On Completely Integrable Systems with Local Torus Actions

This paper concerns with symplectic topology of compact completely integrable Hamiltonian systems with only stable nondegenerate elliptic singularities. We describe all systems whose universal coverings admit actian-angle coordinates and, in particular, prove that some finite cover of a base space is diffeomorphic to a product of a convex polytope and a solvmanifold. We also construct an obstruction, vanishing of which guarantees splitting of some finite cover of a phase space as a toric variety and a torus fibering over a solvmanifold.     

An algorithm for then×n optimum assignment problem

In this paper we present an algorithm for finding an optimum assignment for ann×n matrixM inn iterations. The method uses systematic permutations on the rows ofM and is based on the properties of optimum assignments. The implementation presented in the paper requires at mostO(n ³) in time andn ²+6n memory locations for solving a densen×n problem.This work was supported by the National Science Foundation Grant NSF ENG 74-19788.     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

A comparison of local search methods for flow shop scheduling

Local search techniques are widely used to obtain approximate solutions to a variety of combinatorial optimization problems. Two important categories of local search methods are neighbourhood search and genetic algorithms. Commonly used neighbourhood search methods include descent, threshold accepting, simulated annealing and tabu search. In this paper, we present a computational study that compares these four neighbourhood search methods, a genetic algorithm, and a hybrid method in which descent is incorporated into the genetic algorithm. The performance of these six local search methods is evaluated on the problem of scheduling jobs in a permutation flow shop to minimize the total weighted completion time. Based on the results of extensive computational tests, simulated annealing is found to generate better quality solutions than the other neighborhood search methods. However, the results also indicate that the hybrid genetic descent algorithm is superior to simulated annealing.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

Quaternionic Starters

Let m be an integer, m 2 and set n = 2^m. Let G be a non-cyclic group of order 2n admitting a cyclic subgroup of order n. We prove that G always admits a starter and so there exists a one–factorization of K_2n admitting G as an automorphism group acting sharply transitively on vertices. For an arbitrary even n > 2 we also show the existence of a starter in the dicyclic group of order 2n.Research performed within the activity of INdAM–GNSAGA with the financial support of the Italian Ministry MIUR, project Strutture Geometriche, Combinatoria e loro Applicazioni     

Systematic Construction of <Emphasis Type="Italic">q</Emphasis>-Analogs of <Emphasis Type="Italic">t</Emphasis>−(<Emphasis Type="Italic">v</Emphasis>,<Emphasis Type="Italic">k</Emphasis>,λ)-Designs

In the present paper we consider a q-analog of t–(v,k,)-designs. It is canonic since it arises by replacing sets by vector spaces over GF(q), and their orders by dimensions. These generalizations were introduced by Thomas [Geom.Dedicata vol. 63, pp. 247–253 (1996)] they are called t –(v,k,;q)- designs. A few of such q-analogs are known today, they were constructed using sophisticated geometric arguments and case-by-case methods. It is our aim now to present a general method that allows systematically to construct such designs, and to give complete catalogs (for small parameters, of course) using an implemented software package. &nbsp; In order to attack the (highly complex) construction, we prepare them for an enormous data reduction by embedding their definition into the theory of group actions on posets, so that we can derive and use a generalization of the Kramer-Mesner matrix for their definition, together with an improved version of the LLL-algorithm. By doing so we generalize the methods developed in a research project on t –(v,k,)-designs on sets, obtaining this way new results on the existence of t–(v,k,;q)-designs on spaces for further quintuples (t,v,k,;q) of parameters. We present several 2–(6,3,;2)-designs, 2–(7,3,;2)-designs and, as far as we know, the very first 3-designs over GF(q).classification 05B05     

Cycle Action on Treelike Structures

The purpose of this paper is to study the action on cycles of several known classes of oligomorphic groups, that is, infinite permutation groups of countable degree having only finitely many orbits on k-sets for each k. The groups studied here are all related to trees and treelike relational structures. The sequence whose k-th term is the number of orbits in the action on k-cycles is called Parker sequence. It turns out that, if we are dealing with the automorphism group of a suitable relational structure, this sequence counts also the finite substructures admitting a cyclic automorphism; in calculating these sequences for various groups, we shall thus describe and enumerate such substructures.Di più dirò: ch’a gli alberi dà vita [I shall say more: the trees are given life spirito uman che sente e che ragiona. by a human spirit that perceives and reasons.Di più dirò: ch’a gli alberi dà vita spirito uman che sente e che ragiona. Per prova sollo; io n’ho la voce udita che nel cor flebilmente anco mi suona.[I shall say more: the trees are given life by a human spirit that perceives and reasons. I know it by experience: I heard their voice and it still resounds faintly in my heart.]Torquato Tasso, Gerusalemme liberata, XIII, 49     

Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes

For a positive integer n, does there exist a vertex-transitive graph Γ on n vertices which is not a Cayley graph, or, equivalently, a graph Γ on n vertices such that Aut Γ is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, Marusic and Scapellato, and McKay and the second author) has produced answers to this question if n is prime, or divisible by the square of some prime, or if n is the product of two distinct primes. In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n = 2pq, where 2 < q < p, and p and q are primes. We give a new construction of an infinite family of vertex-transitive graphs on 2pq vertices which are not Cayley graphs in the case where p ≡ 1 (mod q). Further, if p ? 1 (mod q), p ≡ q ≡ 3(mod 4), and if every vertex-transitive graph of order pq is a Cayley graph, then it is shown that, either 2pq = 66, or every vertex-transitive graph of order 2pq admitting a transitive imprimitive group of automorphisms is a Cayley graph.     

The interaction of an atmospheric pressure plasma jet using argon or argon plus hydrogen peroxide vapour addition with bacillus subtilis

This paper reports that an atmospheric pressure dielectric barrier discharge plasma jet, which uses argon or argon + hydrogen peroxide vapour as the working gas, is designed to sterilize the bacillus subtilis. Compared with the pure argon plasma, the bacterial inactivation efficacy has a significant improvement when hydrogen peroxide vapour is added into the plasma jet. In order to determine which factors play the main role in inactivation, several methods are used, such as determination of optical emission spectra, high temperature dry air treatment, protein leakage quantification, and scanning electron microscope. These results indicate that the possible inactivation mechanisms are the synergistic actions of chemically active species and charged species.