Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

The object of this article is to explore a ?-pseudo-?-convex ?-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates functions in defined family. classical Fekete–Szegö inequalities for also estimated. Furthermore, we present some special cases main result...

Consider a convex relaxation f̂ of a pseudo-boolean function f . We say that the relaxation is totally half-integral if f̂(x) is a polyhedral function with halfintegral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi = xj , xi = 1 − xj , and xi = γ where γ ∈ {0, 1, 12} is a constant. A well-known example is the roof duality rela...

Human head movement can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. Typically the axis vector, after a suitable scaling, is assumed to lie in a surface called Donders’ surface. Various descriptions of Donders’ surface are in the literature and in this paper we assume that the surface is described by a quadratic form. We p...

The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-po...