We generalize results about the classical Schottky groups to quasiconvex subgroups in negatively curved groups, answering a question of M. Bestvina.

In the paper, the authors prove that the generalized sine function sinp,q(x) and the generalized hyperbolic sine function sinhp,q(x) are geometrically concave and geometrically convex, respectively. Consequently, the authors verify a conjecture posed in the paper “B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no. 10, 1415–...

A biased Newton direction is introduced for minimizing quasiconvex functions with bounded level sets. It is a generalization of the usual Newton's direction for strictly convex quadratic functions. This new direction can be derived from the intersection of approximating hyperplanes to the epigraph at points on the boundary of the same level set. Based on that direction, an unconstrained minimiz...

Light emitting diode (LED) based visible light positioning (VLP) networks can provide accurate location information in indoor environments. In this manuscript, we propose to employ cooperative localization for visible light networks by designing a VLP system configuration that involves multiple LED transmitters with known locations (e.g., on the ceiling) and visible light communication (VLC) un...

A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described.

In this work we propose a continuous approach for solving one of the most studied problems in combinatorial optimization, known as the 0–1 knapsack problem. In the continuous space, the problem is reformulated as a convex generalized multiplicative problem, a special class of nonconvex problems which involves the minimization of a finite sum of products of convex functions over a nonempty conve...

This note reviews, compares and contrasts three notions of “distance” or “size” that arise often in concentration-ofmeasure inequalities. We review Talagrand’s convex distance and McDiarmid’s diameter, and consider in particular the normal distance on a topological vector space X , which corresponds to the method of Chernoff bounds, and is in some sense “natural” with respect to the duality str...