7,735 research outputs found
On the biparametric quantum deformation of GL(2) x GL(1)
We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit
its cross-product structure. We derive explictly the associated dual algebra,
i.e., the quantised universal enveloping algebra employing the R-matrix
procedure. This facilitates construction of a bicovariant differential calculus
which is also shown to have a cross-product structure. Finally, a Jordanian
analogue of the deformation is presented as a cross-product algebra.Comment: 16 pages LaTeX, published in JM
Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
The quantum group G_r,s provides a realisation of the two parameter quantum
GL_p,q(2) which is known to be related to the two parameter nonstandard
GL_hh'(2) group via a contraction method. We apply the contraction procedure to
G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a
realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then
extended to the coloured quantum group GL_r{\lambda,\mu}(2) to yield a new
Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then
generalised to their coloured versions which inturn provide similar
realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).Comment: 22 pages LaTeX, to be published in J. Math. Phy
Coloured extension of GL_q(2) and its dual algebra
We address the problem of duality between the coloured extension of the
quantised algebra of functions on a group and that of its quantised universal
enveloping algebra i.e. its dual. In particular, we derive explicitly the
algebra dual to the coloured extension of GL_q(2) using the coloured RLL
relations and exhibit its Hopf structure. This leads to a coloured
generalisation of the R-matrix procedure to construct a bicovariant
differential calculus on the coloured version of GL_q(2). In addition, we also
propose a coloured generalisation of the geometric approach to quantum group
duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on
Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna
(Russia); to appear in the proceeding
Real-Time Data Processing in the Muon System of the D0 Detector
This paper presents a real-time application of the 16-bit fixed point Digital
Signal Processors (DSPs), in the Muon System of the D0 detector located at the
Fermilab Tevatron, presently the world's highest-energy hadron collider. As
part of the Upgrade for a run beginning in the year 2000, the system is
required to process data at an input event rate of 10 KHz without incurring
significant deadtime in readout. The ADSP21csp01 processor has high I/O
bandwidth, single cycle instruction execution and fast task switching support
to provide efficient multisignal processing. The processor's internal memory
consists of 4K words of Program Memory and 4K words of Data Memory. In addition
there is an external memory of 32K words for general event buffering and 16K
words of Dual Port Memory for input data queuing. This DSP fulfills the
requirement of the Muon subdetector systems for data readout. All error
handling, buffering, formatting and transferring of the data to the various
trigger levels of the data acquisition system is done in software. The
algorithms developed for the system complete these tasks in about 20
microseconds per event.Comment: 4 pages, Presented and published at the 11th IEEE NPSS Real Time
Conference, held at Santa Fe, New Mexico, USA, from June 14-18, 199
Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
In earlier papers we have applied multiple scattering techniques to calculate
Casimir forces due to scalar fields between different bodies described by delta
function potentials. When the coupling to the potentials became weak,
closed-form results were obtained. We simplify this weak-coupling technique and
apply it to the case of tenuous dielectric bodies, in which case the method
involves the summation of van der Waals (Casimir-Polder) interactions. Once
again exact results for finite bodies can be obtained. We present closed
formulas describing the interaction between spheres and between cylinders, and
between an infinite plate and a retangular slab of finite size. For such a
slab, we consider the torque acting on it, and find non-trivial equilibrium
points can occur.Comment: 4 pages, 3 figure
How does Casimir energy fall? III. Inertial forces on vacuum energy
We have recently demonstrated that Casimir energy due to parallel plates,
including its divergent parts, falls like conventional mass in a weak
gravitational field. The divergent parts were suitably interpreted as
renormalizing the bare masses of the plates. Here we corroborate our result
regarding the inertial nature of Casimir energy by calculating the centripetal
force on a Casimir apparatus rotating with constant angular speed. We show that
the centripetal force is independent of the orientation of the Casimir
apparatus in a frame whose origin is at the center of inertia of the apparatus.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding
A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))
We investigate a two parameter quantum deformation of the universal
enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the
Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown
that possesses a non-commutative, non-cocommutative Hopf
algebra structure. All the results are expressed in the standard form using
quantum Chevalley basis.Comment: 8 pages; IC/93/41
Electromagnetic semitransparent -function plate: Casimir interaction energy between parallel infinitesimally thin plates
We derive boundary conditions for electromagnetic fields on a
-function plate. The optical properties of such a plate are shown to
necessarily be anisotropic in that they only depend on the transverse
properties of the plate. We unambiguously obtain the boundary conditions for a
perfectly conducting -function plate in the limit of infinite
dielectric response. We show that a material does not "optically vanish" in the
thin-plate limit. The thin-plate limit of a plasma slab of thickness with
plasma frequency reduces to a -function plate
for frequencies () satisfying . We show that the Casimir interaction energy between two parallel perfectly
conducting -function plates is the same as that for parallel perfectly
conducting slabs. Similarly, we show that the interaction energy between an
atom and a perfect electrically conducting -function plate is the usual
Casimir-Polder energy, which is verified by considering the thin-plate limit of
dielectric slabs. The "thick" and "thin" boundary conditions considered by
Bordag are found to be identical in the sense that they lead to the same
electromagnetic fields.Comment: 21 pages, 7 figures, references adde
Radar systems for the water resources mission, volume 2
The application of synthetic aperture radar (SAR) in monitoring and managing earth resources was examined. The function of spaceborne radar is to provide maps and map imagery to be used for earth resource and oceanographic applications. Spaceborne radar has the capability of mapping the entire United States regardless of inclement weather; however, the imagery must have a high degree of resolution to be meaningful. Attaining this resolution is possible with the SAR system. Imagery of the required quality must first meet mission parameters in the following areas: antenna patterns, azimuth and range ambiguities, coverage, and angle of incidence
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