Abstract In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the coefficients of descent polynomials D d (t) are logconcave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...

Multi-degree Tchebycheffian splines are with pieces drawn from extended (complete) Tchebycheff spaces, which may differ interval to interval, and possibly of different dimensions. These a natural extension multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms so-called B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties ...

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalarand vector-valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resultingmethod combines the favorable properties of isogeometric collocation and the geometrical and a...

Since the 1970’s B-splines have evolved to become the de facto standard for use in curve and surface representation. This resulted in a relatively recent proliferation of nonrigid image registration techniques based on B-splines. These techniques fall under the general Free-Form Deformation (FFD) approach in which the object to be registered is embedded within a B-spline object. The deformation...

This paper presents the relationship between the Recursive Arbitrary Topology Splines (RATS) method, derived by the authors, and the Catmull and Clark recursive B-Spline method. Both methods are capable of defining surfaces of any arbitrary topology of control points. They "fill-in" n-sided regions with foursided patches. The Catmull & Clark method is derived from the midpoint subdivision of B-...

Piecewise polynomial approximations are fundamental to geometric modeling, computer graphics, and finite element methods. The classical finite element method uses low order piecewise polynomials defined on polygonal domains. The domains are discretized into simple polygons called the mesh. These polygons might be triangles, quadrilaterals, etc., for two-dimensional domains, and tetrahedra, hexa...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dyn...

This paper is on the angle-frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling function...

Stirling numbers of second kind S(n,k) denotes the number ways partitioning a set n elements into k nonempty sets. There are many types stirling which studied up to now. In this study, we use extended defined for arbitrary reals. First, define relation between and q-B-splines by using property that divided differences have representation with q-B-splines. addition, derive identities on q-integr...