Related papers: Polypseudologarithms revisited
Let $\pi$ be an irreducible unitary cuspidal representation for $GL_m({\Bbb A}_{\Bbb Q})$, and let $L(s, \pi)$ be the automorphic $L$-function attached to $\pi$, which has a Dirichlet series expression in the half-plane $\mbox{Re} s>1$.…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We experimentally determine the equation of state of a laser cooled gas. By employing the Lane-Emden formalism, widely used in astrophysics, we derive the equilibrium atomic profiles in large magneto optical traps where the thermodynamic…
A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…
The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral- and Hamiltonian formalism. The aim is to shed some light onto the interrelation between the topology…
The Lorentz covariant statistical physics and thermodynamics is formulated within the preferred frame approach. The transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lorentz-invariant…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
All real three dimensional Poisson-Lie groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the complete classification of real three-dimensional Lie…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers, and Brown,…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat…
We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to…
In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so…
The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multi-component plasma systems is revised within the…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an…
The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of…
We revisit the Karagiannidis-Lioumpas (KL) approximation of the Q-function by optimizing its coefficients in terms of absolute error, relative error and total error. For minimizing the maximum absolute/relative error, we describe the…