Related papers: The difficulties involved in calculating $\delta\r…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
I discuss the issue of uncertainties in parton distributions and in the physical quantities which are determined in terms of them. While there has been significant progress on the uncertainties associated with errors on experimental data,…
In this paper we analyze the dispersion property of some models involving Schr\"odinger equations. First we focus on the discrete case and then we present some results on graphs.
I describe the methodology for the use of dispersion relations in connection with chiral perturbation theory. The conditions for matching the two formalisms are given at $O(E^2)$ and $O(E^4)$. The two have several complementary features, as…
The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of…
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat…
In this talk I review some challenges which await perturbative QCD at the Large Hadron Collider. In particular, I consider the underlying event, Monte Carlo methods and next-to-leading order (NLO) calculations.
A general method for calculating \NLO cross sections in perturbative QCD is presented. The algorithm is worked out for calculating $N$-jet cross sections in hadron-hadron collisions. The generalization of the scheme to performing…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the $\Delta(1232)$ in a systematic…
We review major appearances of the functional expression $\pm \Delta \rho ^{1/2}/ \rho ^{1/2}$ in the theory of diffusion-type processes and in quantum mechanically supported dynamical scenarios. Attention is paid to various manifestations…
We present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics. Our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
Some Open Problems Concerning Orthogonal Polynomials.
In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here,…
Kramers-Kronig type dispersion relations for integer powers of complex reflection coefficient are introduced for testing the consistency of terahertz reflection spectra. By using numerical simulations we show that such dispersion relations…
This is a cursory review of diffractive studies ( mostly elastic scattering)at the LHC with physical interpretation of the experimental data and comments to related problems of theory.
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
We discuss a simple method to evaluate the QCD corrections to $\Delta\rho$. It assumes that the perturbative expansion in terms of $\ms$ parameters is meaningful and, unlike other studies, exploits significant available information…
We discuss a non-intuitive situation concerning percentages.