Related papers: A Complete Analytic Inversion of Supernova Lines i…
We obtain new inversion formulas for the Funk type transforms of two kinds associated to spherical sections by hyperplanes passing through a common point $A$ which lies inside the n-dimensional unit sphere or on the sphere itself.…
We consider the $\alpha$-sine transform of the form $T_\alpha f(y)=\int_0^\infty\vert\sin(xy)\vert^\alpha f(x)dx$ for $\alpha>-1$, where $f$ is an integrable function on $\mathbb{R}_+$. First, the inversion of this transform for $\alpha>1$…
Considering digital ink as plane curves provides a valuable framework for various applications, including signature verification, note-taking, and mathematical handwriting recognition. These plane curves can be obtained as parameterized…
A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an $N$-dimensional hyperrectangle. In particular, it is shown that these functions can be expressed in terms of their highest-order mixed…
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral…
CONTEXT: Spectral-line asymmetries and wavelength shifts are signatures of hydrodynamics in solar and stellar atmospheres. Theory may precisely predict idealized lines, but observed spectra are limited by blends, too few suitable lines,…
In this paper, a new class of optical fibers is studied, i.e. microstructured fibers or photonic crystal fibers (PCF). The main objective is to characterize these fibers using different dispersion diagrams and present an interface that…
We present a spectroscopic analysis of the H-alpha profiles of hydrogen-rich type II supernovae. A total of 52 type II supernovae having well sampled optical light curves and spectral sequences were analyzed. Concentrating on the H-alpha…
We review the Cini-Sawatzky approach to the line shape analysis of Auger CVV transitions, in its basic and original formulation. Then, several extensions of the theory are reviewed, namely the inclusion spin-orbit coupling,…
The measurement of non-zero polarization can be used to infer the presence of departures from spherical symmetry in supernovae (SNe). The origin of the majority of the intrinsic polarization observed in SNe is in electron scattering, which…
In this article some explicit estimates on the decay of the convolutive inverse of a sequence are proved. They are derived from the functional calculus for Sobolev algebras. Applications include localization in spline-type spaces and…
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
Extended Drude model formalism has been successfully utilized for analyzing optical spectra of strongly correlated electron systems including heavy-fermion systems and high-$T_c$ superconducting iron pnictides and cuprates. Furthermore,…
The description of the narrowing effect at high pressures is demonstrated on the example of CO2-He absorption for Q-, P-, and R-branches and for the head of the R-branch. The problem is focused on the physical meaning of this phenomenon…
We examine the light curve parameters of 97 nearby Type Ia supernovae in the ultraviolet and optical using observations from the Swift Ultra-Violet/Optical Telescope. Our light curve models used a linear combinations of templates, which…
We illustrate methods for deriving properties of thermonuclear, or Type Ia, supernovae, including synthesized $^{56}$Ni mass, total ejecta mass, ejecta kinetic energy, and $^{56}$Ni distribution in velocity, from gamma-ray line…
We extend the approximate radiative transfer analysis of Hershkowitz, Linder, and Wagoner (1986) to a more general class of supernova model atmospheres, using a simple fit to the effective continuum opacity produced by lines (Wagoner,…
We present {\tt deepSIP} (deep learning of Supernova Ia Parameters), a software package for measuring the phase and -- for the first time using deep learning -- the light-curve shape of a Type Ia supernova (SN~Ia) from an optical spectrum.…
Let f(x,y)=0 be an equation of plane analytic curve defined in the neighborhood of the origin and let $\pi:M\to(\Cn^2,0)$ be a local toric modification. We give a formula which connects a number of double points \delta_0(f)$ with a sum…
Bogoliubov's 1947 approximation, originally developed in the microscopic theory of superfluidity, laid the foundation for solving previously intractable quantum models and later became part of "quantum mathematics". Regarding mathematically…