Cliques in Steiner systems

A partial Steiner (k,l)-system is a k-uniform hypergraph with the property that every l-element subset of V is contained in at most one edge of . In this paper we show that for given k,l and t there exists a partial Steiner (k,l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of this note, we establish asymptotic lower and upper bounds on the size of such cliques with respect to the order of Steiner systems. Research of the second author partially supported by NSERC grant OGP0025112.     

Σ<Subscript><Emphasis Type="Italic">n</Emphasis>+1</Subscript>-invariant forms of higher degree

In [EGAWA, Y.—SUZUKI, H.: Automorphism groups of Σ _n+1-invariant trilinear forms, Hokkaido Math. J. 11, (1985), 39–47] are explored Σ _n+1-invariant symmetric trilinear forms and their automorphisms. In the paper we generalize their results to d-linear symmetric forms for any d ≥ 3.      

Universal forcing notions and ideals

Our main result states that a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give some results concerning cardinal characteristics of the σ-ideals determined by those universality parameters. Both authors acknowledge support from the United States-Israel Binational Science Foundation (Grant no. 2002323). Also, we would like to thank the referee for valuable comments and suggestions concerning the exposition of the paper. This is publication 845 of the second author     

Centering Problems for Probability Measures on Finite-Dimensional Vector Spaces

The paper deals with various centering problems for probability measures on finite-dimensional vector spaces. We show that for every such measure, there exists a vector h satisfying μ δ(h)=S(μ δ(h)) for each symmetry S of μ, generalizing thus Jurek’s result obtained for full measures. An explicit form of the h is given for infinitely divisible μ. The main result of the paper consists in the analysis of quasi-decomposable (operator-semistable and operator-stable) measures and finding conditions for the existence of a “universal centering” of such a measure to a strictly quasi-decomposable one.     

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.     

The discrete-continuous model of the one-dimension vibrating mechatronic system

This work presents the analysis of the flexural vibrating one-dimension mechatronic system – the cantilever beam and the piezoelectric transducer bonded with the beam's surface by means of a connection layer. The external RC circuit is adjoined to the transducer's clamps. Dynamic equations of motion of the considered mechatronic system were written down using discrete – continuous mathematical model, taking into consideration the influence of the connection layer and the external electric circuit. The dynamic flexibility of the mechatronic system was assigned on the basis of the approximate Galerkin's method. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pareto memetic algorithm with path relinking for bi-objective traveling salesperson problem

The paper presents an effective version of the Pareto memetic algorithm with path relinking and efficient local search for multiple objective traveling salesperson problem. In multiple objective Traveling salesperson problem (TSP), multiple costs are associated with each arc (link). The multiple costs may for example correspond to the financial cost of travel along a link, time of travel, or risk in the case of hazardous materials. The algorithm searches for new good solutions along paths in the decision space linking two other good solutions selected for recombination. Instead of a simple local search it uses short runs of tabu search based on the steepest version of the Lin–Kernighan algorithm. The efficiency of local search is further improved by the techniques of candidate moves and locked arcs. In the final step of the algorithm the neighborhood of each potentially Pareto-optimal solution is searched for new solutions that could be added to this set. The algorithm is compared experimentally to the state-of-the-art algorithms for multiple objective TSP.