On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

Cohomology of the Orlik–Solomon Algebras and Local Systems

The paper provides a combinatorial method to decide when the space of local systems with nonvanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of Orlik–Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg–Kac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.     

Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.     

Aspects of Poincaré’s Program for Dynamical Systems and Mathematical Physics

This article is mainly historical, except for the discussion of integrability and characteristic exponents in Sect.?2. After summarising the achievements of Henri Poincaré, we discuss his theory of critical exponents. The theory is applied to the case of three degrees-of-freedom Hamiltonian systems in (1:2:n)-resonance (n>4). In addition we discuss Poincaré??s mathematical physics, in particular the theory of partial differential equations, rotating fluid masses and relativity. Attention is given to the priority question of Special Relativity.     

（Co）Homology and Universal Central Extension of Hom-Leibniz Algebras

Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory (such as (co)homology groups, universal central extensions) of Hom-Leibniz algebras based on some works of Loday and Pirashvili.     

Painlevé Property and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.     

Painlev′e Prop erty and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has P...     

Product Systems of C*-correspondences and Baaj—Skandalis Duality

Acta Mathematica Sinica, English Series - Let X = {Xp}]p∈P be a product system over a lattice ordered group (G, P) with coefficients in a C*-algebra $${\cal A}$$ . In this paper, we study the...     

Dynamical Systems in the Variational Formulation of the Fokker—Planck Equation by the Wasserstein Metric

R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the Fokker—Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional, and the Gibbs—Boltzmann entropy functional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker—Planck equation and characterize the limit as a solution to a class of variational problems. Accepted 2 June 2000. Online publication 6 October 2000.     

Koszul–Sullivan Models and the Cohomology of Certain Solvmanifolds

In this paper we develop a technique of working with graded differential algebra models of solvmanifolds, overcoming the main difficulty arising from the non-nilpotency of the corresponding Mostow fibrations. A graded differential model for solvmanifolds of the form G/ with G=RN is presented (N is a nilpotent Lie group, G is a semi-direct product). As an application, we prove the Benson–Gordon conjecture in dimension four.     

Fundamental Theorems of Weak Doi–Hopf Modules and Semisimple Weak Smash Product Hopf Algebras

Abstract

This paper, mainly gives a Fundamental Theorem of weak Doi–Hopf modules, which is not only generalizes the Fundamental Theorem of weak Hopf modules but also generalizes the Fundamental Theorem of relative Hopf modules. Moreover, it gives a sufficient and necessary condition for weak smash product algebras to be weak bialgebras, and a sufficient condition for weak smash product algebras to be semisimple weak Hopf algebras.     

The Exit Problem from a Neighborhood of the Global Attractor for Dynamical Systems Perturbed by Heavy-Tailed Lévy Processes

The concept of filtered counting process is used to model several stochastic problems in manufacturing systems. Through a judicious selection of an appropriate response function, several system characteristics are evaluated under distribution-free condition. Applications include a machine shop problem, a machine sequencing problem, a flexible manufacturing problem, a job sequencing problem, a maintenance problem and an inventory problem. The methodology provides a unique, original and simple way to solve a large array of problems     

On Polynomial Solutions of Generalized Moisil-Théodoresco Systems and Hodge-de Rham Systems

The aim of the paper is to study relations between polynomial solutions of generalized Moisil-Théodoresco (GMT) systems and polynomial solutions of Hodge-de Rham systems and, using these relations, to describe polynomial solutions of GMT systems. We decompose the space of homogeneous solutions of GMT system of a given homogeneity into irreducible pieces under the action of the group O(m) and we characterize individual pieces by their highest weights and we compute their dimensions.     

The Semidirect Product of the Pseudovariety of Groups and the Pseudovariety of R-trivial Semigroups

Ｔｈｅｓｅｍｉｄｉｒｅｃｔｐｒｏｄｕｃｔｃｏｎｓｔｒｕｃｔｉｏｎｃａｍｅｔｏｔｈｅｆｏｒｅｉｎｔｈｅｔｗｅｎｔｉｅｓａｎｄｔｈｉｒｔｉｅｓｉｎｔｈｅｓｔｕｄｙｏｆｇｒｏｕｐｅｘｔｅｎｓｉｏｎ［１］．Ｔｈｅｉｍｐｏｒｔａｎｃｅｏｆｔｈｉｓｃｏｎｓｔｒｕ...     

Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

We prove an algebraic and a topological decomposition theorem for complete pseudo-D-lattices (i.e. lattice-ordered pseudo-effect algebras). As a consequence, we obtain a Hammer–Sobczyk type decomposition theorem for group-valued modular measures defined on pseudo-D-lattices and compactness of the range of every \(\mathbb {R}^{n} \)-valued σ-additive modular measure on a σ-complete pseudo-D-lattice.     

On the Ordered K0‐Group of Universal, Free Product C*‐Algebras

The ordered K₀-group of the universal, unital free product C^*-algebra M_k()*M_l()is calculated in the case where k is prime and not a divisor in l. It is shown that the positive cone of K₀(M_k()*M_l())is as small as possible in this case. The article also contains results (full and partial) on the ordered K₀0-group of more general universal, unital free product C^* algebras.     

Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes

Methodology and Computing in Applied Probability - Let be X(t) = x ? μt + σBt ? Nt a Lévy process starting from x >?0, where μ ≥?0, σ...     

Product of Uniform Distribution and Stirling Numbers of the First Kind

Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.     

Dynamical Behavior in Behavior in Simple and Coupled Systems of Continuous Josephson－Junctions

ＤｙｎａｍｉｃａｌＢｅｈａｖｉｏｒｉｎＢｅｈａｖｉｏｒｉｎＳｉｍｐｌｅａｎｄＣｏｕｐｌｅｄＳｙｓｔｅｍｓｏｆＣｏｎｔｉｎｕｏｕｓＪｏｓｅｐｈｓｏｎ－ＪｕｎｃｔｉｏｎｓＱｉａｎＭｉｎ（钱敏）ＺｈｏｕＳｈｅｎｇｆａｎ（周盛凡）（ＤｅｐａｒｔｍｅｎｏｆＭａ...