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...

Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in...

In radar and communication applications not only low time sidelobes but also uniform sidelobes are important. Polyphase codes have low sidelobes and are more Doppler tolerant, but correlated sidelobes are not uniform. New filters are modeled in this paper for polyphase codes to reduce the sidelobes and also to generate uniform sidelobes. Uniform sidelobe pattern is useful for detection of weak ...

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

In “A note on a theorem of Erdös & Gallai” ([6]) one identifies the nonredundant inequalities in a characterization of graphical sequences. We explain how this result may be obtained directly from a simple geometrical observation involving weak majorization. A sequence of positive integers d1, d2, . . . , dp is called graphical if it is the degree sequence of a graph, i.e., there is a graph who...

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