337 research outputs found
A double bounded key identity for Goellnitz's (big) partition theorem
Given integers i,j,k,L,M, we establish a new double bounded q-series identity
from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon
for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the
identity yields a strong refinement of Goellnitz's theorem with a bound on the
parts given by L. This is the first time a bounded version of Goellnitz's (big)
theorem has been proved. This leads to new bounded versions of Jacobi's triple
product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on
Symbolic Computation
Supersymmetric pairing of kinks for polynomial nonlinearities
We show how one can obtain kink solutions of ordinary differential equations
with polynomial nonlinearities by an efficient factorization procedure directly
related to the factorization of their nonlinear polynomial part. We focus on
reaction-diffusion equations in the travelling frame and
damped-anharmonic-oscillator equations. We also report an interesting pairing
of the kink solutions, a result obtained by reversing the factorization
brackets in the supersymmetric quantum mechanical style. In this way, one gets
ordinary differential equations with a different polynomial nonlinearity
possessing kink solutions of different width but propagating at the same
velocity as the kinks of the original equation. This pairing of kinks could
have many applications. We illustrate the mathematical procedure with several
important cases, among which the generalized Fisher equation, the
FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200
Riccati-parameter solutions of nonlinear second-order ODEs
It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear
second-order ODEs it is a very simple task to find one particular solution once
the nonlinear equation is factorized with the use of two first-order
differential operators. Here, it is shown that an interesting class of
parametric solutions is easy to obtain if the proposed factorization has a
particular form, which happily turns out to be the case in many problems of
physical interest. The method that we exemplify with a few explicitly solved
cases consists in using the general solution of the Riccati equation, which
contributes with one parameter to this class of parametric solutions. For these
nonlinear cases, the Riccati parameter serves as a `growth' parameter from the
trivial null solution up to the particular solution found through the
factorization procedureComment: 5 pages, 3 figures, change of title and more tex
Quasi-Lie schemes and Emden--Fowler equations
The recently developed theory of quasi-Lie schemes is studied and applied to
investigate several equations of Emden type and a scheme to deal with them and
some of their generalisations is given. As a first result we obtain t-dependent
constants of the motion for particular instances of Emden equations by means of
some of their particular solutions. Previously known results are recovered from
this new perspective. Finally some t-dependent constants of the motion for
equations of Emden type satisfying certain conditions are recovered
Quantum Clifford-Hopf Algebras for Even Dimensions
In this paper we study the quantum Clifford-Hopf algebras
for even dimensions and obtain their intertwiner matrices, which are
elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of
these new algebras we find the possibility to connect with extended
supersymmetry. We also analyze the corresponding spin chain hamiltonian, which
leads to Suzuki's generalized model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2
uuencoded figures added
Event Stream Processing with Multiple Threads
Current runtime verification tools seldom make use of multi-threading to
speed up the evaluation of a property on a large event trace. In this paper, we
present an extension to the BeepBeep 3 event stream engine that allows the use
of multiple threads during the evaluation of a query. Various parallelization
strategies are presented and described on simple examples. The implementation
of these strategies is then evaluated empirically on a sample of problems.
Compared to the previous, single-threaded version of the BeepBeep engine, the
allocation of just a few threads to specific portions of a query provides
dramatic improvement in terms of running time
Espaces de Berkovich sur Z : \'etude locale
We investigate the local properties of Berkovich spaces over Z. Using
Weierstrass theorems, we prove that the local rings of those spaces are
noetherian, regular in the case of affine spaces and excellent. We also show
that the structure sheaf is coherent. Our methods work over other base rings
(valued fields, discrete valuation rings, rings of integers of number fields,
etc.) and provide a unified treatment of complex and p-adic spaces.Comment: v3: Corrected a few mistakes. Corrected the proof of the Weierstrass
division theorem 7.3 in the case where the base field is imperfect and
trivially value
Construction of exact solutions to eigenvalue problems by the asymptotic iteration method
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36,
11807 (2003)] to solve new classes of second-order homogeneous linear
differential equation. In particular, solutions are found for a general class
of eigenvalue problems which includes Schroedinger problems with Coulomb,
harmonic oscillator, or Poeschl-Teller potentials, as well as the special
eigenproblems studied recently by Bender et al [J. Phys. A: Math. Gen. 34 9835
(2001)] and generalized in the present paper to higher dimensions.Comment: 10 page
Exact solutions of a Flat Full Causal Bulk viscous FRW cosmological model through factorization
We study the classical flat full causal bulk viscous FRW cosmological model
through the factorization method. The method shows that there exists a
relationship between the viscosity parameter and the parameter
entering the equations of state of the model. Also, the factorization method
allows to find some new exact parametric solutions for different values of the
viscous parameter . Special attention is given to the well known case
, for which the cosmological model admits scaling symmetries.
Furthermore, some exact parametric solutions for are obtained through
the Lie group method.Comment: 18 pas. RevTeX4. New solutions. arXiv admin note: text overlap with
arXiv:gr-qc/0107004 by other author
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