Let sμ denote a Schur symmetric function and Qα a fundamental quasisymmetric function. Explicit combinatorial formulas are developed for the fundamental quasisymmetric expansions of the plethysms sμ[sν ] and sμ[Qα], as well as for related plethysms defined by inequality conditions. The key tools for obtaining these expansions are new standardization and reading word constructions for matrices. ...

We give here a simple proof of a well-known integral version of Cebyshev inequality. Using the same method, we give a lower bound in the case of increasing functions and then in the case of convex functions. We also establish a result at limit which shows that the constant 1/12 is sharp, in the sense that it cannot be replaced by a smaller one. Subject Classification: 26D15. It is mentioned in ...

Individual investors often invest actively and lose thereby. Social interaction seems to exacerbate the bias toward active trading. In the model here, conversational biases in the social transmission of performance information favor active over passive investment strategies. Senders’ propensity to communicate their returns is increasing in returns. Receivers’ propensity to attend to and be conv...

We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.

In this paper the extension of Hadamard's type inequality for s– convex function and s–convex functions on the coordinates defined in 2-variables and some applications are given.

We shall show that the three variable cubic inequality t(a + b + c) + (t − 2t)(ab + bc + ca) ≥ (2t − 1)(ab + bc + ca) + (3t − 6t + 3t − 6t + 3)abc holds for non-negative a, b, c, and for any real number t. We also show some similar three variable cyclic quartic inequalities.

The left Hermite-Hadamard inequality of several variables for convex functions on certain convex compact sets is proved via elementary approach, independently of Choquet theory.

Frederica de Laguna’s archaeological, ethnohistorical, and ethnographic research has provided us a rich record of the importance of metal, especially copper, to Native Alaskans. This paper provides a brief review of some of de Laguna’s thoughts on metal, its use and time of appearance in far northwestern North America. Additionally, this paper provides a discussion of the relationship between c...