Beyond elementary catastrophe theory

We give a brief discussion of the relations between elementary catastrophe theory, general catastrophe theory, singularity theory, bifurcation theory, and topological dynamics. This is intended to clarify the status, and potential applicability, of “catastrophe theory,” a phrase used by different authors and at different times with different meanings. Catastrophe theory has often been criticized for (supposed) applicability only to gradient systems of differential equations; but properly speaking this criticism can apply only to the elementary version of the theory (where it is in any case wrong). Roughly speaking, elementary catastrophe theory deals with the singularities of real-valued functions, general catastrophe theory with singularities of flows. Between these lies singularity theory, which deals with vector-valued functions. All relate strongly to bifurcation theory and topological dynamics. The issue is more subtle than it appears to be, and we describe an example where elementary catastrophe theory has been used to solve a long-standing problem about nongradient flows: degenerate Hopf bifurcation.     

心理账户、损失厌恶与行为资产配置实证研究

基于前景理论和三参照点理论,建立了单心理账户和三心理账户下的线性损失厌恶行为投资组合模型,并利用中证基金指数数据构建了不同市场状态下的行为投资组合,实证研究不同损失厌恶系数、不同参照点、不同心理账户资金配置条件下模型的最优资产配置策略和投资组合绩效,研究发现线性损失厌恶模型更关注下侧损失,损失厌恶系数影响资产配置,注重安全性的投资者偏好低风险资产,而寻求实现抱负水平的投资者更偏好高收益资产。     

基于改进Chebyshev级数的层合结构-振动分析新理论

提出了一种基于改进Chebyshev级数的层合结构高阶分层建模理论.该理论位移场由线性位移场和高阶位移场组成，线性位移场控制位移场的总体分布趋势，高阶位移场进行局部修正.高阶位移场由具有统一表达式的改进Chebyshev级数表示，通过改变高阶截断阶数可实现高阶位移场快速配置，能够满足不同建模精度需求.采用该高阶分层理论和广义谱方法推导了层合结构的自由振动特征方程，研究了一般边界条件下层合梁、板、壳的自由振动特性，并将计算结果与其他文献数据对比.结果表明:基于改进Chebyshev级数的层合结构高阶分层理论具有较高的建模精度和计算效率.     

An enhanced tensorial formulation for elastic degradation in micropolar continua

In the past, a lot of applications of the micropolar (or Cosserat) continuum theory have been proposed, especially in the field of granular materials analysis and for strain localization problems in elasto-plasticity, due to its regularization properties. In order to make possible the application of the micropolar theory to different constitutive models and to extend its regularization properties also to damage models, in this work a general formulation for elastic degradation based on the micropolar theory is proposed. Such formulation is presented in a unified format, able to enclose different kinds of elasto-plastic, elastic-degrading and damage constitutive models. A peculiar tensor-based representation is introduced, in order to guarantee the conformity with analogous theories based on the classic continuum, in such a way as to make possible the application to the micropolar theory of theoretical and numerical resources already defined for the classic theory. Peculiar micropolar scalar damage models are also proposed, and derived within the new general formulation.     

New-from-old full dualities via axiomatisation

We study different full dualities based on the same finite algebra. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too. We use this theorem to obtain a better understanding of several important examples from the theory of natural dualities. We also clarify what it means for two full dualities based on the same finite algebra to be different. Throughout the paper, a fundamental role is played by the universal Horn theory of the dual categories.     

Structure and complexity in economic and social systems

An attempt is made to outline a theory of complexity for economics and social science purposes. A methodology is outlined that realizes complexity as an analytical category, and develops a comprehensive theory of structural forms, structural change and qualitative systems behavior based on these methods. Examples of different nature are given to support the need for such a theory of complexity.     

Class field theory for curves over local fields

The purpose of this paper is to generalize some results of Bloch [3] concerning class field theory for curves over local fields. Bloch developed his theory mainly under the assumption that curves have good reduction. By using a different method, we shall develope a theory including the bad reduction case.     

Gains from diversification on convex combinations: A majorization and stochastic dominance approach

By incorporating both majorization theory and stochastic dominance theory, this paper presents a general theory and a unifying framework for determining the diversification preferences of risk-averse investors and conditions under which they would unanimously judge a particular asset to be superior. In particular, we develop a theory for comparing the preferences of different convex combinations of assets that characterize a portfolio to give higher expected utility by second-order stochastic dominance. Our findings also provide an additional methodology for determining the second-order stochastic dominance efficient set.     

