For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...

This paper deals with the problem of estimating multiple transparent motions that can occur in computer vision applications, e.g. in the case of semi-transparencies and occlusions, and also in medical imaging when different layers of tissue move independently. Methods based on the known optical-flow equation for two motions are extended in three ways. Firstly, we include a regularization term t...

We discuss the relationship between the classical Lagrange theorem in mathematics and the quantum statistical mechanics and thermodynamics of an ideal gas of multispecies quasiparticles with mutual fractional exclusion statistics. First, we show that the thermodynamic potential and the density of the system are analytically expressed in terms of the language of generalized cluster expansions, w...

Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on particular aspect the trajectory optimization, related to velocity along predefined path, with aim minimizing power consumption. To tackle problem, functional formulation minimization strategy developed, by means Euler-Lagrange equation. The later performed using...

In this paper, a semi-analytical model for the dispersion relation of nanowire lasers is presented. The approach which is based on the multi-conductor transmission line modeling, makes use of the Fourier expansion technique. The cross-section of the nanowire is assumed to be hexagonally-shaped. To determine the accuracy, the model results are compared to the numerical results obtained from FDTD...

It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In this paper we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. ...

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric field E. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nédélec edge elements and standard nodal finite elements to defi...