The primary intent of the present paper is to adapt familiar notions of algebraic topology, such as the fundamental group, homology, and cohomology to the context of algebraic maps and their (ramified) covering projections. The notion of a principal derived map is already fairly well understood in terms of the defining voltages; however, once it is recognized that voltages are essentially cohom...

This paper outlines the formal representation of the environment in which it is assumed that a wayfinding process has been occurred through a street network. Wayfinding is a process in which people navigate themselves from an origin to a destination by their common sense geospatial knowledge. Naı̈ve Geography is a field of study that investigates the body of knowledge that people have about the ...

We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let Z be a real algebraic variety. We say that Z is generic if there exist a finite family {Di}i=1 of irreducible real algebraic curves with genus ≥ 2 and a biregular embedding of Z into the product variety Qn i=1 Di. A bijective map φ : e Z −→ Z from a real algebraic variety e Z to...

A natural numberm is called a minimal period of a map f if f m has a fixed point which is not fixed by any earlier iterates. One important device for studying minimal periods are the integers im( f )= ∑ k/m μ(m/k)L( f k), where L( f k) denotes the Lefschetz number of f k and μ is the classical Möbius function. If im( f ) = 0, then we say that m is an algebraic period of f . In many cases the fa...

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational algebraic geometry. The Euclidean distance degre...

For projectivizations of rational maps Bellon and Viallet defined the notion of algebraic entropy using the exponential growth rate of the degrees of iterates. We want to call this notion to the attention of dynamicists by computing algebraic entropy for certain rationalmaps of projective spaces (Theorem6.2) and comparing it with topological entropy (Theorem 5.1). The particular rational maps w...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...