Finite element analysis of arches undergoing large rotations - I: Theoretical comparison

In this two part paper, the first part deals with five different nonlinear theories applicable to the analysis of arches in the context of solving the large displacement and the large rotation problem. These theories include, classical theory, first-order shear deformation theory, third-order shear deformation theory, modified classical theory and the Donnell-type theory. All the theories are developed using the Total Lagrangian approach. Simplifications and assumptions used in each of the theory are discussed. Explicit strain displacement gradient relations and element independent equilibrium equations in terms of displacement gradients are given for all the theories. Limitations of each of theory are discussed. In the second part of this paper, application of these theories for the classification of arch geometries is considered.     

Canonical transformations,umbral calculus,and orthogonal theory

We present a theory of representations of canonical transformations which links together the theories of evolution semigroups, Hamiltonian flows, umbral operators, and cross-sequences. We also present a different approach to the orthogonal theory of moment systems.     

Eine abstrakte Theorie der Kegel- und Segmentbedingungen

We develop an abstract theory of geometric regularity conditions for subsets of normed linear spaces, of the type which occurs in the theory of Sobolev spaces (cone conditions, …). The theory is to systematize the diversity of existing conditions, to replace complicated conditions by simpler ones, and to clarify the interplay between different conditions. Our main result is a very general decomposition theorem.     

Left-symmetric algebras, or pre-Lie algebras in geometry and physics

In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs play an important role. Furthermore we study the algebraic theory of LSAs such as structure theory, radical theory, cohomology theory and the classification of simple LSAs. We also discuss applications to faithful Lie algebra representations.     

基于RCE条件下双头垄断的福利分析

应用RCE(RationalConjecturesEquilibrium)条件来分析双头垄断企业(厂商)在成本不对称、需求不对称、产品差异化条件下对社会福利产生的不同影响,并说明了RCE条件下的双头垄断模型与Cournot模型及社会最优模型的关系,提出在“结构—行为—绩效(SCP)”研究中,行为是一个重要的因素,即使在同一结构下,不同的行为将会产生不同的绩效与福利.     

个性粒化k-匿名隐私保护方法研究

结合粒计算粗糙集理论和k-匿名理论的最新研究现状,从粒化角度出发,提出个性粒化k-匿名隐私保护方法.针对电子商务中隐私保护个性粒化决策选择度的不同,提出一种新的隐私保护方法:个性粒化k-匿名并给出了相关算法和定义,旨在实现更为合理的个性化隐私保护,提高隐私保护的精度.     

Comparison of linear beam theories

In this paper we consider three models for a cantilever beam based on three different linear theories: Euler–Bernoulli, Timoshenko and two-dimensional elasticity. Using the natural frequencies and modes as a yardstick, we conclude that the Timoshenko theory is close to the two-dimensional theory for modes of practical importance, but that the applicability of the Euler–Bernoulli theory is limited.     

General linear methods with external stages of different orders

The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. In this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.The work of the first author was supported by the National Science Foundation under grant NSF DMS-9208048. The work of the second author was supported by the Italian Consiglio Nazionale delle Richerche.     

An Iterative Analytical Theory in the Mechanics of Layered Composite Systems

An iterative analytical theory in the mechanics of layered composite systems is developed. The prehistory of the nonclassical theory of layered systems is presented. The division of this theory into two principal directions - discrete-structural and continuous-structural - is mentioned. The basic iterative Ambartsumyan theory, which belongs to the second direction, is described. The formation of the generalized iteration theory of first approximation is shown. In this theory, the disagreement between the kinematic and static models is removed, i.e., a generalization of these models is realized. The theory of second approximation is described. An iterative principle is presented for the formation of a higher-approximation nonclassical theory. Based on this principle, theories of anisotropic composite shallow shells, plates, and beams are formulated. Comparative calculation results for different layered composite systems are presented.     

Characterizations of Morita equivalent inverse semigroups

We prove that four different notions of Morita equivalence for inverse semigroups motivated by C^∗-algebra theory, topos theory, semigroup theory and the theory of ordered groupoids are equivalent. We also show that the category of unitary actions of an inverse semigroup is monadic over the category of étale actions. Consequently, the category of unitary actions of an inverse semigroup is equivalent to the category of presheaves on its Cauchy completion. More generally, we prove that the same is true for the category of closed actions, which is used to define the Morita theory in semigroup theory, of any semigroup with right local units.     

Ruin-based risk measures in discrete-time risk models

For an insurance company, effective risk management requires an appropriate measurement of the risk associated with an insurance portfolio. The objective of the present paper is to study properties of ruin-based risk measures defined within discrete-time risk models under a different perspective at the frontier of the theory of risk measures and ruin theory. Ruin theory is a convenient framework to assess the riskiness of an insurance business. We present and examine desirable properties of ruin-based risk measures. Applications within the classical discrete-time risk model and extensions allowing temporal dependence are investigated. The impact of the temporal dependence on ruin-based risk measures within those different risk models is also studied. We discuss capital allocation based on Euler’s principle for homogeneous and subadditive ruin-based risk measures.     

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.