24,046 research outputs found
A comparison of computational methods and algorithms for the complex gamma function
A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries
Symbolic integration of a class of algebraic functions
An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions
A general algorithm for the solution of Keplers equation for elliptic orbits
Algorithm and subroutine for solving Kepler equation for elliptical orbit
Symbolic-numeric interface: A review
A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach
A numerical table of Lommel functions with two imaginary arguments
Numerical table of Lommel functions with two imaginary argument
Dynamical stability of entanglement between spin ensembles
We study the dynamical stability of the entanglement between the two spin
ensembles in the presence of an environment. For a comparative study, we
consider the two cases: a single spin ensemble, and two ensembles linearly
coupled to a bath, respectively. In both circumstances, we assume the validity
of the Markovian approximation for the bath. We examine the robustness of the
state by means of the growth of the linear entropy which gives a measure of the
purity of the system. We find out macroscopic entangled states of two spin
ensembles can stably exist in a common bath. This result may be very useful to
generate and detect macroscopic entanglement in a common noisy environment and
even a stable macroscopic memory.Comment: 4 pages, 1 figur
A COEVOLUTIONARY APPROACH TO UNDERSTANDING THE PARADOX OF SOCIAL PRESSURES VERSUS ECONOMIC EFFICIENCY ACROSS THE WORLD'S FOOD CHAINS
Institutional and Behavioral Economics,
A mini-array for large air showers
A mini-array that utilizes the Linsley effect is proposed for the measurement of large air showers. An estimate of the detectable shower rates for various shower sizes is made. Details of the detection and data collection systems are also described
Information and Particle Physics
Information measures for relativistic quantum spinors are constructed to
satisfy various postulated properties such as normalisation invariance and
positivity. Those measures are then used to motivate generalised Lagrangians
meant to probe shorter distance physics within the maximum uncertainty
framework. The modified evolution equations that follow are necessarily
nonlinear and simultaneously violate Lorentz invariance, supporting previous
heuristic arguments linking quantum nonlinearity with Lorentz violation. The
nonlinear equations also break discrete symmetries. We discuss the implications
of our results for physics in the neutrino sector and cosmology
Idealized Slab Plasma approach for the study of Warm Dense Matter
Recently, warm dense matter (WDM) has emerged as an interdisciplinary field
that draws increasing interest in plasma physics, condensed matter physics,
high pressure science, astrophysics, inertial confinement fusion, as well as
materials science under extreme conditions. To allow the study of well-defined
WDM states, we have introduced the concept of idealized-slab plasmas that can
be realized in the laboratory via (i) the isochoric heating of a solid and (ii)
the propagation of a shock wave in a solid. The application of this concept
provides new means for probing the dynamic conductivity, equation of state,
ionization and opacity. These approaches are presented here using results
derived from first-principles (density-functional type) theory, Thomas-Fermi
type theory, and numerical simulations.Comment: 37 pages, 21 figures, available, pdf file only. To appear in: Laser
and Particle beams. To appear more or less in this form in Laser and Particle
beam
- …