A vertex v in an exponential dominating set assigns weight ( 1 2 )dist(v,u) to vertex u. An exponential dominating set of a graph G is a subset of V (G) such that every vertex in V (G) has been assigned a sum weight of at least 1. In this paper the exponential dominating number for the graph Cm × Cn, denoted by γe(Cm × Cn) is discussed. Anderson et. al. [1] proved that mn 15.875 ≤ γe(Cm × Cn) ≤...

In this paper, we consider heterogeneous distributed storage systems (DSSs) having flexible reconstruction degree, where each node in the system has dynamic repair bandwidth and dynamic storage capacity. In particular, a data collector can reconstruct the file at time t using some arbitrary nodes in the system and for an arbitrary node failure the system can be repaired by some set of arbitrary...

Signal to Noise Ratio (SNR) is an important index for wireless communications. There are many methods for increasing SNR. In CDMA systems, spreading sequences are used. To increase SNR, we have to improve spreading sequences. In classical approaches, the expression of SNR is not differentiable in terms of the parameter of the spreading sequences even in no fading situations. Thus, we express it...

Naddef [3] shows that the Hirsch conjecture is true for (0,1)-polytopes by proving that the diameter of any (0, 1)-polytope in d-dimensional Euclidean space is at most d. In this short paper, we give a simple proof for the diameter. The proof is based on the number of solutions generated by the simplex method for a linear programming problem. Our work is motivated by Kitahara and Mizuno [2], in...

T his exposition of linear programming and the simplex method is intended as a companion piece to the article in this issue on the life and work of George B. Dantzig in which the impact and significance of this particular achievement are described. It is now nearly sixty years since Dantzig’s original discovery [3] opened up this whole new area of mathematics. The subject is now widely taught t...