49,337 research outputs found
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 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
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
Duality picture between antiferromagnetism and d-wave superconductivity in t-J model at two dimensions
We show in this paper an interesting relation between elementary and
topological excitations in the antiferromagnetic and d-wave superconducting
phases of the t-J model at two dimenions. The topological spin and charge
excitations in one phase have the same dynamics as elementary excitations in
the other phase, except the appearance of energy gaps. Moreover, the transition
from one phase to another can be described as a quantum disordering transition
associated with the topological excitations. Based on the above picture, a
plausible phase diagram of t-J model is constructed.Comment: 28 pages, 3 figure
A numerical table of Lommel functions with two imaginary arguments
Numerical table of Lommel functions with two imaginary argument
Critique of proposed limit to space--time measurement, based on Wigner's clocks and mirrors
Based on a relation between inertial time intervals and the Riemannian
curvature, we show that space--time uncertainty derived by Ng and van Dam
implies absurd uncertainties of the Riemannian curvature.Comment: 5 pages, LaTex, field "Author:" correcte
Gravitational Theory with a Dynamical Time
A gravitational theory involving a vector field , whose zero
component has the properties of a dynamical time, is studied. The variation of
the action with respect to gives the covariant conservation of an
energy momentum tensor . Studying the theory in a
background which has killing vectors and killing tensors we find appropriate
shift symmetries of the field which lead to conservation laws. The
energy momentum that is the source of gravity is different
but related to and the covariant conservation of determines in general the vector field . When is chosen to be proportional to the metric, the theory
coincides with the Two Measures Theory, which has been studied before in
relation to the Cosmological Constant Problem. When the matter model consists
of point particles, or strings, the form of , solutions for
are found. For the case of a string gas cosmology, we find that
the Milne Universe can be a solution, where the gas of strings does not curve
the spacetime since although , , as a model for the early universe, this solution is also free
of the horizon problem. There may be also an application to the "time problem"
of quantum cosmology.Comment: 21 pages, discussions extended, some more explicit proofs included,
more references include
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