1.1. Principal G-bundles. Topology is concerned with topological spaces and continuous maps between them. But the data is a topological space of so complicated and infinite in nature that it can be very difficult even to tell when two topological spaces are “the same.” For instance, all n-dimensional manifolds look locally the same. A central theme in algebraic topology is to attach algebraic i...

We study a family of the generalized principal series and obtain necessary and sufficient conditions under which the induced representation of studied form contains a discrete series subquotient. Furthermore, we show that if the generalized principal series which belongs to the studied family has a discrete series subquotient, then it has a discrete series subrepresentation.

On 2005, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy setsto neutrosophic sets. Also, this author and some co-workers introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. We study in this paper relations between i...

R.Devi, K.Balachandran and H.Maki, Generalized α-closed maps and α-generalized closed maps, Indian J. Pure.Appl.Math, 29(1)(1998),37-49. R.Devi, K.Bhuvaneshwari and H.Maki, Weak form on gr-closed sets, where rÎ{a,a*,a**} and the digital plane, Mem. Fac. Sci. Kochi Univ. (Math.), Vol.25(2004), 37-54. R.Devi, S.N.Rajappriya, K.Muthukumaraswamy and H.Maki, -closed sets in topological spaces and d...

Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group AX, natural with respect to pullbacks. These classes are analogous to topological characteristic classes (which take values in cohomology), and two ...

The reasons of the crisis in the contemporary (Riemannian) geometry are discussed. The conventional method of the generalized geometries construction, based on a use of the topology, leads to a overdetermination of the Riemannian geometry. In other words, at the Riemannian geometry construction one uses the needless information (topology), which disagrees with other original axioms. The crisis ...

A generalized autoassociator model for face processing and sex categorization: From principal components to multivariate analysis. ABSTRACT In this paper we propose a generalized version of the classical linear au-toassociator that can be shown to implement a generalized least-squares approximation under linear constraints. The standard linear autoassociator is known to implement principal comp...