in this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. thena relation between totally fuzzy bounded sets and n-compactness is discussed.finally, a geometric characterization for fuzzy totally bounded sets in i- topologicalvector spaces is derived.

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

We prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of Lie type of bounded rank is bounded. For exceptional groups this solves a longstanding open problem. The proof uses, among other tools, some methods from Geometric Invariant Theory. Using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of L...

1 (t) then the tangent vector ^ T ips direction as can be shown by its dot product with ^ T. Rewriting equation 13 as ^ T (t) = (x 0 (t); y 0 (t)) + (?y 00 (t); x 00 (t))d k ^ Tk + (y 0 (t); ?x 0 (t))k ^ Tk 0 d k ^ Tk 2 and substituting it into ^ T (t) ^ T(t) = " (x 0 (t); y 0 (t)) + (?y 00 (t); x 00 (t))d k ^ Tk + (y 0 (t); ?x 0 (t))k ^ Tk 0 d k ^ Tk 2 # (x 0 (t); y 0 (t)) = (x 0 (t) 2 + y 0 (...