Related papers: Systematic derivation of angular--averaged Ewald p…
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for…
Darmon's conjecture on a relation between cyclotomic units over real quadratic fields and certain algebraic regulators was recently solved by Mazur and Rubin by using their theory of Kolyvagin systems. In this paper, we formulate a…
We study the Euler-Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this…
We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equations. The approach introduces a notion of generalized…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
Leonhard Euler likely developed his summation formula in 1732, and soon used it to estimate the sum of the reciprocal squares to 14 digits --- a value mathematicians had been competing to determine since Leibniz's astonishing discovery that…
We discuss in some detail the general problem of computing averages of convergent Euler products, and apply this to examples arising from singular series for the $k$-tuple conjecture and more general problems of polynomial representation of…
Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their…
We present quantitative versions of Bohr's theorem on general Dirichlet series $D=\sum a_{n} e^{-\lambda_{n}s}$ assuming different assumptions on the frequency $\lambda:=(\lambda_{n})$, including the conditions introduced by Bohr and…
We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-B\"acklund transformations based on…
In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the $2d$ Aharonov-Bohm magnetic potential and the $3d$ Coulomb potential. The proof makes use…
We probe the application of the calculus of conormal distributions, in particular the Pull-Back and Push-Forward Theorems, to the method of layer potentials to solve the Dirichlet and Neumann problems on half-spaces. We obtain full…
Cigler simple derivation of usual and extended Dobinski formula is recalled and it is noted that both may be interpreted as averages of powers of random variables with the corresponding usual or extended Poisson distributions. In parallel…
In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \cite{Yoshida2013}, which establishes Edgeworth…
Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the…
This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on…
This paper presents an Euler--Lagrange system for a continuous-time model of the accelerated gradient methods in smooth convex optimization and proposes an associated Lyapunov-function-based convergence analysis framework. Recently,…
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…
In this work, we consider the pressure of Coulomb systems, in which particles interact via a volume-dependent potential (in particular, the Ewald potential). We confirm that the expression for virial pressure should be corrected in this…
We calculate interdiffusion coefficients in a two-component, weakly or strongly coupled ion plasma (gas or liquid, composed of two ion species immersed into a neutralizing electron background). We use an effective potential method proposed…