This paper generalizes the axiomatic approach to the design of income inequality measures to the multiattribute context. While the extension of most axioms considered desirable for inequality indices is straightforward, it is not entirely clear when a situation is more unequal than another when each person is characterised by a vector of attributes of wellbeing. We explore two majorization crit...

In this paper we obtain some majorization results for some classes of multivalent functions defined by certain differential operator. Mathematics subject classification (2010): 30C45.

We show that, in general, inequalities between integrands with respect to Brownian motion do not lead to majorization in the convex order for the corresponding stochastic integrals. Particular examples and counter-examples are discussed.

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

Write |w| = m, the length of w, and |w|1 = card({1 ≤ i ≤ m : wi = 1}) its 1-length. Define the cyclic shift σ : {0, 1}m → {0, 1}m by σ(w1 . . . wm) = w2 . . . wmw1. A cyclic subword of w is any length-q prefix of some σi−1(w), 1 ≤ i, q ≤ m. To any word w = w1 . . . wm we associate its orbit O(w), the vector O(w) = (O1(w), . . . ,Om(w)) consisting of the iterated cyclic shifts w, σ(w), . . . , σ...

Non-convex optimization is ubiquitous in machine learning. The MajorizationMinimization (MM) procedure systematically optimizes non-convex functions through an iterative construction and optimization of upper bounds on the objective function. The bound at each iteration is required to touch the objective function at the optimizer of the previous bound. We show that this touching constraint is u...

Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and seve...

Suppose π = (d1, d2, . . . , dn) and π = (d1, d ′ 2 , . . . , dn) are two positive nonincreasing degree sequences, write π ⊳ π if and only if π 6= π, ∑n i=1 di = ∑n i=1 d ′ i, and ∑j i=1 di ≤ ∑j i=1 di for all j = 1, 2, . . . , n. Let ρ(G) and μ(G) be the spectral radius and signless Laplacian spectral radius of G, respectively. Also let G and G be the extremal graphs with the maximal (signless...

This work was aimed to evaluate and compare the performances of the solvents D2EHPA (Di-(2-ethylhexyl) phosphoric acid), Cyanex 272 (bis (2,4,4-trimethylpentyl) phosphinic acid), and a mixture system of D2EHPA and Cyanex272 in the separation of some rare earth elements (REEs) including lanthanum, gadolinium, neodymium, and dyspersym from a nitric acid solution. The results obtained showed that ...

Given a linear map T on Euclidean Jordan algebra of rank n, we consider the set all nonnegative vectors q in Rn with decreasing components that satisfy pointwise weak-majorization inequality λ(|T(x)|)≺w⁡q∗λ(|x|), where λ is eigenvalue and ∗ denotes componentwise product Rn. With respect to ordering, show existence least vector this set. When positive map, shown be join (in order) T(e) T∗(e), e ...