We present the construction of an exponentially accurate time–dependent Born– Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to ǫ−4, where ǫ is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time–dependent...

This paper investigates a new property of formal languages called \(\mathrm {REG}\)-measurability where {REG}\) is the class regular languages. Intuitively, language \(L\) {REG}\)-measurable if there exists an infinite sequence that “converges” to \(L\). A without has complex shape in some sense so it can not be (asymptotically) approximated by We show several context-free are (including with t...

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

Using the two-dimensional 3-disk system (in the A 1 representation) we compare the quantum mechanical cumulant expansion of the characteristic determinant, detM(k), and the semi-classical curvature expansion of the corresponding Gutzwiller-Voros zeta-function, Z GV (k). We will show that { independent of the wave number regime { the Gutzwiller-Voros curvature expansion is only an asymptotic app...

In this paper, we propose a simple approach for approximating small sample distributions based on the method of Maximum Entropy (maxent) density. Unlike previous studies that use the maxent method as a curve-fitting tool, we focus on the “small sample asymptotics” of the approximation. We show that this method obtains the same asymptotic order of accuracy as that of the classical Edgeworth expa...

In the present paper, we introduce some Stancu type generalization of Szász-Mirakyan-Baskakov type operators. We estimate the moments for these operators using the hypergeometric series, which can be related to Laguerre polynomials. We estimate point wise convergence, asymptotic expansion and error estimate in terms of higher order modulus of continuity of function in simultaneous approximation...

Asymptotic expansions for the RT (Raviart-Thomas) mixed finite element approximation by the lowest-order rectangular element associated with a second-order elliptic equation on a rectangular domain are derived. Superconvergence for the vector field along the Gauss lines is obtained as a result of the expansion. A procedure of postprocessed extrapolation is presented for the scalar field, as wel...

multi frequency vibrations of a system of two isotropic circular plates interconnected by a rolling visco-elastic layer that has nonlinear characteristics are considered. the system with two circular plates and interconnecting discrete continually distributed rolling visco nonlinear elastic rheological elements presents the model of hybrid nonlinear system. the analytical solutions of first asy...

QCD corrections to inclusive Higgs boson production at the LHC are evaluated at next-tonext-to leading order. By performing asymptotic expansion of the cross section near the limit of infinitely heavy top quark we obtained a few first top mass-suppressed terms. The corrections to the hadronic cross sections are found to be small compared to the scale uncertainty, thus justifying the use of heav...

This paper explores feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on finite-length codes (with blocklength N ) and decoding attempts only at certain specified decoding times, this paper presents the asymptotic expansion achieved by random coding, provides rate-compatible spherepacking (RCSP) performance approximations,...