Let n be a positive integer. We may write (or split) n as sums of n nonincreasing nonnegative integers p1, p2, . . . , pn in different ways (or partitions; see Section 2). For example, 3 = 3 + 0 + 0 = 2 + 1 + 0 = 1 + 1 + 1. If we denote by P (n) the number of different partitions of n, then P (3) = 3. One may check that P (5) = 7. As n gets large, P (n) increases rapidly. It is astounding that ...

Optimal power allocation for maximizing the sum capacity of multiple access channel (MAC) with quality-of-service (QoS) constraints is investigated in this paper. Majorization theory is the underlying mathematical theory on which our method hinges. It is shown that the optimal structure of the solution can be easily obtained via majorization theory. Furthermore, based on our new approach, an ef...

In this paper, we obtain Markovian bounds on a function of a homogeneous discrete time Markov chain. For deriving such bounds, we use well known results on stochastic majorization of Markov chains and the Rogers-Pitman’s lumpability criterion. The proposed method of comparison between functions of Markov chains is not equivalent to generalized coupling method of Markov chains although we obtain...

We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable...

 In this paper, we study stochastic comparisons of order statistics of independent random variables with proportional hazard rates, using the notion of variance majorization.

The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...