Related papers: Computing with almost periodic functions
The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The paper studies semi-almost periodic holomorphic functions on a polydisk which have, in a sense, the weakest possible discontinuities on the boundary torus. The basic result used in the proofs is an extension of the classical Bohr…
We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…
We describe the use of quasiperiodic oscillators for computation and control of robots. We also describe their relationship to central pattern generators in simple organisms and develop a group theory for describing the dynamics of these…
Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
In this paper, a technique for constructing quasiperiodic structures is suggested, which allows one by the assigned matching to restore the atoms density distribution formula of a corresponding quasicrystal. The algorithm to restore the…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine…
In this paper a semidiscrete Fourier pseudospectral method for approximating Benjamin-type equations is introduced and analyzed. A study of convergence is presented.
We give an exposition of results from a crossroad between geometric function theory, harmonic analysis, boundary value problems and approximation theory, which characterize quasicircles. We will specifically expose the interplay between the…
Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…
The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies…