Related papers: A Corrigendum to Unreasonable Slightness
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
This paper has been withdrawn by the authors as requested by the journal.
In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on…
We re-examine the exponentially improved expansion for $\log\,\g(z)$, first considered in Paris and Wood in 1991, to point out that the recent treatment by Kowalenko [Exactification of Stirling's approximation for the logarithm of the gamma…
Let $b \ge 2$ be an integer and $\xi$ an irrational real number. We prove that, if the irrationality exponent of $\xi$ is equal to $2$ or slightly greater than $2$, then the $b$-ary expansion of $\xi$ cannot be `too simple', in a suitable…
In this paper uniformly rotating relativistic rings are investigated analytically utilizing two different approximations simultaneously: (1) an expansion about the thin ring limit (the cross-section is small compared with the size of the…
We find that the electric field is not a suitable physical quantity to describe the response of a non-metallic material in the study of non-resonant near-field optics. In practice, we show the spin-less one-electron two-level system…
Let G be an arbitrary Abelian group and let A be a finite subset of G. A has small additive doubling if |A+A| < K|A| for some K>0. These sets were studied in papers of G.A. Freiman, Y. Bilu, I. Ruzsa, M.C.--Chang, B. Green and T.Tao. In the…
We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr. [7] they have…
We prove that there is at least one irrationnal among the nine numbers zeta(5), zeta(7),..., zeta(21).
Radiative corrections to neutrino deep inelastic scattering are revisited. One-loop electroweak corrections are re-calculated within the automatic SANC system. Terms with mass singularities are treated including higher order leading…
This is a correction to the afore-mentioned paper in Duke Math. J. vol. 75 (1994), 99-119 by S. Keel, K. Matsuki, and J. McKernan. We completely rewrite Chapter 6 according to the original manuscript of the second author, in order to fix…
The present experimental and theoretical knowledge of the physics of electroweak symmetry breaking is reviewed. Data still favor a light Higgs boson, of a kind that can be comfortably accommodated in the Standard Model or in its Minimal…
We comment on the Reply of G. Su and M. Suzuki [cond-mat/9808011] to our Comment [cond-mat/9807402] about the papers of G. Su [Phys. Rev. B 54, 8291 (1996)] and G. Su and M. Suzuki [Phys. Rev. B 57, 13367 (1998)]. The algebraic mistake…
For a $n$-dimensional spin manifold $M$ with a fixed spin structure and a spinor bundle $\Sigma M$, we prove an $\epsilon$-regularity theorem for weak solutions to the nonlinear Dirac equation of cubic nonlinearity. This, in particular,…
The second author formulated quantum unique ergodicity for Eisenstein series in the prime level aspect in "Equidistribution of Eisenstein series in the level aspect", Commun. Math. Phys. 289(3), 1131-1150 (2009). We point out errors and…
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest second occurrence time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words…
We repeat our previous calculation of the spectrum distortion of massless neutrinos in the early universe with a considerably better accuracy and corrected for a missing numerical factor in one of the two ways of calculations presented in…
After a short review of the algebraic setting of N=2 superconformal field theories, their chiral ring and their perturbations, I present some recent results on curious relations between the integrability of their perturbations and algebraic…