In this paper we propose a non-stationary uniform tension controlled interpolating 4-point scheme which provides users with a single tension parameter that, for any value in the range of definition, generates a C1-continuous limit curve. This curve scheme unifies non-stationary interpolating 4-point rules that are capable of representing elements of the linear space spanned by trigonometric, po...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

We construct a commutative algebra Az , generated by d algebraically independent q-difference operators acting on variables z1, z2, . . . , zd, which is diagonalized by the multivariable Askey-Wilson polynomials Pn(z) considered by Gasper and Rahman [6]. Iterating Sears’ 4φ3 transformation formula, we show that the polynomials Pn(z) possess a certain duality between z and n. Analytic continuati...

The recent construction of Siegel modular forms of degree 2n from elliptic cusp forms by Ikeda is interpreted as a special case of Langlands functoriality. This is then used to express the (full) spin L–function of an Ikeda lift as a product of symmetric power L–functions for GL(2). As a corollary one obtains the desired analytic properties of these spin L–functions provided the analogous prope...

This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, min-max boxes, and surface/surface intersections. The class of surfaces that can be handled are all parametric C 2 surfaces. All the algorithms are related by theorems from approximation theory which give infor...

Abstract. As a first application of a very old theorem, known as Herschel’s theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals with the analytical continuation of the polylogarithmic function of complex argument beyond the circle of convergence.

In a recent paper, Pukanszky [6] has classified all the irreducible unitary representations of the universal covering group G of Gi = SL(2, R). We construct analytic continuations of the "principal series" of representations of G into certain domains in the complex plane. The representations obtained by continuation are uniformly bounded and, in special cases, they are equivalent to those const...

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, wellknown to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models...

Ferromagnetic resonance (FMR) spectroscopy, x-ray magnetic circular dichroism (XMCD) spectroscopy and magnetic transmission soft x-ray microscopy (MTXM) experiments have been performed to gain insight into the magnetic anisotropy and domain structure of ultrathin Co9Ni multilayer films with a thin permalloy layer underneath. MTXM images with a spatial resolution better than 25 nm were obtained ...

We define higher-order analogs to the piecewise linear surface finite element method studied in [Dz88] and prove error estimates in both pointwise and L2-based norms. Using the Laplace-Beltrami problem on an implicitly defined surface Γ as a model PDE, we define Lagrange finite element methods of arbitrary degree on polynomial approximations to Γ which likewise are of arbitrary degree. Then we ...