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.

     

基于选择性支持向量机集成的混沌时间序列预测

提出了一种基于聚类的选择性支持向量机集成预测模型.为提高支持向量机集成的泛化能力，采用自组织映射和K均值聚类算法结合的聚类组合算法，从每簇中选择出精度最高的子支持向量机进行集成，可以保证子支持向量机有较高精度并提高了子支持向量机之间的差异度.该方法能以较小的代价显著提高支持向量机集成的泛化能力.采用该方法对Mackey-Glass混沌时间序列和Lorenz系统生成的混沌时间序列进行预测实验，结果表明可以对混沌时间序列进行准确预测，验证了该方法的有效性. 关键词： 支持向量机 集成 混沌时间序列 聚类     

Relative difference sets,graphs and inequivalence of functions between groups

For cryptographic purposes, we want to find functions with both low differential uniformity and dissimilarity to all linear functions and to know when such functions are essentially different. For vectorial Boolean functions, extended affine equivalence and the coarser Carlet–Charpin–Zinoviev (CCZ) equivalence are both used to distinguish between nonlinear functions. It remains hard to tell when CCZ equivalent functions are EA‐inequivalent. This paper presents a framework for solving this problem in full generality, for functions between arbitrary finite groups. This common framework is based on relative difference sets (RDSs). The CCZ and EA equivalence classes of perfect nonlinear (PN) functions are each derived, by quite different processes, from equivalence classes of splitting semiregular RDSs. By generalizing these processes, we obtain a much strengthened formula for all the graph equivalences which define the EA equivalence class of a given function, amongst those which define its CCZ equivalence class. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 260–273, 2010     

Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux

We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions.