In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

We measured the form factor of bottle-brush macromolecules under good solvent conditions with small-angle neutron scattering and static light scattering. The systems under investigation are brushes, synthesized via the grafting-from route, built from a poly(alkyl methacrylate) backbone to which poly(n-butyl acrylate) side chains are densely grafted. The aim of our work is to study how the syste...

IN a recent analysis of the dynamics of the history of the older, more mature sciences Kuhn (1962, 1963) holds that each of them has reached the level of guidance by a paradigm. In one of its meanings a paradigm is a contentual model, universally accepted by practitioners of a science at a particular temporal period in its development. With this agreement among its practitioners, the paradigm d...

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak constraint qualifications.

Science, Thomas Kuhn argued in The Structure of Scientific Revolutions (1962), proceeds at two different paces. One is what he called “normal science”, which professionals, the general public, the press and politicians generally understand as “research firmly based upon one or more past achievements that some particular scientific community acknowledges for a time as supplying the foundation fo...

Children have many opportunities to learn about science before they start studying science in school. From an early age, children engage in deep conversation with parents and build their own theories for understanding how the world works (e.g., Callanan & Jipson, 2001; Callanan & Oakes, 1992). As children grow, they frequently have opportunities to visit zoos, botanical gardens, parks, science ...