Related papers: Watanabe and Hu Reply
As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.
The two regular super-exponentials to base exp(1/e) are constructed. An efficient algorithm for the evaluation of these super-exponentials and their inverse functions is suggested and compared to the already published results.
I summarize a part of the work done with Bamert, Burgess, London and Nardi (hep-ph/9602438) in which we find simplified expressions for the possible one-loop contributions to the $R_b$ parameter from new virtual particles, including…
Howes et al. Reply to Comment on "Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas" arXiv:0711.4355
In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…
In a recent paper, the authors propose to separately calculate the volumetric and chemical contributions to the elastic stiffness coefficients of systems containing solutes, as it is "computationally more efficient". We show that this is…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
In light of the well-known fact that the $n$th divided difference of any polynomial of degree $m$ must be zero while $m<n$,the present paper proves the $(\alpha,\beta)$-inversion formula conjectured by Hsu and Ma [J. Math. Res. $\&$…
In this paper, we first review Huei's formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill…
Reply to the Comment physics/0307134 by A. Helmstetter and D. Sornette
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
In this paper we prove Shapiro's 1958 Conjecture on exponential polynomials, assuming Schanuel's Conjecture.
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
In the preprint cond-mat/0408050 M. V. Cheremisin noticed that some results (namely Fig. 4) of our recent work (cond-mat/0407364) have been taken from his paper cond-mat/0405176. As clear from the caption to Fig. 4 as well as from the text…
The preceding Comment by Xu et al. (Phys. Rev. Lett. 122, 059803 (2019); arXiv:1808.05390) erroneously applies the entropic stress expression in our Letter (T.C. O'Connor et al., Phys. Rev. Lett. 121, 047801 (2018); arXiv:1806.09509) to…
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.
We present a model independent closed form expression for |V_{ub}|^2/|V_{tb} V_{ts}^*|^2, which includes the resummation of large endpoint logarithms as well as the interference effects from the operators $O_2$ and $O_8$. We demonstrate…
We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed,…
We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vall\'{e}e Poussin operator will also be given.