I present a model in which people develop certain traits (or skills) and also assign worth to those traits. The worth a person assigns to different traits are the person’s values. These values can be used to evaluate one’s own traits and the traits of others. I show that when people are incentivized to place more value on skills for which they are comparatively advantaged, people with lower opp...

In this work, we establish Hölder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. c © 2008 Published by Elsevier Ltd

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; Φ((C) ∫ fdμ) ≤ (C) ∫ Φ(f)dμ, where f is Choquet integrable, Φ : [0,∞) −→ [0,∞) is convex, Φ(α) ≤ α for all α ∈ [0,∞) and μf (α) ≤ μΦ(f)(α) for all α ∈ [0,∞). Furthermore, we give some examples assuring both satisfaction ...

In this paper we prove a quantitative version of the isoperimetric inequality on the sphere with a constant independent of the volume of the set E.

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the continuous Fano inequality established in [DW13, Corollary 1, Propositions 1 and 2], as well as the generalized Fano inequality in [HV94, Equation following (10)].

We show that the Heisenberg groups H 2n+1 of dimension ve and higher, considered as Rieman-nian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area L 2). This implies several important results about isoperimetric inequalities for discrete groups that act either on H 2n+1 or on complex hyperbolic space, and provides interesting ex...

Social stratification, formation of various classes and appearance of various layers in the society is a fact resulting from social conditions of public life and a wide variety of material, economic and subsistence factors as well as political situation, religious beliefs and public customs and thoughts; also ethnic divisions play an essential and undeniable role in this field. Greed and coveto...

We present some recent stability results concerning the isoperimetric inequality and other related geometric and functional inequalities. The main techniques and approaches to this field are discussed.

The traditional solution to the Minkowski problem for polytopes involves two steps. First, the existence of a polytope satisfying given boundary data is demonstrated. In the second step, the uniqueness of that polytope (up to translation) is then shown to follow from the equality conditions of Minkowski’s inequality, a generalized isoperimetric inequality for mixed volumes that is typically pro...