Let S ⊂ (0, 1). Given a known function f : S → (0, 1), we consider the problem of using independent tosses of a coin with probability of heads p (where p ∈ S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed interval and f is real analytic on S, then f has a fast simulation on S (the number of p-coin tosses needed has exponential tails). Conversely, i...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

We investigate notions of randomness in the space C(2N) of continuous functions on 2N. A probability measure is given and a version of the Martin-Löf Test for randomness is defined. Random ∆2 continuous functions exist, but no computable function can be random and no random function can map a computable real to a computable real. The image of a random continuous function is always a perfect set...

We present a method of representing some classes of default theories as normal logic programs. The main point is that the standard semantics (i.e. SLDNF-resolution) computes answer substitutions that correspond exactly to the extensions of the represented default theory. We explain the steps of constructing a logic program LogProg(P,D) from a given default theory (P,D), and present the proof id...

2.1. Basic properties: separation, countability, separability, compactness, connectedness. A space X is Tychonoff if for u, v ∈ X, there exists a neighborhood of u not containing v (and by symmetry a neighborhood of v not containing u). It is Hausdorff if every two points can be separated by disjoint neighborhoods. It is regular if it is Tychonoff and every closed set and point not in the set c...

We define the limiting density of a minor-closed family of simple graphs F to be the smallest number k such that every n-vertex graph in F has at most kn(1+o(1)) edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, well-ordered, and closed; its order type is at least ωω. It is the closure of the set of densities of density-minimal graphs...

Let CD be the category of all continuous domains and all mappings which preserve directed sups and the way-below relation. That is, a mapping f : P → Q is a morphism of CD if and only if f(sup D) = sup f(D) for any directed set D ⊂ P and f(x) œ f(y) if x œ y for any x, y ∈ P . We shall prove that the category CD is cartesian closed. 1991 Mathematics Subject Classification 06B35.

Given a compact topological dynamical system $(X, f)$ with positive entropy and upper semicontinuous map, any closed invariant subset $Y \subset X$ entropy, we show that there exists continuous roof function such the set o