The Sylvester equation and its particular case, the Lyapunov equation, are widely used in image processing, control theory, stability analysis, signal model reduction, many more. We present basis-free solution to Clifford (geometric) algebra of arbitrary dimension. solutions involve only operations product, summation, conjugation. To obtain results, we use concepts characteristic polynomial, de...

The present paper is a continuation of the previous publication by author in this journal devoted to cultural-symbolic world picture Latin Christian Middle Ages. Unlike one, second text reproduces historical “picture” era with an emphasis not on ontological, but its proper cultural expression. as philosopher so much focused “fact” (this business historians) “meaning”, taking care meaningful mod...

Perception and action are the result of an integration of various sources of information, such as current sensory input, prior experience, or the context in which a stimulus occurs. Often, the interpretation is not trivial hence needs to be learned from the co-occurrence of stimuli. Yet, how do we combine such diverse information to guide our action? Here we use a distance production-reproducti...

we need sociology theories, for that understand of sociology and politic problems. french sociologist pierre bourdieu's theory practice and symbolic power are our best resource; for understanding social and political fields. this article reviews the language and symbolic power; indicating its function in social and political fields. we need sociology theories, for that understand of sociol...

We discuss changing the variable ordering for a regular chain in positive dimension. This quite general question has applications going from implicitization problems to the symbolic resolution of some systems of differential algebraic equations. We propose a modular method, reducing the problem to dimension zero and using Newton-Hensel lifting techniques. The problems raised by the choice of th...

Knots are obtained by embedding a circle in R. Pictures and handicrafts of knots have appeared in ancient Chinese art several hundred years B.C. The first systematic study of knots though started in the 19th century by a Scottish physicist Peter Guthrie Tait who classified all knots to 10 crossings and made several important conjectures about knots (the most recent of these conjectures is prove...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

A particularly simple and mathematically elegant example of chaos in a threedimensional flow is examined in detail. It has the property of cyclic symmetry with respect to interchange of the three orthogonal axes, a single bifurcation parameter that governs the damping and the attractor dimension over most of the range 2 to 3 (as well as 0 and 1) and whose limiting value b = 0 gives Hamiltonian ...