Torsion units in integral group rings of metacyclic groups

It is proved that if G is a split extension of a cyclic p-group by a cyclic p′-group with faithful action then any torsion unit of augmentation one of $\text{Z}$G is rationally conjugate to a group element. It is also proved that if G is a split extension of an abelian group A by an abelian group X with (|A|, |X|) = 1 then any torsion unit of $\text{Z}$G of augmentation one and order relatively prime to |A| is rationally conjugate to an element of X.     

A theoretical analysis of acoustic microscopy with converging acoustic beams

A theoretical analysis is carried out to synthesize acoustic material signatures (AMS) of solid plates immersed in water. The distinctive feature of this analysis is that it avoids three major simplifying assumptions of the presently available techniques, which are, paraxial approximation, assumption of perfect reflection and Gaussian summation of the incident field. Presently available techniques can avoid some but not all of these simplifying assumptions for computing the AMS. In this paper the analysis is carried out for lowfrequency acoustic waves generated by a cylindrical transducer without a lens rod. Reasons for these changes in the conventional acoustic microscope geometry is given. The AMS is synthesized for an aluminium plate in presence as well as in absence of water on its one side. As expected a significant difference is observed between the signatures generated under these two situations.     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.     

Properties of quantum Markovian master equations

In this paper we give an essentially self-contained account of some general structural properties of the dynamics of quantum open Markovian systems. We review some recent results regarding the problem of the classification of quantum Markovian master equations and the limiting conditions under which the dynamical evolution of a quantum open system obeys an exact semigroup law (weak coupling limit and singular coupling limit). We discuss a general form of quantum detailed balance and its relation to thermal relaxation and to microreversibility.     

Extreme affine transformations

We classify the extreme points of the compact convex set of affine maps of IR ⁿ which map into itself the closed unit ball. This work is a preliminary step towards solving the problem of finding the extreme points of the compact convex set of affine maps of theN×N density matrices (dynamical maps of anN-level system) and forn=3 furnishes the solution of the problem in the simplest case of a two-level system.The bulk of this work was performed while the first author was visiting the Center for Particle Theory of the University of Texas at Austin under the partial support of the U.S.A.E.C. under contract ORO-(40-1) 3992. A travel grant under the Fulbright-Hays program is acknowledged.     

Gauge independence and unitarity in the Weinberg unified theory

We formulate the Weinberg theory with the help of the Lagrangian multiplier formalism. A new fictitious Lagrangian is obtained, which differs from the usual one. We show by explicit calculation that it restores unitarity and gauge independence of the theory.     

A factorization theorem for a certain class of graphs

In this note we give a necessary and sufficient condition for factorization of graphs satisfying the “odd cycle property”. We show that a graph G with the odd cycle property contains a [k_i] factor if and only if the sequence [H]+[k_i] is graphical for all subgraphs H of the complement of G.A similar theorem is shown to be true for all digraphs.     

Bounds on the number of disjoint spanning trees

It is shown that an n-edge connected graph has at least ?$\text{(n ? 1)}\text{2}$? pairwise edge-disjoint spanning trees. This bound is best possible in general. A maximal planar graph with four or more vertices contains two edge-disjoint spanning trees. For a maximal toroidal graph, this number is three.     

The superfluid vacuum state,time-varying cosmological constant,and nonsingular cosmological models

Some cosmological consequences of the superfluid vacuum state developed previously by the authors are discussed, particularly with regard to the initial stages of the universe. The transition temperature of the hadronic superfluid (superfluid during the hadron era) is estimated to be 10 ¹³ K, which is the same as the Hagedorn temperature, giving a physical basis of the thermodynamic bootstrap model.