Knowledge goals are used by reasoning entities to fill in information required for decision making and are an important part of computational understanding systems. Simple knowledge goals can be solved through traditional information retrieval techniques or database queries. In order to solve complex knowledge goals, however, a plan must be composed and executed in an investigative manner. Duri...

This paper outlines a proof of the conjecture that every compact, differentiable, n-dimensional manifold immerses in Euclidean space of dimension 2n - alpha(n), where alpha(n) is the number of ones in the dyadic expansion of n.

In this article we survey known results on geometric and topological obstructions to various important classes of isometric immersions in submanifold theory. In addition we present several related open problems. The main purpose of this article is an invitation for further research on the topics that it deals with.

We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. The geometric lemma underlying these conjectures is a statement about smooth immersions of disks and of certain 2-complexes, capped gropes, in a 4-manifold. We also mention a reformulation in terms of the A − B slice p...

First order invariants of generic immersions of manifolds of dimension nm−1 into manifolds of dimension n(m+1)−1, m, n > 1 are constructed using the geometry of self-intersections. The range of one of these invariants is related to Bernoulli numbers. As by-products some geometrically defined invariants of regular homotopy are found.

Together with the Möbius strip, the Klein bottle is one of the intriguing objects in the universe of geometry, sometimes appearing in non-mathematical contexts too. Until now, several parametrizations of it as a surface immersed in ordinary three-space have been found, some of which are very elegant and lead to nice and well understandable shapes. Nevertheless, these shapes are quite different ...

We extend Witten’s spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension n less than 26 which admit codimension 3 immersions into Euclidean space.

In this paper we emphasize the geometry of affine immersions, widely developed in recent years. Mathematics Subject Classification: 01-02, 01A65.

The paper is devoted to the problems of investigating media text influence on semantic, ethical, aesthetical, and spiritual benchmarks recipients. investigator’s effective tools form creation are presented. Emphasis placed meaningful techniques focused meeting needs demands different social groups, dissemination investigative information, its rhythm scale, determined by nature development funct...