The γ-borel conjecture

In this paper we prove that it is consistent that every -set is countable while not every strong measure zero set is countable. We also show that it is consistent that every strong -set is countable while not every -set is countable. On the other hand we show that every strong measure zero set is countable iff every set with the Rothberger property is countable.Thanks to Boise State University for support during the time this paper was written and to Alan Dow for some helpful discussions and to Boaz Tsaban for some suggestions to improve an earlier version.     

On relations between γ-operations

Let expX be the power set of a non-empty set?X. A function γ:?expX→expX is said to be monotonic iff A?B?X implies γA?γB. Császár?[2] investigated relations between the monotonic functions. The purpose of the paper is to investigate some results concerning particular monotonic functions.     

∗-regularities of γ-rings

A general regularity for weak Nobusawa γ-rings is defined which takes into account the nature of the factor r-rings in this category. The class of

?-regularities is defined and studied. We show that ?-regularities represent only six different algebraic properties for elements of γ-rings. Right (left weak-regularity, Von Neumann-regularity, α-regularity and f-regularity are identified as special cases of ?-regularities. Various characterzations o the different types of regular γ-rings are given. Relationships amongst the operator rings are also, established for the above mentioned regularities     

The γ-connected assignment problem

Given a graph and costs of assigning to each vertex one of k different colors, we want to find a minimum cost assignment such that no color q induces a subgraph with more than a given number (γ_q) of connected components. This problem arose in the context of contiguity-constrained clustering, but also has a number of other possible applications. We show the problem to be NP-hard. Nevertheless, we derive a dynamic programming algorithm that proves the case where the underlying graph is a tree to be solvable in polynomial time. Next, we propose mixed-integer programming formulations for this problem that lead to branch-and-cut and branch-and-price algorithms. Finally, we introduce a new class of valid inequalities to obtain an enhanced branch-and-cut. Extensive computational experiments are reported.     

Alcune caratterizzazioni della γ-convergenza multipla

Summary The main features considered in this paper are characterisations of multiple -convergence in the saddle function case and in the general case. The main results for saddle case are theorems II.1.1 II.1.2 II.2.1 III.3.3 III.3.4and for general case theorem IV.1.2. In the fifth section we introduce vF-convergence and give equivalence results between vF.

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Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

HAMILTONIAN DECOMPOSITION OF COMPLETE BIPARTITE γ-HYPERGRAPHS

1. IntroductionHypergraphs are most general structure in discrete mathematics. Computer scientistsintroduced the concept of acyclic hypergraphs and proved that acyc1ic hypergraphs are veryuseful in database theory['--']. In [l], a new system of axioms fOr paths, connectivity andcycles of hypergraphs was introduced. In this paper, we wiIl introduce the concepts ofbipartite hypergraphs and Hamiltonian paths and cycles of a hypergraph.Let V be a finite set. n = (V e) is called a hypergraph on …     

Galois Module Structure and the γ-Filtration

We describe a general method for calculating equivariant Euler characteristics. The method exploits the fact that the -filtration on the Grothendieck group of vector bundles on a Noetherian quasi-projective scheme has finite length; it allows us to capture torsion information which is usually ignored by equivariant Riemann–Roch theorems. As applications, we study the G-module structure of the coherent cohomology of schemes with a free action by a finite group G and, under certain assumptions, we give an explicit formula for the equivariant Euler characteristic in the Grothendieck group of finitely generated Z[G]-modules, when X is a curve over Z and G has prime order.     

Constructive characterizations of （γp, γ）- and （γp, γpr）-trees

Let G =(V,E) be a graph without isolated vertices.A set S  V is a domination set of G if every vertex in V -S is adjacent to a vertex in S,that is N[S] = V .The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S  V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S]has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S  V is a power domination set of G if all vertices of V can be observed recursively by the following rules:(i) all vertices in N[S] are observed initially,and(ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed(by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively.     

Applications of the γ*-Relation to Polygroups

The γ*-relation was introduced by Freni. In this article, we use the γ*-relation in a given polygroup. In this way, the γ*-relation is the smallest equivalence relation on a polygroup P such that P/γ* is an abelian group. Results are obtained on extension polygroups, derived hypergroups, γ-parts, and semi-direct hyperproduct.     

Generalized γ-Valid Cut Procedure for Concave Minimization

The concept of a -valid cutting plane has been used in many types of algorithms for solving concave minimization problems. Unfortunately, the procedures proposed to date for constructing these cuts are valid only under certain assumptions that often may not hold in practice. Chief among these is the requirement that the feasible region of the concave minimization problem in question have full dimension, and that the objective function of this problem be concave rather than quasiconcave. In this article, we propose, validate, and show how to implement a more general -valid cutting plane procedure which eliminates these restrictions.     

Constructive characterizations of （γp, γ）- and （γp, γpr）-trees

Let G = （V, E） be a graph without isolated vertices. A set S lohtain in V is a domination set of G if every vertex in V - S is adjacent to a vertex in S, that is N[S] = V. The domination number of G, denoted by γ（G）, is the minimum cardinality of a domination set of G. A set S lohtain in V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching. The paired-domination number, denoted by γpr（G）, is defined to be the minimum cardinality of a paired-domination set S in G. A subset S lohtain in V is a power domination set of G if all vertices of V can be observed recursively by the following rules： （i） all vertices in N[S] are observed initially, and （ii） if an observed vertex u has all neighbors observed except one neighbor v, then v is observed （by u）. The power domination number, denoted by γp（G）, is the minimum cardinality of a power domination set of G. In this paper, the constructive characterizations for trees with γp=γ and γpr = γp are provided respectively.     

Partial γ-positivity for quasi-Stirling permutations of multisets

We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial γ-positive, thereby confirming a recent conjecture posed by Lin, Ma and Zhang. This is accomplished by proving the partial γ-positivity of the enumerative polynomials of certain ordered labeled trees, which are in bijection with quasi-Stirling permutations of multisets. As an application, we provide an alternative proof of the partial γ-positivity of the enumerative polynomials on Stirling permutations of multisets.     

Coderivative Conditions for Error Bounds of γ-paraconvex Multifunctions

In this paper, error bounds for ??-paraconvex multifunctions are considered. Characterizations of a ??-paraconvex multifunction are given. In terms of normal cone and coderivative, some results on the existence of error bounds are presented.     

A generalization of semi prime indeals in γ-rings

The purpose of this paper is to generalize the concept of semi prime ideals in Γ-rings. We use a general definition of a regularity F for Γ-rings to define and F- prime ideal. Relationships between F-semi prime ideals of a Γ-ring M and F-semi prime ideals of the operator rings R and L are discussed. D-regularity, f-regularity and λ-regularity for Γ-rings are introduced and studied against the background of the concept F-semi prime ideal. Finally, D-, λ- and f-regular Γ-rings are characterized.     

Control of biopolymer poly-β-hydroxybutyrate characteristics by γ-irradiation

The influence of γ-irradiation on the structure and some mechanical properties of poly-β-hydroxybutyrate was studied. Specimens of PHB were γ-irradiated with various doses (1–20 Mrad) in air and vacuum. The molecular weight, structural characteristics of the crystalline and amorphous phases, characteristics of thermal degradation, and deformation of the polymer were determined. The crystallinity was found to increase with increase in the radiation dose and with the corresponding reduction in molecular weight. The increase of crystallinity was the greater the smaller the length of macromolecules (higher radiation dose). The melting temperature T _m , which characterizes the crystalline order, decreased with decrease in the molecular weight. The results of calorimetric studies suggest that radiation-caused degradation, which occurs at a temperature at which “cold” crystallization (60°C) is possible, might also affect the crystalline part of the polymer.     

Some properties of the psi function and evaluations of γ

In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function,the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler's constant γ.