Related papers: Expansion into Clifford Prolate Spheroidal Wave Fu…
We study in special limiting cases quasinormal modes of massive scalar fields in the Schwarzschild-de Sitter black hole backgrounds. We determine the lower limit on the mass parameter of the scalar field that allows the waves with…
We study the propagation of massive scalar fields in the background of asymptotically flat regular black holes supported by a phantom scalar field with a scalar charge $A$. This parameter regularizes the geometry by removing the central…
We study the spectral form factor (SFF) for hydrodynamic systems with a sound pole, a large class including any fluid with momentum conservation and energy conservation, or any extended system with spontaneously broken continuous symmetry.…
We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical…
This work is concerned with the gradient flow of absolutely $p$-homogeneous convex functionals on a Hilbert space, which we show to exhibit finite ($p<2$) or infinite extinction time ($p \geq 2$). We give upper bounds for the finite…
We discuss properties of the $\epsilon$-expansion in $d=4-\epsilon$ dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in $\epsilon$ in terms of the…
Using the method of separation of variables and a new approach to calculations of the prolate spheroidal wave functions, we study the optical properties of very elongated (cigar-like) spheroidal particles. A comparison of extinction…
We study exponential decay rates of eigenfunctions of self-adjoint higher order elliptic operators on R^n. We are interested in decay rates as a function of direction. We show that the possible decay rates are to a large extent determined…
Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is…
The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…
The effects of both density stratification and magnetic field expansion on torsional Alfven waves in solar spicules are studied. Also, their eigenfrequencies, eigenfunctions, and the period ratio P_1/P_2 are obtained with a novel…
The aim of this paper is to investigate the quality of approximation of almost time and almost band-limited functions by its expansion in three classical orthogonal polynomials bases: the Hermite, Legendre and Chebyshev bases. As a…
In this paper spatial correlations of parallel edge dislocations are studied. After closing a hierarchy of equations for the many-particle density functions by the Kirkwood superposition approximation, we derive evolution equations for the…
The spheroidal wave functions, which are the solutions to the Helmholtz equation in spheroidal coordinates, are notoriously difficult to compute. Because of this, practically no programming language comes equipped with the means to compute…
In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Additionally, we provide an application to probability theory…
We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated by Meissner…
This paper focuses on the development of harmonic and Clifford analysis techniques in the context of some conformally flat manifolds that arise from factoring out a simply-connected domain from $R^n$ by special arithmetic subgroups of the…
We construct a basis of conformal primary wavefunctions (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also…
In this paper we show that the eigenfunctions can be found exactly for systems whose delay-Doppler spread function is concentrated along a straight line and they can be found in approximate sense for systems having a spread function…
Let $(\Omega,g)$ be a compact, real-analytic Riemannian manifold with real-analytic boundary $\partial \Omega.$ The harmonic extensions of the boundary Dirchlet-to-Neumann eigenfunctions are called Steklov eigenfunctions. We show that the…