We characterize the planar central configurations of the 4body problem with masses m1 = m2 ̸= m3 = m4 which have an axis of symmetry. It is known that this problem has exactly two classes of convex central configurations, one with the shape of a rhombus and the other with the shape of an isosceles trapezoid. We show that this 4-body problem also has exactly two classes of concave central configu...

In this paper we investigate the similarity solutions of a plane mixed convection boundary layer flow near a semi-vertical plate, with a prescribed power law function of the distance from the leading edge for the temperature, that is embedded in a porous medium. We show the existence and uniqueness of convex and concave solutions for positive values of the power law exponent.

We use entropy rates and Schur concavity to prove that, for every integer k ≥ 2, every nonzero rational number q, and every real number α, the base-k expansions of α, q + α, and qα all have the same finite-state dimension and the same finitestate strong dimension. This extends, and gives a new proof of, Wall’s 1949 theorem stating that the sum or product of a nonzero rational number and a Borel...

I analyze a stochastic bargaining game in which a renewable surplus is divided among n ≥ 5 committee members in each of an infinite number of periods, and the division implemented in one period becomes the status quo allocation of the surplus in the ensuing period. I establish existence of equilibrium exhibiting minimum winning coalitions, assuming sufficiently mild concavity of stage preferenc...

In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some well-known results for the volume Ωn of the unit ball Bn ⊂ Rn, the surface area ωn−1 of the unit sphere Sn−1, and some related constants.

Perception based function (PBF) is given by the set of rules Ri:“If X is Ti then Y is Si”, where Ti is a linguistic term describing some fuzzy intervals Ai on the domain of real values of X and Si is a linguistic description of the shape of the function Y(X) on this interval. The methods of explicitation of such type of rules when Si are given by words QUICKLY INCREASING AND SLIGHTLY CONVEX, SL...

In this note, we generalize the affine rank minimization problem and the vector cardinality minimization problem and show that the resulting generalized problem can be solved by solving a sequence of continuous concave minimization problems. In the case of the vector cardinality minimization problem, we show that it can be solved by solving the continuous concave minimization problem.

We give a simple proof of the “concavity of entropy power”.

We establish a combinatorial connection between the sequence (in,k) counting the involutions on n letters with k descents and the sequence (an,k) enumerating the semistandard Young tableaux on n cells with k symbols. This allows us to show that the sequences (in,k) are not log-concave for some values of n, hence answering a conjecture due to F. Brenti.

We derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under Cournot competition. To do so, we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of ρ-concavity and ρ-convexity. The ”more concave” is demand, the larger the share of producer surplus in overall surplus, the smaller is consumer surplus relative t...