2,120 research outputs found
Cross sections for geodesic flows and \alpha-continued fractions
We adjust Arnoux's coding, in terms of regular continued fractions, of the
geodesic flow on the modular surface to give a cross section on which the
return map is a double cover of the natural extension for the \alpha-continued
fractions, for each in (0,1]. The argument is sufficiently robust to
apply to the Rosen continued fractions and their recently introduced
\alpha-variants.Comment: 20 pages, 2 figure
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
Natural extensions and entropy of -continued fractions
We construct a natural extension for each of Nakada's -continued
fractions and show the continuity as a function of of both the entropy
and the measure of the natural extension domain with respect to the density
function . In particular, we show that, for all , the product of the entropy with the measure of the domain equals .
As a key step, we give the explicit relationship between the -expansion
of and of
Large closed queueing networks in semi-Markov environment and its application
The paper studies closed queueing networks containing a server station and
client stations. The server station is an infinite server queueing system,
and client stations are single-server queueing systems with autonomous service,
i.e. every client station serves customers (units) only at random instants
generated by a strictly stationary and ergodic sequence of random variables.
The total number of units in the network is . The expected times between
departures in client stations are . After a service completion
in the server station, a unit is transmitted to the th client station with
probability , and being processed in the th client
station, the unit returns to the server station. The network is assumed to be
in a semi-Markov environment. A semi-Markov environment is defined by a finite
or countable infinite Markov chain and by sequences of independent and
identically distributed random variables. Then the routing probabilities
and transmission rates (which are expressed via
parameters of the network) depend on a Markov state of the environment. The
paper studies the queue-length processes in client stations of this network and
is aimed to the analysis of performance measures associated with this network.
The questions risen in this paper have immediate relation to quality control of
complex telecommunication networks, and the obtained results are expected to
lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat
A Probabilistic Analysis of The Trading The Line Strategy
We provide analytic models for which the appropriate statistics of the trading the line strategy, N h , can be derived in closed form. In particular, we provide closed-form expressions concerning the average duration of the open position, E(N h ), the variance of the open duration, Var(N h ), the average of the stopped log price, E(S N h ), the variance of the stopped log price, Var(S N h ), the correlation, Corr(N h , S N h ), and the Laplace transform, E(e−s N h ). These results are obtained, in discrete time settings, for binomial and other price scenarios. Furthermore, when analytic results are not possible, such as the case of a normal distribution for log returns, we show by simulation that our general conclusions still hold. Using these statistics we point out some of the subtle features of the trailing stops strategy
A Probabilistic Analysis of The Trading The Line Strategy
We provide analytic models for which the appropriate statistics of the trading the line strategy, N h , can be derived in closed form. In particular, we provide closed-form expressions concerning the average duration of the open position, E(N h ), the variance of the open duration, Var(N h ), the average of the stopped log price, E(S N h ), the variance of the stopped log price, Var(S N h ), the correlation, Corr(N h , S N h ), and the Laplace transform, E(e−s N h ). These results are obtained, in discrete time settings, for binomial and other price scenarios. Furthermore, when analytic results are not possible, such as the case of a normal distribution for log returns, we show by simulation that our general conclusions still hold. Using these statistics we point out some of the subtle features of the trailing stops strategy
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