Related papers: On Some Generalizations of B-Splines
In this paper we present a method for knot insertion and degree elevation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. The use of local structures makes the refinement routines…
The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…
B-splines of order $k$ can be viewed as a mapping $N$ taking a $(k+1)$-tuple of increasing real numbers $a_0 < \cdots < a_k$ and giving as a result a certain piecewise polynomial function. Looking at this mapping $N$ as a whole, basic…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…
The Concepts of poly-Bernoulli numbers $B_n^{(k)}$, poly-Bernoulli polynomials $B_n^{k}{(t)}$ and the generalized poly-bernoulli numbers $B_{n}^{(k)}(a,b)$ are generalized to $B_{n}^{(k)}(t,a,b,c)$ which is called the generalized…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
We introduce discrete analogues of the exponential, sine, and cosine functions. Then using a discrete trigonometric version of a non-polynomial divided difference, we define discrete analogues of the trigonometric B-splines. We derive a…
We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family…
The paper considers the extension of the T-spline approach to the Generalized B-splines (GB-splines), a relevant class of non-polynomial splines. The Generalized T-splines (GT-splines) are based both on the framework of classical polynomial…