Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries

The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method called "Anticommutator Technique." Among the wide range of such pairs, the most striking examples are provided on (4k-1)-dimensional spheres, where k > 2. One of these metrics is homogeneous (since it is the metric on the geodesic sphere of a 2-point homogeneous space), while the other is locally inhomogeneous. These examples demonstrate the surprising fact that no information about the isometries is encoded in the spectrum of Laplacian acting on functions. In other words, "The group of isometries, even the local homogeneity property, is lost to the "Non-Audible" in the debate of "Audible versus Non-Audible Geometry"."Comment: 43 pages. After retrieving source, read README file or type tex whole to typeset (in Unix

Induced Dilaton in Topologically Massive Quantum Field Theory

We consider the conformally-invariant coupling of topologically massive gravity to a dynamical massless scalar field theory on a three-manifold with boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl symmetries, this theory induces the target space zero mode of the vertex operator for the string dilaton field on the boundary of the three-dimensional manifold. By a further coupling to topologically massive gauge fields in the bulk, we demonstrate directly from the three-dimensional theory that this dilaton field transforms in the expected way under duality transformations so as to preserve the mass gaps in the spectra of the gauge and gravitational sectors of the quantum field theory. We show that this implies an intimate dynamical relationship between T-duality and S-duality transformations of the quantum string theory. The dilaton in this model couples bulk and worldsheet degrees of freedom to each other and generates a dynamical string coupling.Comment: 26 pages RevTeX, 1 figure, uses epsf.st

Rational blow-downs and smoothings of surface singularities

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are also presented; these include singularities with resolution graph having valency four nodes.Comment: 61 pages, 28 figure

COOPERATIVE MOVEMENTS SETTING EXAMPLE FOR CLASSIC TEAMWORKS OF COUNTRYSIDES IN TRANSYLVANIA

Cooperative movements assured economic welfare of villages, led them to the way of becoming real citizens in the first half of the XXth century. By that period we can say that for improving competitivity advancing coops, and their social role is necessary. In an active coop continuous modernization is needed. This is due to global challenges and multinational companies, and also smaller dominant ones. This is why Hangya cooperative organisations are to be remembered for being the first in the Carpatian basin from the late 19th century. Manufacturers can realize their interests by building their own organizations. This is the cooperation of separate farmers, today dealing with very complicated transnational organizations. Realizing these may be the way to improve livings in the countryside, especially in the agriculture. Joining the following forms of groups is a unique and necessary way to reach these. By this the conclusion is: there must be an integrated network system for production branches controlled by coops with cooperative tenets in Transylvania. For this historical examples of helping farmers remain separate, reach markets must be known and adopted into today’s circumstances.Cooperatives of Transylvania, Judiciary bases, Improving competitiveness, Integrated product channel, Security of income, Community/Rural/Urban Development, Industrial Organization,