On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves

Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.

General Aspects of Constructing an Autonomous Adaptive Agent

There are a great deal of approaches in artificial intelligence, some of them also coming from biology and neirophysiology. In this paper we are making a review, discussing many of them, and arranging our discussion around the autonomous agent research. We highlight three aspect in our classification: type of abstraction applied for representing agent knowledge, the implementation of hypothesis processing mechanism, allowed degree of freedom in behaviour and self-organizing. Using this classification many approaches in artificial intelligence are evaluated. Then we summarize all discussed ideas and propose a series of general principles for building an autonomous adaptive agent.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.