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High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
The potential of constraints on the angle alpha of the Unitarity Triangle from studies of B0 -> pi+ pi- pi0 decays is reviewed. The experimental inputs needed for an isospin analysis are starting to become available. The precision of…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
A reanalysis of $\pi\pi$ amplitudes for all important partial-waves below about 2 GeV is presented. A set of once subtracted dispersion relations with imposed crossing symmetry condition is used to modify unitary multi-channel amplitudes in…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
We study the properties of marginal distributions-projections of the phase space representation of a physical system-under relativistic transforms. We consider the Galileo case as well as the Lorentz transforms exploiting the relativistic…
A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT). We revise WT theory using a generalisation of the random phase approximation (RPA). This…
It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
We report the first application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the…
We express the amplitudes for charmless three-body B decays in terms of diagrams. In addition, we show how to use Dalitz-plot analyses to obtain decay amplitudes which are symmetric or antisymmetric under the exchange of two of the…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that…
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
An analytical representation for the spatial and temporal dynamics of the simplest of the diffusions -- Bronwian diffusion in an homogeneous slab geometry, with radial symmetry -- is presented. This representation is useful since it…