Abstract. The space which consists of measures having finite second moment is an infinite dimensional metric space endowed with Wasserstein distance, while the space of Gaussian measures on Euclidean space is parameterized by mean and covariance matrices, hence a finite dimensional manifold. By restricting to the space of Gaussian measures inside the space of probability measures, we manage to ...

This paper presents how the shape of a brass instrument can be optimized with respect to its intonation properties. The instrument is modeled using a hybrid method between a lossy one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a two-dimensional finite element model for the rapidly flaring part. The optimization employs gradient-based algorithms, and...

The main objective of this paper is to discuss a convexity theorem for a certain class of Riemannian manifolds, so-called isoparametric submanifolds, and how this relates to other convexity theorems. In the introduction we will present the convexity theorems. In Section 2 we will describe the geometry of isoparametric submanifolds and in Section 3 we will relate this to the geometries of the ot...

We study the interplay between the behaviour of approximately convex (and approximately affine) functions on the unit ball of a Banach space and the geometry of Banach K-spaces. Introduction This paper deals with the local stability of convexity, affinity and Jensen functional equation on infinite dimensional Banach spaces. Recall that a function f : D → R is said to be ε-convex if it satisfies...

The preservation of surface shape is important in geometric modelling and approximation theory. In geometric modelling one would like to manipulate the shape of the surface being modelled by the simpler task of manipulating the control points. In scattered data approximation one might wish to approximate bivariate data sampled from a function with a shape property by a spline function sharing t...

Restricted-orientation convexity, also called O-convexity, is the study of geometric objects whose intersection with lines from some xed set is empty or connected. We introduce restricted-orientation halfspaces, which are an O-convexity analog of halfspaces, explore their properties, and demonstrate their relationship to restricted-orientation convex sets. ABSTRACT Restricted-orientation convex...

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several...

the calculation of rts amounts to measuring a relationship between inputs and outputs in a production structure. there are many methods to measure rts in the primal space or the dual space. one of the main approaches is using the multiplier on the convexity constraint. but returns to scale measurements in dea models are affected by the presence of regulatory constraints. these additional constr...

Here presented is a survey for the log-convexity of some famous combinatorial sequences. We develop techniques for dealing with the log-convexity of sequences satisfying a three-term recurrence. We also introduce the concept of q-log-convexity and establish the link with linear transformations preserving the log-convexity. MSC: 05A20; 11B73; 11B83; 11B37