108,511 research outputs found
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
On the variable capacity property of CC/DS-CDMA systems
A complete complementary code based direct sequence code
division multiple access (CC/DS-CDMA) system has been proposed recently
as a potential candidate for beyond third generation (B3G) wireless
communications. This paper addresses the issues that design of efficient
code assignment schemes should be based on a flexible physical layer
support, which is extremely important for emerging cross-layer designs
in future wireless applications. The study in this paper considers a
CC/DS-CDMA system with multiple time slots, three traffic classes and
two dynamic code-flock assignment schemes, namely random assignment
(RA) and compact assignment (CA). Simulation results show that the
CC/DS-CDMA system has variable capacity property (VCP), which is
sensitively affected by different code-flock assignment schemes. In general,
CA can offer lower blocking probability, whereas RA can offer a larger
mean system capacity and higher throughput when offered traffic is heavy
Fast quantum information transfer with superconducting flux qubits coupled to a cavity
We present a way to realize quantum information transfer with superconducting
flux qubits coupled to a cavity. Because only resonant qubit-cavity interaction
and resonant qubit-pulse interaction are applied, the information transfer can
be performed much faster, when compared with the previous proposals. This
proposal does not require adjustment of the qubit level spacings during the
operation. Moreover, neither uniformity in the device parameters nor exact
placement of qubits in the cavity is needed by this proposal.Comment: 6 pages, 3 figure
- …