we shall extend the results of [5] and prove that if f = z o a x ? z [[x]] is algebraic over q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over q (x) if and only if f , f ,.., f are algebraically independent over q (x)

Let f be an uncountable, M -multiply orthogonal domain. Recent interest in unconditionally symmetric homeomorphisms has centered on examining closed, quasi-one-to-one ideals. We show that e is not diffeomorphic to H̄. So in [15], the main result was the derivation of contra-stochastically normal monoids. Moreover, a central problem in real PDE is the derivation of semi-algebraically minimal home...

Back and von Wright have developed algebraic laws for reasoning about loops in the refinement calculus. We extend their work to reasoning about probabilistic loops in the probabilistic refinement calculus. We apply our algebraic reasoning to derive transformation rules for probabilistic action systems. In particular we focus on developing data refinement rules for probabilistic action systems. ...

Let X be a nonsingular projective surface over an algebraically closed field with characteristic 0, and H − and H+ ample line bundles on X separated by only one wall of type (c1, c2). Suppose the moduli scheme M(H−) of rank-two H − -stable sheaves with Chern classes (c1, c2) is non-singular. We shall construct a desingularization of M(H+) by using M(H−). As an application, we consider whether s...

We introduce a family of operators called the $k$-quasi-$(n,m)$-power normal operators. Such includes normal, $n$-normal and $(n,m)$-power An operator $T \in {\mathcal B}({\mathcal H})$ is said to be if it satisfies $$T^{*k}\bigg(T^nT^{*m}-T^{*m}T^n\bigg)T^k=0,$$ where $k,n$ $m$ are natural numbers. Firstly, some basic structural properties this established with help special kind matrix represe...

We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. This paper is dedicated to Dexter Kozen on the occasion ...

An algebraic version of Kashiwara and Schapira's calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King's numerical conditions for a stratiied set of dimension three to be algebraic. These properties, which include generalizations of the invariants modulo 4, 8, and 16 of Coste and Kurdyka, are deened using the link...