Related papers: Reply to 'Comment on "Relativistic shape invariant…
In the comment, Zanardi and Rasetti argue that several claims in our recent letter (Phys. Rev. Lett. 79, 1953, 1997) are questionable. The reply shows these claims remain true.
The size of non-perturbative corrections to event shape observables is predicted to fall like powers of the inverse centre of mass energy. These power corrections are investigated for different observables from $e^+e^-$-annihilation…
The purpose of this note is to correct statements of some assertions in \cite{l}.
Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the…
We refute in this Reply the criticisms made by M. Abdel-Aty [Phys. Rev. A 70, 047801 (2004)]. We show that none of them are founded and we demonstrate very explicitly what is wrong in the arguments developed by this author.
Quantum lattice models describe a wide array of physical systems, and are a canonical way to numerically solve the Schrodinger equation. Here we prove the potential inversion theorem, which says that wavefunction probability in these models…
In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, noncompact Riemannian $3$-manifold satisfying the…
We reply to the criticisms moved in [1] against our results presented in [2]. In particular, we show that our fractal model has none of the problems claimed in [1]. The latters can be addressed to the overlooked nonlinear behaviour of the…
We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.
This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001) 028901) on a paper written by the author (B. Vacchini, ``Completely positive quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
For weak solutions to the evolutional $p$-Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potential.
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.
We show that given a suitable but essentially arbitrary function Q(x,t,h) there are "generalized" quantum theories having Q as a quantum potential.
The Comment by Xiong et al. (arXiv:1610.06275) criticizing my Letter [Phys. Rev. Lett. 116, 133903 (2016)] was rejected by Physical Review Letters. In this Reply, I show that all their claims are wrong.
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out…