We report here the results of fuzzy term proximity method applied to Terabyte Task. Fuzzy proxmity main feature is based on the idea that the closer the query terms are in a document, the more relevant this document is. With this principle, we have a high precision method so we complete by these obtained with Zettair search engine default method (dirichlet). Our model is able to deal with Boole...

We prove that the decision problem of whether or not a finite semigroup has the representation extension property is decidable. 1. The main theorem and preliminaries It is an immediate consequence of the normal form theorem for amalgamated free products of groups that every amalgam of groups embeds in some group. However, this result fails for semigroup amalgams: an early result of Kimura [6] s...

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold M admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × R, η) admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equ...

It was proved earlier that there are constants M, c > 0 such that for every n M (resp., every n M , n / ≡ 0, 3mod 12) there are at least c2n/6 nonisomorphic nonorientable (resp., orientable) genus embeddings ofKn. In the present paper we show that for s 6 there are at least 2s−6 nonisomorphic OT-embeddings of K12s . As a byproduct, we give a relatively simple method of constructing index four c...

Let p(n) denote the ordinary partition function. In 1966, Subbarao [18] conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N (resp. M) ≡ r (mod t) for which p(N) is even (resp. odd). We prove Subbarao’s conjecture for all moduli t of the form m · 2 where m ∈ {1, 5, 7, 17}. To obtain this theorem we make use of recent results of Ono and Taguchi [14] on ...

In this paper we present embeddings of complete binary trees into butter y networks with or without wrap-around connections. Let m be an even integer and q = m+ blogmc 1. We show how to embed a 2q+1 1-node complete binary tree T (q) into a (m + 1)2m+1node wrap-around butter y Bw(m+1) with a dilation of 4; and how to embed T (q) into a (m+2)2m+2-node wrap-around butter y Bw(m+2) with an optimal ...

A thrackle (resp. generalized thrackle) is a drawing of a graph in which each pair of edges meets precisely once (resp. an odd number of times). For a graph with n vertices and m edges, we show that, for drawings in the plane, m ≤ 32 (n− 1) for thrackles, while m ≤ 2n − 2 for generalized thrackles. This improves theorems of Lovász, Pach, and Szegedy. The paper also examines thrackles in the mor...

In the case when M is an orientable Riemannian manifold of negative curvature L (M) and L(M) are related to the eigenvalue spectrum of M; that is, the set E (M) of all eigenvalues of the Laplace–Beltrami operator acting on L2(M) counted with multiplicities. For example, in this setting it is known that E (M) determines L(M) (see [3]). In the case of closed hyperbolic surfaces, the stronger stat...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...