The aim of the present study was to obtain quantitative information concerning the three-dimensional (3D) arrangement of the facial soft tissues of subjects with Down's syndrome. The 3D co-ordinates of 50 soft tissue facial landmarks were recorded by an electromechanical digitizer in 17 male and 11 female subjects with Down's syndrome aged 12-45 years, and in 429 healthy individuals of the same...

Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of nontraditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity,...

IT IS WELL KNOWN that for a finite exchange economy, where preferences are not assumed to be convex, there may be no price equilibrium or even the core may be empty. For this reason it was proposed to enlarge the set of price equilibria and the core by introducing the concepts of "approximate equilibrium" and "approximate core." The existence of approximate equilibria for exchange economies, wh...

Radzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity co...

Classical convexity can be naturally translated to graphs considering shortest paths, giving rise to the geodesic convexity. Moreover, if we consider induced paths between vertices, we get the so-called monophonic convexity. In this work, we present some results involving monophonic sets.

Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som [11] and Jungck and Sessa [7] and some known results [4], [9], [12] are obtained as consequence. To achieve our goal, we hav...

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...