Some fixed point results on a metric space with a graph

Combining some branches is a typical activity in different fields of science, especially in mathematics. Naturally, it is notable in fixed point theory. Over the past few decades, there have been a lot of activity in fixed point theory and another branches in mathematics such differential equations, geometry and algebraic topology. In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using main idea of their work and the idea of combining fixed point theory and graph theory, we present some iterative scheme results for G-contractive and G-nonexpansive mappings on graphs.     

Analysis of Mindlin micro plates with a modified couple stress theory and a meshless method

A modified couple stress theory and a meshless method is used to study the bending of simply supported micro isotropic plates according to the first-order shear deformation plate theory, also known as the Mindlin plate theory. The modified couples tress theory involves only one length scale parameter and thus simplifies the theory, since experimentally it is easier to determine the single scale parameter. The equations governing bending of the first-order shear deformation theory are implemented using a meshless method based on collocation with radial basis functions. The numerical method is easy to implement, and it provides accurate results that are in excellent agreement with the analytical solutions.     

The Yang-Mills theory as a massless limit of a massive gauge-invariant model

We construct a gauge-invariant infrared regularization of the Yang-Mills theory applicable beyond the perturbation theory.     

环上的Clifford代数

§1. 引言与记号 如众周知,域上的Clifford代数乃是概括域上的Grassmann代数(外代数)以及广义四元数代数的一个代数。它不但在数学的一些分支(如群表示论、二次型理论等)中有着重要的应用,而且也是近代理论物理中的有用工具之一(比如参看[1])。1954年,C.Chevalley在[2]中完美地给出了域上Clifford代数的基本理论。本文的主要目的是建立可换环上的Clifford代数,即给出它的定义、存在性与唯一性等。容易看出,这是域上的Clifford代     

On the contact of a rigid sphere and a thin plate

We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a deformation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. However, for both small deflections using classical linear elastic theory and large deflections using von Kármán theory, looking at some typical parameter values we find that the radius of the ring is so small that for practical purposes it should be considered as a point load.     

Transitive reduction of a nilpotent boolean matrix

Boolean matrices are widely used in many fields, and the theory of boolean matrices is related to the algebra of relations, switching theory, and graph theory. First some basic properties of nilpotent matrices are shown in the paper. A nilpotent boolean matrix plays an important role in the theory of boolean matrices. The purpose is to present those properties of boolean matrices which are related to finding the transitive reduction of a nilpotent matrix, or an acyclic graph.     

Existence results for a nonlinear system with a parameter

In this paper, the monotone operator principle, the critical point theory and the morse theory are employed to discuss the system of nonlinear equations of the form Au=λf(u), some existence results are obtained.     

When is the self-intersection of a subvariety a fibration?

We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz–Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry.     

Development of a higher order finite element on a Winkler foundation

Analyzing thick plates as a construction component has been of interest to structural engineering research for several decades. In particular, thick plates resting on elastic foundations are more specific. Mindlin's plate theory for thick plate analysis and the Winkler theory for elastic foundation analyses have wide applications. The current research considers analysis of isotropic plates on a Winkler foundation according to Mindlin's plate theory. The analysis uses a higher order plate element to avoid shear locking phenomena in the plate. The main features of this element are representation of real displacement functions of the plate perfect and shear locking do not occur at the plates modeled with this element. Derivation of the equations for finite element formulation for thick plate theory uses fourth-order displacement shape functions. A computer program using the finite element method, coded in C++, analyzes the plates resting on an elastic foundation. The analysis involves a 17-noded finite element. The study's graphs and tables assist engineers' designs of thick plates resting on elastic foundations. The study concludes with the computer-coded program, which allows effective use for the shear locking-free analysis of thick Mindlin plates resting on elastic foundations.     

Towards a general theory of formallyp-adic fields

The work is devoted to develop a general framework for the theory of formallyp-adic fields and to prove in this context some analogues of certain results of the theory of formallyp-adic fields in the sense of Kochen-Roquette. The general theory is illustrated by examples.     

Double Operator Integrals in a Hilbert Space

Double operator integrals are a convenient tool in many problems arising in the theory of self-adjoint operators, especially in the perturbation theory. They allow to give a precise meaning to operations with functions of two ordered operator-valued non-commuting arguments. In a different language, the theory of double operator integrals turns into the problem of scalarvalued multipliers for operator-valued kernels of integral operators.The paper gives a short survey of the main ideas, technical tools and results of the theory. Proofs are given only in the rare occasions, usually they are replaced by references to the original papers. Various applications are discussed.     

Scattering on a resonator with a small opening

By the methods of the theory of extensions, one constructs an explicitly solvable resonator model with a small opening. One computes the high-frequency resonances, i.e., the eigenvalues of the dissipative operator, associated with the considered problem of resonance scattering in the framework of the Lax-Phillips theory.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 159–169, 1983.     

