Concave envelopes of monomial functions over rectangles

2004 ◽  
Vol 51 (4) ◽  
pp. 467-476 ◽  
Author(s):  
Harold P. Benson
Keyword(s):  
Concave Envelopes ◽  
Monomial Functions

scholarly journals On the Jensen convex and Jensen concave envelopes of means

2020 ◽  
Author(s):  
Zsolt Páles ◽  
Paweł Pasteczka
Keyword(s):  
Quasiarithmetic Means ◽  
Concave Envelopes

Abstract In recent papers, the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper concave quasiarithmetic envelope.

scholarly journals Determinantal Expression and Recursion for Jack Polynomials

10.37236/1539 ◽  
1999 ◽  
Vol 7 (1) ◽  
Author(s):  
Luc Lapointe ◽  
A. Lascoux ◽  
J. Morse
Keyword(s):  
Schur Functions ◽  
Jack Polynomials ◽  
Efficient Computation ◽  
Monomial Basis ◽  
Determinantal Formula ◽  
Kostka Numbers ◽  
Determinantal Expression ◽  
Monomial Functions

We describe matrices whose determinants are the Jack polynomials expanded in terms of the monomial basis. The top row of such a matrix is a list of monomial functions, the entries of the sub-diagonal are of the form $-(r\alpha+s)$, with $r$ and $s \in {\bf N^+}$, the entries above the sub-diagonal are non-negative integers, and below all entries are 0. The quasi-triangular nature of these matrices gives a recursion for the Jack polynomials allowing for efficient computation. A specialization of these results yields a determinantal formula for the Schur functions and a recursion for the Kostka numbers.

A characterization of monomial functions

1997 ◽  
Vol 54 (1-2) ◽  
pp. 289-307 ◽  
Author(s):  
Attila Gilányi
Keyword(s):  
Monomial Functions

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes

2004 ◽  
Vol 29 (2) ◽  
pp. 125-155 ◽  
Author(s):  
Clifford A. Meyer ◽  
Christodoulos A. Floudas
Keyword(s):  
Concave Envelopes
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