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We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \ge 1$) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E.…
We show how to simulate the clustering of rich clusters of galaxies using a technique based on the Zel'dovich approximation. This method well reproduces the spatial distribution of clusters obtainable from full N-body simulations at a…
In this paper, the problem of approximate symmetries of a class of non-linear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we…
The low-energy amplitude of Compton scattering on the bound state of two charged particles of arbitrary masses, charges and spins is calculated. A case in which the bound state exists due to electromagnetic interaction (QED) is considered.…
Lemaitre-Tolman-Bondi inhomogeneous spacetimes can be used as a cosmological model to account for the type Ia supernova data. However, such models also give rise to large velocities of galaxy clusters with respect to the cosmic microwave…
This work presents a novel derivation of the expressions that describe the distortions of the cosmic microwave background curve due to the interactions between photons and the electrons present in dilute ionized systems. In this approach, a…
We analysed the 3D clustering of the Planck sample of Sunyaev-Zeldovich (SZ) selected galaxy clusters, focusing on the redshift-space two-point correlation function (2PCF). We compared our measurements to theoretical predictions of the…
We propose an improved methodology to constrain spatial variations of the fine structure constant using clusters of galaxies. We use the {\it Planck} 2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of 618 X-ray…
We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
While third-generation CMB experiments have allowed to release the first maps of Compton-$y$ distortion due to thermal Sunyaev-Zeldovich (SZ) effect, next-generation CMB experiments should allow us to map also the electron gas temperature,…
The Planck cluster catalog is expected to contain of order a thousand galaxy clusters, both newly discovered and previously known, detected through the Sunyaev-Zeldovich effect over the redshift range 0 < z < 1. Follow-up X-ray observations…
A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several model systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Its order-by-order…
Uncertainty in the mass-observable scaling relations is currently the limiting factor for galaxy cluster based cosmology. Weak gravitational lensing can provide a direct mass calibration and reduce the mass uncertainty. We present new…
Future high-resolution measurements of the cosmic microwave background (CMB) will produce catalogs of tens of thousands of galaxy clusters through the thermal Sunyaev-Zel'dovich (tSZ) effect. We forecast how well different configurations of…
Cosmological perturbations with wavelengths smaller than Hubble radius can be handled in the context of Newtonian theory with very high accuracy. The application of this Newtonian approximation, however, is restricted to nonrelativistic…
We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by perfect matchings of snake graphs as in the classical case. In…
The detailed spectral and spatial characteristics of the signature imprinted on the cosmic microwave background (CMB) radiation by Compton scattering of the radiation by electrons in the hot gas in clusters of galaxies - the…
In the weak field limit, analytic $f(R)$ models of gravity introduce a Yukawa-like correction to the Newtonian gravitational potential. These models have been widely tested at galactic scales and provide an alternative explanation to the…
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those…