Related papers: Watanabe and Hu Reply
We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Letter/comment on M. Rini, Physics $\textbf{13}$, s94 (July 27, 2020) and A. Sanna et al., Phys. Rev. Lett. $\textbf{125}$, 057001 (2020).
In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the…
In this paper, we will present several new congruences involving binomial coefficients under integer moduli, which are the continuation of the previous two work by Cai \textit{et al.} (2002, 2007).
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle…
We comment on a recent Letter by Maunuksela et al. [Phys. Rev. Lett. 79, 1515 (1997)].
This is a comment on Phys. Rev. A 67, 022104(2003).
In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…
Answer to the comment of E. Chudnovsky concerning the following papers: (1) N.V. Prokof'ev, P.C.E. Stamp, Phys. Rev. Lett.80, 5794 (1998). (2) W. Wernsdorfer, T. Ohm, C. Sangregorio, R. Sessoli, D. Mailly, C. Paulsen, Phys. Rev. Lett. 82,…
This paper is based on the lectures given by the first author at Harvard in February and March, 2009. It begins with an introduction to the classical p-adic theory of the Macdonald, Matsumoto and Whittaker functions. Its major directions…
We perform the Kaluza-Klein reduction of M-theory on warped Calabi-Yau fourfolds with non-trivial four-form flux turned on. The resulting scalar- and superpotential is computed and compared with the superpotential obtained by Gukov, Vafa…
In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the…
In Early Transcendentals (The American Mathematical Monthly, Vol. 104, No 7) Steven Weintraub presents a rigorous justifcation of the "early transcendental" calculus textbook approach to the exponential and logarithmic functions. However,…
This paper has been withdrawn, as it is superseded by arXiv:0806.2122 (Bloch-Kato exponential maps for local fields with imperfect residue fields), which is a more recent version of the same paper.
This comment has been withdrawn by the authors due to crucial error.
Lyapunov exponents of a hyperbolic ergodic measure are approximated by Lyapunov exponents of hyperbolic atomic measures on periodic orbits.
We prove the "strong conjecture" expressed by Gazeau et al. in arXiv:1203.3936v1 [math-ph] about the coefficients of the Taylor expansion of the exponential of a polynomial. This implies the "weak conjecture" as a special case. The proof…
We reply to comment on recent paper by Pieplow and Henkel (New J. Phys. 15 (2013) 023027) and our results made by Volokitin and Persson (arXiv: 1405.2525)