here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.

Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726–736] conjectured that the multirate three-stage Clos network C(n, 2n− 1, r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p1, p2, . . . , pk} where 1 ≥ p1 > p2 > · · · > pk > 0 and pi is an integer multiple of pk, denoted by pk | pi, for 1 ≤ i ≤ k − 1. In this paper,...

A balanced ternary design of order v with block size three, index 2 and P2 = 1 is a collection of multi-subsets of size 3 (of type { x, y, z} or {x, x, y }) called blocks, in which each unordered pair of distinct elements occurs twice possibly in one block and in which each element is repeated in just one block. So there are precisely v blocks of type {x, x, y}. Necessarily v == 0 (mod 3). We d...

the emph{harary index} $h(g)$ of a connected graph $g$ is defined as $h(g)=sum_{u,vin v(g)}frac{1}{d_g(u,v)}$ where $d_g(u,v)$ is the distance between vertices $u$ and $v$ of $g$. the steiner distance in a graph, introduced by chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. for a connected graph $g$ of order at least $2$ and $ssubseteq v(g)$, th...