Related papers: Steps to the Planck Function : A Centenary Reflect…
Photons radiated from an evaporating black hole in principle provide complete information on the particle spectrum of nature up to the Planck scale. If an evaporating black hole were to be observed, it would open a unique window onto models…
To date, Galactic Astronomy has largely concerned itself with astrophysical processes, and with the locations, space motions and compositions of objects. Consider, for example, the elucidation of the components of the Galaxy over the past…
The QCD structure of the electroweak bosons is reviewed and the lepton structure function is defined and calculated. The leading order splitting functions of electron into quarks are extracted, showing an important contribution from…
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of…
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…
The Planck's radiation law for the blackbody radiation spectrum was capable to explain the experimentally-measured blackbody spectrum. In order to get this result, Planck proposed his radiation law in a two-fold way: 1) by an \textit{ad…
100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large…
To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of…
We add a new scalar field in the no-scale Brans-Dicke gravity and require it to have a global O(2) symmetry with the original scalar field in the Brans-Dicke gravity. This gives us a new massless scalar field in the Einstein frame due to…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
This is a survey of accumulated spectral analysis observations spanning more than a century, referring to the double layer potential integral equation, also known as Neumann-Poincar\'e operator. The very notion of spectral analysis has…
We study the evaporation of (4+n)-dimensional rotating black holes into scalar degrees of freedom on the brane. We calculate the corresponding absorption probabilities and cross-sections obtaining analytic solutions in the low-energy…
Problems solved? Pulsar research must be considered - 35 years after the detection of pulsars - a mature science, where the basic questions have been raised and discussed. One would hope that many if not all generic and important problems…
We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.
The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…
Thermal distribution functions can only be of the Fermi-Dirac or Bose-Einstein types, whereas distorted spectra encompass any possible deviations from these shapes. It is fruitful to devise parametrizations of these distortions with only a…
The speckle statistics of optical coherence tomography images of biological tissue have been studied using several historical probability density functions. A recent hypothesis implies that underlying power-law distributions in the medium…
The problem of black-body radiation is considered in the Born-Infeld theory of electrodynamics. In particular, at 2-loop order the deviation from the Planck expression due to the self-interaction of photons is calculated. It is seen that…
We describe the gluon parton distribution function (PDF) in the proton, deduced by data from the ATLAS and HERA experiments, in the framework of the parton statistical model. The best fit parameters involved in the Planck formula that…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…