In this article, we study the problem of finding the next-to-shortest path in circular-arc graph. A next-to-shortest path between any pair of vertices in a shortest path amongst all paths between those vertices with length strictly greater than the length of the shortest path. The next-to-shortest path problem in a directed graph in NP-hard. Here we deigned a polynomial time algorithm to solve ...

Let z1, . . . , zN be complex numbers situated on the unit circle |z| = 1, and write S := z1 + · · · + zN . Generalizing a well-known lemma by Freiman, we prove the following. (i) Suppose that any open arc of length φ ∈ (0, π] of the unit circle contains at most n of the numbers z1, . . . , zN . Then |S| ≤ 2n−N + 2(N − n) cos(φ/2). (ii) Suppose that any open arc of length π of the unit circle c...

The propagation of local arcs are necessary for a flashover to occur on an ice-covered insulator. It was supposed that the local AC arc extended when it satisfied the arc re-ignition conditions. In this paper an attempt has been made to model Va = f ( I , L , x ) for estimating the arc re-ignition conditions as function of leakage current and insulator length using multi-layer feed-forward neur...

We classify the sets of four lattice points that all lie on a short arc of a circle which has its center at the origin; specifically on arcs of length tR on a circle of radius R, for any given t > 0. In particular we prove that any arc of length ( 40 + 40 3 √ 10 )1/3 R on a circle of radius R, with R > √ 65, contains at most three lattice points, whereas we give an explicit infinite family of 4...

the hotelling's  control chart, is the most widely used multivariate procedure for monitoring  two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. recently, the variable sampling intervals (vsi) control scheme in which the length of successive sampling intervals is determined upon the preceding values has been pro...