Search results for "convexity"

An experimental study of the esthetic effect of facial profiles

1998

In this study good-looking "male" and "female" as well as ugly facial profiles were shaped by 104 lay persons using an especially constructed device according to specific instructions. These profiles were photographed and subsequently evaluated using a series of parameters from soft tissue profile analyses. Although some significant mean value differences were found between the good-looking and ugly profile variants, they were not substantial. In contrast, markedly significant differences were revealed between the variances of all variables. In some instances the variance of the ugly profiles was more than 3 to 4 times higher than that of the good-looking profiles. These findings were convi…

Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

2013

We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].

Turán type inequalities for generalized inverse trigonometric functions

2013

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.

The validity of the “liminf” formula and a characterization of Asplund spaces

2014

Abstract We show that for a given bornology β on a Banach space X the following “ lim inf ” formula lim inf x ′ ⟶ C x T β ( C ; x ′ ) ⊂ T c ( C ; x ) holds true for every closed set C ⊂ X and any x ∈ C , provided that the space X × X is ∂ β -trusted. Here T β ( C ; x ) and T c ( C ; x ) denote the β-tangent cone and the Clarke tangent cone to C at x. The trustworthiness includes spaces with an equivalent β-differentiable norm or more generally with a Lipschitz β-differentiable bump function. As a consequence, we show that for the Frechet bornology, this “ lim inf ” formula characterizes in fact the Asplund property of X. We use our results to obtain new characterizations of T β -pseudoconve…

Further monotonicity and convexity properties of the zeros of cylinder functions

1992

AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.

Differential properties of the Moreau envelope

2014

International audience; In a vector space endowed with a uniformly Gâteaux differentiable norm, it is proved that the Moreau envelope enjoys many remarkable differential properties and that its subdifferential can be completely described through a certain approximate proximal mapping. This description shows in particular that the Moreau envelope is essentially directionally smooth. New differential properties are derived for the distance function associated with a closed set. Moreover, the analysis, when applied to the investigation of the convexity of Tchebyshev sets, allows us to recover several known results in the literature and to provide some new ones.

Convex bodies and convexity on Grassmann cones

1962

A reconstruction algorithm for L-convex polyominoes

2006

AbstractWe give an algorithm that uniquely reconstruct an L-convex polyomino from the size of some special paths, called bordered L-paths.

k-Weakly almost convex groups and ? 1 ? $$\tilde M^3 $$

1993

We extend Cannon's notion ofk-almost convex groups which requires that for two pointsx, y on then-sphere in the Cayley graph which can be joined by a pathl1 of length ≤k, there is a second pathl2 in then-ball, joiningx andy, of bounded length ≤N(k). Ourk-weakly almost convexity relaxes this condition by requiring only thatl1 ∝l2 bounds a disk of area ≤C1(k)n1 - e(k) +C2(k). IfM3 is a closed 3-manifold with 3-weakly almost convex fundamental group, then π1∞\(\tilde M^3 = 0\).

Complete weights andv-peak points of spaces of weighted holomorphic functions

2006

We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n ,C n ,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.