1,871 research outputs found
Calculation of resonances in the Coulomb three-body system with two disintegration channels in the adiabatic hyperspherical approach
The method of calculation of the resonance characteristics is developed for
the metastable states of the Coulomb three-body (CTB) system with two
disintegration channels. The energy dependence of K-matrix in the resonance
region is calculated with the use of the stabilization method. Resonance
position and partial widths are obtained by fitting the numerically calculated
K(E)-matrix with the help of the generalized Breit-Wigner formula.Comment: Latex, 11 pages with 5 figures and 2 table
Improved linear response for stochastically driven systems
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents. However, in the case of stochastically
driven dynamics, one typically resorts to the classical fluctuation-dissipation
formula, which has the drawback of explicitly requiring the probability density
of the statistical state together with its derivative for computation, which
might not be available with sufficient precision in the case of complex
dynamics (usually a Gaussian approximation is used). Here we adapt the
short-time linear response formula for stochastically driven dynamics, and
observe that, for short and moderate response times before numerical
instability develops, it is generally superior to the classical formula with
Gaussian approximation for both the additive and multiplicative stochastic
forcing. Additionally, a suitable blending with classical formula for longer
response times eliminates numerical instability and provides an improved
response prediction even for long response times
Hypersymmetry: a Z_3-graded generalization of supersymmetry
We propose a generalization of non-commutative geometry and gauge theories
based on ternary Z_3-graded structures. In the new algebraic structures we
define, we leave all products of two entities free, imposing relations on
ternary products only. These relations reflect the action of the Z_3-group,
which may be either trivial, i.e. abc=bca=cab, generalizing the usual
commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\pi i)/3}. The usual
Z_2-graded structures such as Grassmann, Lie and Clifford algebras are
generalized to the Z_3-graded case. Certain suggestions concerning the eventual
use of these new structures in physics of elementary particles are exposed
Continuity theorems for the queueing system
In this paper continuity theorems are established for the number of losses
during a busy period of the queue. We consider an queueing
system where the service time probability distribution, slightly different in a
certain sense from the exponential distribution, is approximated by that
exponential distribution. Continuity theorems are obtained in the form of one
or two-sided stochastic inequalities. The paper shows how the bounds of these
inequalities are changed if further assumptions, associated with specific
properties of the service time distribution (precisely described in the paper),
are made. Specifically, some parametric families of service time distributions
are discussed, and the paper establishes uniform estimates (given for all
possible values of the parameter) and local estimates (where the parameter is
fixed and takes only the given value). The analysis of the paper is based on
the level crossing approach and some characterization properties of the
exponential distribution.Comment: Final revision; will be published as i
Algebras with ternary law of composition and their realization by cubic matrices
We study partially and totally associative ternary algebras of first and
second kind. Assuming the vector space underlying a ternary algebra to be a
topological space and a triple product to be continuous mapping we consider the
trivial vector bundle over a ternary algebra and show that a triple product
induces a structure of binary algebra in each fiber of this vector bundle. We
find the sufficient and necessary condition for a ternary multiplication to
induce a structure of associative binary algebra in each fiber of this vector
bundle. Given two modules over the algebras with involutions we construct a
ternary algebra which is used as a building block for a Lie algebra. We
construct ternary algebras of cubic matrices and find four different totally
associative ternary multiplications of second kind of cubic matrices. It is
proved that these are the only totally associative ternary multiplications of
second kind in the case of cubic matrices. We describe a ternary analog of Lie
algebra of cubic matrices of second order which is based on a notion of
j-commutator and find all commutation relations of generators of this algebra.Comment: 17 pages, 1 figure, to appear in "Journal of Generalized Lie Theory
and Applications
On a graded q-differential algebra
Given a unital associatve graded algebra we construct the graded
q-differential algebra by means of a graded q-commutator, where q is a
primitive N-th root of unity. The N-th power (N>1) of the differential of this
graded q-differential algebra is equal to zero. We use our approach to
construct the graded q-differential algebra in the case of a reduced quantum
plane which can be endowed with a structure of a graded algebra. We consider
the differential d satisfying d to power N equals zero as an analog of an
exterior differential and study the first order differential calculus induced
by this differential.Comment: 6 pages, submitted to the Proceedings of the "International
Conference on High Energy and Mathematical Physics", Morocco, Marrakech,
April 200
The Hopf algebra structure of the Z-graded quantum supergroup GL
In this work, we give some features of the Z-graded quantum supergroup
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