Related papers: The difficulties involved in calculating $\delta\r…
We present some old and new results on dispersive estimates for Schroedinger equations.
A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.
In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations.…
Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…
Myerson's regularity condition of a distribution is a standard assumption in economics. In this paper, we study the complexity of describing a regular distribution within a small statistical distance. Our main result is that…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
This article presents a new spectral analysis approach for dispersion error and a methodology to numerically evaluate it. In practice, this new analysis allows the numerical study of dispersion errors on all types of mesh and for multiple…
I consider the uncertainties in parton distributions and the consequences for hadronic cross-sections. There is ever-increasing sophistication in the relationship between the uncertainties of the distributions and the errors on the…
We derive the dispersion decay for solutions of the 1D discrete Schroedinger and wave equations. Based on previous works, we weaken the conditions on potentials.
Employing the concept of time-delay, a relation is found which counts the number of quantal resonances supported by a potential. Several simple and advanced illustrations include a treatment of square-well, Dirac delta barrier, an…
A discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined. One of the central problems is the criteria used to judge what variation of the parameters describing a set of…
These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one…
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
We compute the modified factorization contributions to the $\Lambda\rightarrow N\rho$ and $\Sigma\rightarrow N\rho$ couplings and demonstrate that these contributions naturally include $\Delta I=3/2$ terms which are comparable ($\simeq 0.4$…
We give a brief survey of theoretical evaluations of light vector mesons in hadronic matter, focusing on results from hadronic many-body theory. We emphasize the importance of imposing model constraints in obtaining reliable results for the…
In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute…
This article derives an equation for exponentiation that can be used for calculating exponents using a parallel computing architecture.
In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the…
The rate region of the task-encoding problem for two correlated sources is characterized using a novel parametric family of dependence measures. The converse uses a new expression for the $\rho$-th moment of the list size, which is derived…
We present a study of the results obtained combining LO partonic matrix elements with different orders of partons distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim…