Related papers: General Shells and Generalized Functions
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasma come mainly from the use of very CPU-consuming particle-in-cell or (gyro)kinetic codes which…
Dynamics of a null thin shell immersed in a generic spherically symmetric spacetime is obtained within the distributional formalism. It has been shown that the distributional formalism leads to the same result as in the conventional…
Shell structures are generally modeled based on kinematic hypotheses, where some of the parameters are preferentially evaluated in a phenomenological manner. In this article, asymptotic analysis against the underlying three-dimensional…
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…
Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical…
Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x->1. The factorization theorem for the structure…
Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been…
We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…
We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We…
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
We investigate spherically symmetric solutions with pressure and discuss the existence of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating not only the…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…