, some dual problems to it. The relations between the optimal objective values of these duals are studied. Moreover, sufficient conditions are given in order to achieve equality between the optimal objective values of the duals and strong duality between the primal and the dual problems, respectively. Finally, some special cases of this problem are presented.      

基于可信性理论的运输机会约束模型

基于可信性理论,将提出一类带有模糊参数的运输计划机会约束模型.然后,讨论可信性函数的逼近方法并且设计一个基于逼近方法、神经网络和遗传算法的启发式算法来求解这个模糊运输计划机会约束模型.最后,给出一个数值例子来表明所设计算法的实用性和有效性.     

Fredholm theory for pairs of closed subspaces of a Banach space

We study the Fredholm theory for pairs of closed subspaces of a Banach space developed by Kato. We define the strictly singular and the strictly cosingular pairs of subspaces, and we show that some of the results of operator theory can be extended to this context. However, there are some notable differences. On the one hand, the perturbation classes problem has a positive answer in this context: the upper and lower semi-Fredholm pairs are stable under strictly singular and strictly cosingular perturbations, respectively, and this stability characterizes the strictly singular and the strictly cosingular pairs. Note that it has been proved recently that the perturbation classes problem for continuous semi-Fredholm operators has a negative answer. On the other hand, unlike in the case of operators, the Fredholm pairs are not stable under perturbation by strictly singular or strictly cosingular pairs. We also show the stability under composition of the compact, the strictly singular and the strictly cosingular pairs of subspaces.     

Fuzzy perturbation analysis,part I: Directional perturbation

In this paper, a new idea, fuzzy perturbation, is advanced. The stability of the solutions of a fuzzy relation equation and the generalized solution of the unsolvable equation are defined by means of this idea. Thereupon, a part of the theory of fuzzy perturbation analysis, fuzzy directional perturbation, is formed. By use of the theory an approach to solving two open problems in the inverse problem of fuzzy multifactorial decision is made.