Spin Factors as Generalized Hermitian Algebras

We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two. S. Pulmannová was supported by Research and Development Support Agency under the contract No. APVV-0071-06, grant VEGA 2/0032/09 and Center of Excellence SAS, CEPI I/2/2005.     

On the Schröder-Bernstein problem for carathéodory vector lattices

In this note we prove that there exists a Carathéodory vector lattice V such that V ≌ V ³ and V ?V ². This yields that V is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.     

BOUNDARY BEHAVIOR OF CAUCHY-TYPE INTEGRALS IN CLIFFORD ANALYSIS

In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.     

The Relative Transpose over Cohen-Macaulay Finite Artin Algebras

The relative transpose via Gorenstein projective modules is introduced, and some corresponding results on the Auslander-Reiten sequences and the Auslander-Reiten formula to this relative version are generalized.     

完备布尔代数商格的注

本文研究了完备布尔代数L的商格Q(L),建立 L上q-集构成的集合Q′(L)与Q(L)之间的同构,得出了完备布尔代数的商格仍是完备布尔代数,并给出了完备布尔代数范畴的某些性质.     

The simplified methodology for obtaining the Lie algebra structures of nonlinear evolution equations

The technique for obtaining the prolongation structure of differential equations is simplified. This new simplified method is used to obtain the Lie algebra structure of the Burgers–KdV equation.     

Output feedback stabilization for a class of nonlinear time-evolution systems

A variety of problems in nonlinear time-evolution systems such as communication networks, computer networks, manufacturing, traffic management, etc., can be modelled as min–max-plus systems in which operations of min, max and addition appear simultaneously. Systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original nonlinear system in the traditional sense into linear system in this framework. Min-max-plus systems are extensions of max-plus systems and nonlinear even in the max-plus algebra view. Output feedback stabilization for min–max-plus systems with min–max-plus inputs and max-plus outputs is considered in this paper. Max-plus projection representation for the closed-loop system with min–max-plus output feedback is introduced and the formula to calculate the cycle time is presented. Stabilization of reachable systems with at least one observable state and a further result for reachable and observable systems are worked out, during which max-plus output feedbacks are used to stabilize the systems. The method based on the max-plus algebra is constructive in nature.     

Natural examples of Valdivia compact spaces

We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L¹ spaces, Banach lattices and noncommutative L¹ spaces.     

Fourier algebras on locally compact hypergroups

In the present paper we introduce a new definition for the Fourier space A (K) of a locally compact Hausdorff hypergroup K and prove that it is a Banach subspace of B (K). This definition coincides with that of Amini and Medghalchi in the case where K is a tensor hypergroup, and also with that of Vrem which is given only for compact hypergroups. We prove that A_p (K)* = PM_q (K), where q is the exponent conjugate to p, in particular A (K)* = VN (K). Also we show that for Pontryagin hypergroups, A (K) = L²(K) * L²(K) = F (L¹( )), where F stands for the Fourier transform on . Furthermore there is an equivalent norm on A (K) which makes A (K) into a Banach algebra isomorphic with L¹( ). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)