Search results for "Formula"
showing 10 items of 755 documents
Ionization energy ofLi6,7determined by triple-resonance laser spectroscopy
2007
Rydberg level energies for $^{7}\mathrm{Li}$ were measured using triple-resonance laser excitation, followed by drifted field ionization. In addition to the principal $n\phantom{\rule{0.2em}{0ex}}^{2}P$ series, weak Stark mixing from residual electric fields allowed observation of $n\phantom{\rule{0.2em}{0ex}}^{2}S$ and hydrogenic Stark manifold series at higher $n$. Limit analyses for the series yield the spectroscopic ionization energy ${E}_{I}(^{7}\mathrm{Li})=43\phantom{\rule{0.2em}{0ex}}487.159\phantom{\rule{0.2em}{0ex}}40(18)\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The $^{6,7}\mathrm{Li}$ isotope shift (IS) was measured in selected $n\phantom{\rule{0.2em}{0ex}}^{2}…
Rational Hermite Interpolation and Quadrature
1993
Rational Hermite interpolation is used in two different ways in order to derive and analyze quadrature rules. One approach yields quadratures of Gaussian-type whereas the other one generalizes Engels’ dual quadratures exhibiting the close connection between rational Hermite interpolation and quadrature in general.
Quantitative approximation of certain stochastic integrals
2002
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.
Particle-Laden Turbulent Channel Flow with Wall-Roughness
2015
Turbulent flows transporting a dispersed-phase are found in many environmental applications and engineering devices. Particle-laden flows are characterized by several peculiar phenomenologies such as preferential particle concentration and turbulence modulation of the carrier-phase due to the presence of the inertial particles [1].
In vivo methods for drug absorption - comparative physiologies, model selection, correlations with in vitro methods (IVIVC), and applications for for…
2013
This review summarizes the current knowledge on anatomy and physiology of the human gastrointestinal tract in comparison with that of common laboratory animals (dog, pig, rat and mouse) with emphasis on in vivo methods for testing and prediction of oral dosage form performance. A wide range of factors and methods are considered in addition, such as imaging methods, perfusion models, models for predicting segmental/regional absorption, in vitro in vivo correlations as well as models to investigate the effects of excipients and the role of food on drug absorption. One goal of the authors was to clearly identify the gaps in today's knowledge in order to stimulate further work on refining the e…
Ship Roll Motion under Stochastic Agencies Using Path Integral Method
2009
The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamica…
Path integral solution for nonlinear systems under parametric Poissonian white noise input
2016
Abstract In this paper the problem of the response evaluation in terms of probability density function of nonlinear systems under parametric Poisson white noise is addressed. Specifically, extension of the Path Integral method to this kind of systems is introduced. Such systems exhibit a jump at each impulse occurrence, whose value is obtained in closed form considering two general classes of nonlinear multiplicative functions. Relying on the obtained closed form relation liking the impulses amplitude distribution and the corresponding jump response of the system, the Path Integral method is extended to deal with systems driven by parametric Poissonian white noise. Several numerical applica…
A three-dimensional boundary element model for the analysis of polycrystalline materials at the microscale
2012
A three-dimensional multi-domain anisotropic boundary element formulation is presented for the analysis of polycrystalline microstructures. The formulation is naturally expressed in terms of intergranular displacements and tractions that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been ap…
Introduction to Part IV
2018
When looking at the early development of relativity theory, one finds an astonishing number of contributions by mathematicians, some of which deeply influenced the work of leading theoretical physicists. Within the context of special relativity, Hermann Minkowski’s writings come immediately to mind (Walter 2008). Klein and Hilbert followed Minkowski’s ideas from their infancy, and both pursued some of their consequences after the latter’s premature death in January 1909. Two other figures with close ties to Gottingen, Max Born and Arnold Sommerfeld, were both instrumental in elaborating Minkowski’s 4-dimensional approach for physicists (Walter 2007). Born had been Minkowski’s assistant for …
Constructions of Nonagency in the Clients’ Initial Problem Formulations at the Outset of Psychotherapy
2019
This multiple case study investigated how clients construct nonagentic positions when formulating their problems in the beginning of their first psychotherapy session. The initial problem formulations of nine clients entering psychotherapy were analyzed with a detailed model drawing on discursive methodology, the 10 Discursive Tools model (10DT). We found ten problem formulation categories, each one distinguished by the tool from the 10DT model primarily used to construct nonagency. All clients gave several problem formulations from different categories and constructed nonagentic positions with a variety of discursive tools. When the resulting problem formulation categories were read in com…