On Constantive Simple and Order-Primal Algebras

A finite algebra is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order ≤ on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; ≤). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras.* Research supported by the Hungarian research grant No. TO34137 and by the János Bolyai grant.** Research supported by the Thailand Research Fund.     

On the existence of positive solutions of second order differential equations

Using the fixed point method we prove an existence result for positive solutions of nonlinear second order ordinary differential equations. An application to semilinear Schrödinger equations in exterior domains is also presented. Mathematics Subject Classification (2000) 34C10     

New Rosenbrock W-Methods of Order 3 for Partial Differential Algebraic Equations of Index 1

In this note new Rosenbrock methods for ODEs, DAEs, PDEs and PDAEs of index 1 are presented. These solvers are of order 3, have 3 or 4 internal stages, and fulfil certain order conditions to obtain a better convergence if inexact Jacobians and approximations of are used. A comparison with other Rosenbrock solvers shows the advantages of the new methods. AMS subject classification (2000) 34A09, 65L80     

Markov inequalities on partially ordered spaces

Let X(ω) be a random element taking values in a linear space $\text{X}$ endowed with the partial order ≤; let $\text{G}$₀ be the class of nonnegative order-preserving functions on $\text{X}$ such that, for each g∈$\text{G}$₀, E[g(X)] is defined; and let $\text{G}$₁?$\text{G}$₀ be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf_$\text{G}$0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf_$\text{G}$1E[g(X)]/g(x) ≤ inf_$\text{G}$1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability.     

Group decisions I. In arbitrary spaces of fuzzy binary relations

This article solves the problem of finding a set of group decisions that satisfy the classical Pareto unanimity principle for the case of initial data represented as fuzzy relations of individual preference. The solution proceeds from results obtained in studying the structure of convex (in the sense defined here) sets and their convex hulls. In the first part that study is carried out for spaces of arbitrary fuzzy binary relations.     

The extendible cell method for closest point problems

The extendible cell method is an application of order preserving extendible hashing to multidimensional point files. We derive some of its performance characteristics and show its expected case optimality for closest point problems.     

一类三阶非线性分布时滞动力方程的振动结果

研究一类三阶非线性分布时滞动力方程的振动性,通过构造广义Riccati变换得到一类新的广义Riccati不等式,利用积分平均技巧等方法,建立了保证该方程一切解均振动或收敛于0的若干新的振动结果,推广和改进了近期文献的相关结论,并给出了若干例子。     

Study of orientational order in a nematic polysiloxane by utilizing the “guest–host” effect

A nematogenic side-chain polysiloxane is investigated by means of absorption and fluo-rescence spectroscopy.4-Dimethylamino-4′-nitrostilbene (DANS) is dissolved in the poly-meric matrix as a guest probe. The orientational order and the molecular distribution function have been determined from measurements of polarized absorption and fluorescence spectra. It has been found that fluorescence spectroscopy affords a method for determination of the phase transition temperatures of liquid–crystalline polymers. © 1993 John Wiley & Sons, Inc.