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...

This paper presents a management process for creating adaptive, real-time security policies within the Six Sigma 6σ framework. A key challenge for the creation of a management process is the integration with models of known Industrial processes. One of the most used industrial process models is Six Sigma which is a business management model wherein customer centric needs are put in perspective ...

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...

Spo0A, a classical two-component-type response regulator in Bacillus subtilis, binds to a specific DNA sequence found in many promoters to repress or activate the transcription of over 100 genes. On the spoIIG promoter, one of the Spo0A binding sites, centered at position -40, overlaps a consensus -35 element that may also interact with region 4 of the sigma A (sigma(A)) subunit of RNA polymera...

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...

The notion of a prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares these prolongation spaces with algebraic jet spaces is introduced and studied.

Abstract Let $Q$ be a bipartite quiver, $V$ real representation of $Q$, and $\sigma $ an integral weight orthogonal to the dimension vector $V$. Guided by quiver invariant theoretic considerations, we introduce Brascamp–Lieb (BL) operator $T_{V,\sigma }$ associated $(V,\sigma )$ study its capacity, denoted $\textbf{D}_Q(V, \sigma )$. When is $m$-subspace capacity data intimately related BL cons...

Let A be an abelian variety over the function field K of a compact Riemann surface B. Fix model $$f :{\mathcal {A}} \rightarrow B$$ A/K and effective horizontal divisor $${\mathcal {D}}\subset {\mathcal {A}}$$ . We give sufficient condition on {D}}$$ for finiteness set $$(S, {D}})$$ -integral sections every finite subset $$S \subset These integral $$\sigma $$ are algebraic satisfy geometric ( \...