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

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

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

Continuity theorems for the M/M/1/nM/M/1/n queueing system

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ 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 Z3_3-graded quantum supergroup GLq,j(1∣1)_{q,j}(1|1)

In this work, we give some features of the Z$_3$-graded quantum supergroup