In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

In this paper we consider the cocircuit graph G M of an oriented matroid M, the 1-skeleton of the cell complex W formed by the span of the cocircuits of M. In general, W is not determined by G M. However, we show that if the vertex set resp. edge set] of G M is properly labeled by the hyperplanes resp. colines] of M, G M determines W. Also we prove that, when M is uniform, the cocicuit graph to...

The main purpose of this work is to characterize computably enumerable (c.e.) sets and generalized c.e. sets according to Kolmogorov complexity hierarchy. Given a set A, we consider A m, the initial segment of length m of the characteristic sequence of A. We show that the characteristic sequence of a 2 x-c.e. set can be random in the sense of Martin-LL of. We show that for x n-c.e. sets A, the ...

Based on the idea that the closer the query terms are in a document, the more relevant this document is, we experiment an IR method based on a fuzzy proximity degree of the query term occurences in a document to compute its relevance to the query. Our model is able to deal with Boolean queries, but contrary to the traditional extensions of the basic Boolean IR model, it does not explicitly use ...

Within the algebraic analysis approach to linear systems theory, the purpose of this paper is to study how left Dhomomorphisms between two finitely presented left D-modules associated with two linear systems induce natural transformations on the autonomous elements of the two systems and on the potentials of the parametrizations of the parametrizable subsystems. Extension of these results are a...

Let (Mt)t∈IR+ be a real locally integrable martingale starting from 0, with jumps of height one on a probability space (Ω, (Ft),F∞, P ), with the decomposition M = M c + X − ν, where (M c t )t∈IR+ is the continuous part of (Mt)t∈IR+ , (Xt)t∈IR+ is a point process on IR+ independent of (M c t )t∈IR+ , and (νt)t∈IR+ is the compensator of (Xt)t∈IR+ . Let β =< M c > denote the quadratic variation o...

In this paper, we study the capacity of cognitive networks. We focus on the network model consisting of two overlapping ad hoc networks, called the primary ad hoc network (PaN) and secondary ad hoc network (SaN), respectively. PaN and SaN operate on the same space and spectrum. For PaN (or SaN resp.) we assume that primary (or secondary resp.) nodes are placed according to a Poisson point proce...