Related papers: Formal oscillatory distributions
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
We study a notion of generalized H\"older continuity for functions on $\mathbb{R}^d$. We show that for any bounded function $f$ of bounded support and any $r>0$, the $r$-oscillation of $f$ defined as $osc_r f (x):= \sup_{B_r(x)} f -…
Stellar oscillation under the combined influences of incident gravitational wave and radiation loss is studied in a simple toy model. The star is approximated as a uniform density ellipsoid in the Newtonian gravity including radiation…
We provide a computational method for quickly determining the correct distribution of optically active nanoparticles for a desired response. This is achieved by simulating the optical response of single nanoparticles and performing a…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…
A solid is typically deemed amorphous when there are no Bragg peaks in its diffraction pattern. We discuss a two dimensional configuration of Ising spins with an autocorrelation function which vanishes at all nonzero distances, so that its…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number…
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…
We study certain families of oscillatory integrals $I_\varphi(a)$, parametrised by phase functions $\varphi$ and amplitude functions $a$ globally defined on $\mathbb{R}^d$, which give rise to tempered distributions, avoiding the standard…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
The speed of quantum random number generators is a major concern for practical quantum applications. However, the bit extraction process limits the final bit rate due to lack of comparably fast electronics. Here we introduce optical…
Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the…
We consider the gravitational potential and the gravitational rotation field generated by an spherical mass distribution with exponential density, when the force between any two mass elements is not the usual Newtonian one, but some general…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
A simple numerical scheme is presented for the construction of three-integral phase-space distribution functions for oblate galaxy models with a gravitational potential of St\"{a}ckel form, and an arbitrary axisymmetric luminous density…
We study oscillations and instabilities of relativistic stars using perturbation theory in general relativity and take into account the contribution of a dynamic spacetime. We present the oscillation spectrum as well as the critical values…
Given a function $f$ on a smooth Riemannian manifold without boundary, we prove that if $p \in M$ is a non-degenerate critical point of $f$, then a neighborhood of $p$ contains a foliation by spheres with mean curvature proportional to $f$.…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
We consider the semilinear harmonic oscillator $$i\psi_t=(-\Delta +\va{x}^{2} +M)\psi +\partial_2 g(\psi,\bar \psi), \quad x\in \R^d, t\in \R$$ where $M$ is a Hermite multiplier and $g$ a smooth function globally of order 3 at least. We…