Equivalence Groups for First-Order Balance Equations and Applications to Electromagnetism

We investigate the groups of equivalence transformations for first-order balance equations involving an arbitrary number of dependent and independent variables. We obtain the determining equations and find their explicit solutions. The approach to this problem is based on a geometric method that depends on Cartan's exterior differential forms. The general solutions of the determining equations for equivalence transformations for first-order systems are applied to a class of the Maxwell equations of electrodynamics.     

Wreath Products and Universal Equivalence

We consider the question of preservation of universal equivalence for the cartesian and direct wreath products of lattice-ordered groups and groups. We prove that the basic rank is infinite of the quasivariety of torsion-free nilpotent groups of nilpotence length c (c2)     

On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes

Abstract For the multidimensional ARMA system A(z)y_k=C(z)w_k it is shown that stability(det A(z)≠0,z:│z│≤1)of A(z) is equivalent to the trajectory boundedness in the mean square sense(MSS)which,as a rule,is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAXsystem to a steady state ARMA system.In comparison with existing results the stability condition imposed onC(z)is no longer needed.The only structural requirement on the system is that det A(z) and det C(z) have nounstable common factor.     

Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

Basis Problem for Turbulent Actions II: c0-Equalities

Let (Xⁿ,dⁿ) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c₀-equality.A systematic study is made of c₀-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics d_n, are obtainedfor a c₀-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c₀-equality D either reducesa c₀-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c₀-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c₀-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15.     

Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.     

Linear algebraic groups and countable Borel equivalence relations

If is an equivalence relation on a standard Borel space , then we say that is Borel reducible to if there is a Borel function such that . An equivalence relation on a standard Borel space is Borel if its graph is a Borel subset of . It is countable if each of its equivalence classes is countable. We investigate the complexity of Borel reducibility of countable Borel equivalence relations on standard Borel spaces. We show that it is at least as complex as the relation of inclusion on the collection of Borel subsets of the real line. We also show that Borel reducibility is -complete. The proofs make use of the ergodic theory of linear algebraic groups, and more particularly the superrigidity theory of R. Zimmer.

     

求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

函数两种凸性定义等价性的今惑前世之初探

通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.     

Approximation of titration curves and other sigmoidal functions by proportionally spaced cubic B-splines

Proportionally spaced cubicB-splines are an appropriate function system for the approximation of titration curves and other sigmoidal functions. They give a smooth weighted leastsquares fit without instability problems. The degree of smoothing depends only on the number of spline function which can be chosen by the user. The equivalence points of titration curves can be estimated with high accuracy from the zeros of the second derivative.The method gives good approximation curves even in the case of empty data regions, i. e. there are no artefacts in subranges where no data points exist. The routine has been tested successfully with large series of simulated and experimental data.