51,901 research outputs found
Non-degenerate colorings in the Brook's Theorem
Let and be two integers. We will call a proper coloring
of the graph a \textit{-nondegenerate}, if for any vertex of
with degree at least there are at least vertices of different colors
adjacent to it. In our work we prove the following result, which generalizes
Brook's Theorem. Let and be a graph without cliques on
vertices and the degree of any vertex in this graph is not greater than .
Then for every integer there is a proper -nondegenerate vertex
-coloring of , where During the primary proof,
some interesting corollaries are derived.Comment: 18 pages, 10 figure
Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms
The random phase approximation (RPA) for the correlation energy functional of
density functional theory has recently attracted renewed interest. Formulated
in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve
some of the fundamental limitations of the local density and generalized
gradient approximations, as for instance their inability to account for
dispersion forces. First results for atoms, however, indicate that the RPA
overestimates correlation effects as much as the orbital-dependent functional
obtained by a second order perturbation expansion on the basis of the KS
Hamiltonian. In this contribution, three simple extensions of the RPA are
examined, (a) its augmentation by an LDA for short-range correlation, (b) its
combination with the second order exchange term, and (c) its combination with a
partial resummation of the perturbation series including the second order
exchange. It is found that the ground state and correlation energies as well as
the ionization potentials resulting from the extensions (a) and (c) for closed
sub-shell atoms are clearly superior to those obtained with the unmodified RPA.
Quite some effort is made to ensure highly converged RPA data, so that the
results may serve as benchmark data. The numerical techniques developed in this
context, in particular for the inherent frequency integration, should also be
useful for applications of RPA-type functionals to more complex systems.Comment: 11 pages, 7 figure
Helical motions in the jet of blazar 1156+295
The blazar 1156+295 was observed by VLBA and EVN + MERLIN at 5 GHz in June
1996 and February 1997 respectively. The results show that the jet of the
source has structural oscillations on the milliarcsecond scale and turns
through a large angle to the direction of the arcsecond-scale extension. A
helical jet model can explain most of the observed properties of the radio
structure in 1156+295.Comment: 6 pages, 2 figures, to appear in New Astronomy Reviews (EVN/JIVE
Symposium No. 4, special issue
Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
Algorithms are presented for the tanh- and sech-methods, which lead to
closed-form solutions of nonlinear ordinary and partial differential equations
(ODEs and PDEs). New algorithms are given to find exact polynomial solutions of
ODEs and PDEs in terms of Jacobi's elliptic functions.
For systems with parameters, the algorithms determine the conditions on the
parameters so that the differential equations admit polynomial solutions in
tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples
illustrate key steps of the algorithms.
The new algorithms are implemented in Mathematica. The package
DDESpecialSolutions.m can be used to automatically compute new special
solutions of nonlinear PDEs. Use of the package, implementation issues, scope,
limitations, and future extensions of the software are addressed.
A survey is given of related algorithms and symbolic software to compute
exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at
http://www.mines.edu/fs_home/whereman
Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 2: User's manual
A user's manual which describes input/output routines and recommended operating procedures relating to MAPSEP is presented. Samples runs are included
Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual
The mission analysis program for solar electric propulsion (MAPSEP) is comprised of the basic modes: TOPSEP (trajectory generation), GODSEP (linear error analysis), and SIMSEP (simulation). The program is designed to analyze any low thrust mission with respect to trajectory performance, guidance and navigation, and to provide system related requirements for the purpose of vehicle design. The MAPSEP organization is described along with all models and algorithms. Topics discussed include: trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes
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