A rational quadratic trigonometric Bézier curve with two shape parameters, which is analogous to cubic Bézier curve, is presented in this paper. The shape of the curve can be adjusted as desired, by simply altering the value of shape parameters, without changing the control polygon. The rational quadratic trigonometric Bézier curve can be made close to the rational cubic Bézier curve or closer ...

We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient ...

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadrat...

In this paper, we prove the generalized Hyers–Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.

A notion of the graph of minimal distances of bent functions is introduced. It is an undirected graph (V , E) where V is the set of all bent functions in 2k variables and (f, g) ∈ E if the Hamming distance between f and g is equal to 2 (it is the minimal possible distance between two different bent functions). The maximum degree of the graph is obtained and it is shown that all its vertices of ...

X iv :m at h/ 03 10 27 6v 2 [ m at h. N T ] 1 3 M ay 2 00 4 ON THE HEIGHT OF THE SYLVESTER RESULTANT CARLOS D’ANDREA AND KEVIN G. HARE Abstract. Let n be a positive integer. We consider the Sylvester resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant’s height. If f is a cubic pol...

In the framework of multi-criteria decision making whose aggregation process is based on the Choquet integral, we present a maximum entropy like method enabling to determine, if it exists, the “least specific” capacity compatible with the initial preferences of the decision maker. The proposed approach consists in solving a strictly convex quadratic program whose objective function is equivalen...

and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...

Abstract The current bottleneck of globally solving mixed-integer (nonconvex) quadratically constrained problems (MIQCPs) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are present. We propose a cutting-surface method based on multiple diagonal perturbations to derive convex quadratic relaxations for nonconvex quadratic probl...

The minimum of quadratic functionals of the gradient on the set of convex functions ABSTRACT We study the innmum of functionals of the form R Mruru among all convex functions u 2 H 1 0 (() such that R jruj 2 = 1. (is a convex open subset of R N , and M is a given symmetric N N matrix.) We prove that this innmum is the smallest eigenvalue of M if is C 1. Otherwise the picture is more complicated...