the aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. in this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. in particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. finally, dimension of a fuzzy hypervector space isdefined and the basi...

To date, the tightest upper and lower-bounds for the active learning of general concept classes have been in terms of a parameter of the learning problem called the splitting index. We provide, for the first time, an efficient algorithm that is able to realize this upper bound, and we empirically demonstrate its good performance.

The Extensible Authentication Protocol (EAP) provides a standard mechanism for support of various authentication methods. This document defines the Command-Codes and AVPs necessary for a Diameter Hiller & Zorn [Page 1] INTERNET-DRAFT Diameter EAP Application June 2002 node to support the PPP Extensible Authentication Protocol (EAP). 1. Conventions used in this document The key words "MUST", "MU...

In a generalized Maker-Breaker positional game, Maker and Breaker play in turns. Maker makes a moves in each turn and Breaker makes b moves in each turn. We choose Maker to be the first player, although this nearly always makes no difference in the outcome of the game. We call such games (a : b)-games. If a = b, the game is fair, otherwise it is biased. If a = b > 1, the game is accelerated. In...

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a continues region (Imprecise model) or a finite set of points (Indecisive model). Given a set of inexact points in one of Imprecise or Indecisive models, we wish to provide a lower-bound on the diameter...

A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly increases the diameter. In this paper, we prove several results related to a conjecture often attributed to Murty and Simon, regarding the maximum number of edges that any diameter-k-critical graph can have. In particular, we disprove a longstanding conjecture of Caccetta and Häggkvist (that in ever...

Let G be a connected graph of order n. The diameter of a graph is the maximum distance between any two vertices of G. In this paper, we will give some bounds on the diameter of G in terms of eigenvalues of adjacency matrix and Laplacian matrix, respectively.

Given an edge-weighted undirected graph G = (V,E, c, w), where each edge e ∈ E has a cost c(e) and a weight w(e), a set S ⊆ V of terminals and a positive constant D0, we seek a minimum cost Steiner tree where all terminals appear as leaves and its diameter is bounded by D0. Note that the diameter of a tree represents the maximum weight of path connecting two different leaves in the tree. Such p...

The main result of the paper is to prove for every r ≥ 0 and n > n0(r) that every antichain on n vertices and consisting of more than ( n r ) sets contains two members whose symmetric difference is at least 2r + 2. The bound is best possible and all the extremal families are determined. For r ≥ 3 we show that n > 6(r + 1)2 is sufficient.

By Margulis’ result, in our setting diameter and injectivty radius are inversely related. Thus, our theorem can also be viewed as a lower bound on injectivity radius; that is, with the above hypothesis, inj(M) > 1 R(l(P )) . It is known that that infinitely many closed, hyperbolic 3-manifolds of volume less than a given upper bound may be obtained by hyperbolic Dehn surgery on a finite list of ...