in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

The symbol S( X ) denotes the hyperspace of finite unions convergent sequences in a Hausdor˛ space . This hyper-space is endowed with Vietoris topology. First all, we give characterization sequence ). Then consider some cardinal invariants on ), and compare character, pseudocharacter, sn-character, so-character, network weight cs-network S ( corresponding function Moreover, rank k -diagonal 2 s...

Fractal Brownian motions have been introduced as a statistical description of natural images. We analyze the Gaussian scale-space scaling of derivatives of fractal images. On the basis of this analysis we propose a method for estimation of the fractal dimension of images and scale-space normalisation used in conjunction with automatic scale selection assuming either constant energy over scale o...

ABSTRACT Using techniques from geometric measure theory and descriptive set theory we prove a general result concerning sets in the plane which meet each straight line in exactly two points As an application we show that no such two point set can be expressed as the union of countably many recti able sets together with a set with Hausdor measure zero Also as another corollary we show that no an...

Attempts at extending spline subdivision schemes to operate on compact sets are reviewed The aim is to develop a procedure for ap proximating a set valued function with compact images from a nite set of its samples This is motivated by the problem of reconstructing a D object from a nite set of its parallel cross sections The rst attempt is limited to the case of convex sets where the Minkowski...

This paper concerns the maximum value and the set of maximum points of a random version of Takagi's continuous, nowhere di erentiable function. Let F (x) := ∑∞ n=1 ( 1 2 )n−1 εnφ(2 n−1x), x ∈ R, where ε1, ε2, . . . are independent, identically distributed random variables taking values in {−1, 1}, and φ is the tent map de ned by φ(x) = 2dist (x,Z). Let p := P (ε1 = 1), M := max { F (x) : x ∈ R}...

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

This work demonstrates that the distance measuring the likelihood of the graphs of two functions, usually referred as Hausdor distance between functions and widely used in function approximation tasks and signal processing, can be calculated e ciently using grey scale morphological operations even in the case of noncontinuous (discrete as well as nondiscrete) functions. Also we have presented a...

In this paper we discuss the Erdős-Falconer distance problem. The classical Erdős distance problem in R, d 2, asks for the smallest possible size of (E) = {|x y| : x, y 2 E} with E ⇢ R a finite set. An analogous problem is the Falconer distance problem which asks how large does the Hausdor↵ dimension of a compact set E ⇢ R, d 2, needs to be to ensure that the Lebesgue measure of (E), defined as...

let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.