The regional evaluation of monitoring stations for water resources can be of great importance due to its role in finding appropriate locations for stations, the maximum gathering of useful information and preventing the accumulation of unnecessary information and ultimately reducing the cost of data collection. Based on the theory of discrete entropy, this study analyzes the density of rain gag...

Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...

in the restructured environment of electricity market, firstly the generating companies and the customers are looking for maximizing their profit and secondly independent system operator is looking for the stability of the power network and maximizing social welfare. in this paper, a one way auction in the electricity market for the generator companies is considered in both perfect and imperfec...

1.2. Optimal code length for a known source. In the case when PXn (the distribution of X n = (X1, . . . , Xn)) is known and c is arbitrary, minimizing the code length is achieved by sorting A in order of decreasing probabilities. More precisely, let us write A = {bi, i = 1, . . . , d}, where d = |A| is the size of the alphabet and where the blocks of n letters are indexed by order of decreasing...