表示湍流场的一种新设想

本文仿照量子场论中描述基本粒子产生湮灭的方法来描述湍流中涡旋的产生和消灭.因为当某一基本粒子存在的时候,我们可以认为它是一个不变实体,而湍流中涡旋则在时间过程中不断变化和耗散,所以在类比应用量子场论方法时首先要解决怎样的湍流涡旋可认为是同一个涡旋.根据线性化理论的特点,我们认为在时间过程中按相似性规律变化时湍流涡旋才算是同一个涡旋,而把不具有相似性的涡旋出现或消失,看成是方程(2.6)中相互作用项φ_i所引起的湮火和产生的结果.然后,我们采用和量子场论相类似的产生算符和消灭算符来描述湍流涡旋系统所处的状态.最后,我们利用原N-S方程中相互作用项来构成涡旋相互作用的“Schr?dinger”方程以描述其状态的变化.这样就得类似于量子场论的湍流涡旋相互作用理论.     

Frame Multiplication Theory and a Vector-Valued DFT and Ambiguity Function

Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time–frequency analysis is essential. The definition of the DFT requires associated uncertainty principle inequalities. The definition of the ambiguity function requires a component that leads to formulating a mathematical theory in which two essential algebraic operations can be made compatible in a natural way. The theory is referred to as frame multiplication theory. These definitions, inequalities, and theory are interdependent, and they are the content of the paper with the centerpiece being frame multiplication theory. The technology underlying frame multiplication theory is the theory of frames, short time Fourier transforms, and the representation theory of finite groups. The main results have the following form: frame multiplication exists if and only if the finite frames that arise in the theory are of a certain type, e.g., harmonic frames, or, more generally, group frames. In light of the complexities and the importance of the modeling of time-varying and dynamical systems in the context of effectively analyzing vector-valued multi-sensor environments, the theory of vector-valued DFTs and ambiguity functions must not only be mathematically meaningful, but it must have constructive implementable algorithms, and be computationally viable. This paper presents our vision for resolving these issues, in terms of a significant mathematical theory, and based on the goal of formulating and developing a useful vector-valued theory.

     

Mathematical foundations for a theory of confidence structures

This paper introduces a new mathematical object: the confidence structure. A confidence structure represents inferential uncertainty in an unknown parameter by defining a belief function whose output is commensurate with Neyman–Pearson confidence. Confidence structures on a group of input variables can be propagated through a function to obtain a valid confidence structure on the output of that function. The theory of confidence structures is created by enhancing the extant theory of confidence distributions with the mathematical generality of Dempster–Shafer evidence theory. Mathematical proofs grounded in random set theory demonstrate the operative properties of confidence structures. The result is a new theory which achieves the holistic goals of Bayesian inference while maintaining the empirical rigor of frequentist inference.     

B—模糊集合代数和广义互信息公式

基于两种概率的区分，推导出了一个广义Shannon熵公式和一个广义互信息公式。后者和模糊性有关，并且柯用于语言和感觉中的信息度量。为了由原子语句为真的条件概率求出合语句为真的条件概率，提出了一个遵循存尔运算的模糊集合代数。所谓的模糊信息被还原为概率信息。新的理论在经典理论－概率论，集合论及Shannon信息论－的基础上容易理解。     

A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.     

Uniform asymptotic expansion of $J_\nu(\nu a)$ via a difference equation

Summary. There are two ways of deriving the asymptotic expansion of , as , which holds uniformly for . One way starts with the Bessel equation and makes use of the turning point theory for second-order differential equations, and the other is based on a contour integral representation and applies the theory of two coalescing saddle points. In this paper, we shall derive the same result by using the three term recurrence relation . Our approach will lead to a satisfactory development of a turning point theory for second-order linear difference equations. Received December 15, 2000 / Published online September 19, 2001     

Cotorsion Theories Cogenerated by a Torsionfree Class

Let R be a right perfect ring, and let (?, 𝒞) be a cotorsion theory in the category of right R-modules ? _R . In this article, it is shown that every right R-module has a superfluous ?-cover if and only if there exists a torsion theory (𝒜, ?) such that (?, 𝒞) is cogenerated by ?. It is also proved that if (𝒜, ?) is a cosplitting torsion theory, then (^⊥?, (^⊥?)^⊥) is a hereditary and complete cotorsion theory, and if (𝒜, ?) is a centrally splitting torsion theory, then (^⊥?, (^⊥?)^⊥) is a hereditary and perfect cotorsion theory.     

Qualitative properties of a continuum theory for thin films

We discuss qualitative aspects of a continuum theory for thin films rigorously derived in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig]. The stored energy density is examined for convexity properties and limiting behavior under large and small strains. A study of the dependence of the theory on relaxation parameters leads to the result that the scale of convergence used in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig] is the only scale for which a limiting theory that also accounts for atomic relaxation effects is non-trivial.