25,614 research outputs found
Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras
The concept of biperfect (noncocommutative) weak Hopf algebras is introduced
and their properties are discussed. A new type of quasi-bicrossed products are
constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which
are generalizations of the Hopf pairs introduced by Takeuchi. As a special
case, the quantum double of a finite dimensional biperfect (noncocommutative)
weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid
as well as a noncommutative and noncocommutative weak Hopf algebra are given,
generalizing quantum doubles from a group and a noncommutative and
noncocommutative Hopf algebra, respectively. Moreover, some characterisations
of quantum doubles of finite dimensional biperfect weak Hopf algebras are
obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need
pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty
Experimental evidence for new symmetry axis of electromagnetic beams
The new symmetry axis of a well-behaved electromagnetic beam advanced in
paper Physical Review A 78, 063831 (2008) is not purely a mathematical concept.
The experimental result reported by Hosten and Kwiat in paper Science 319, 787
(2008) is shown to demonstrate the existence of this symmetry axis that is
neither perpendicular nor parallel to the propagation axis.Comment: 10 pages and 3 figure
Impulsive cylindrical gravitational wave: one possible radiative form emitted from cosmic strings and corresponding electromagnetic response
The cosmic strings(CSs) may be one important source of gravitational
waves(GWs), and it has been intensively studied due to its special properties
such as the cylindrical symmetry. The CSs would generate not only usual
continuous GW, but also impulsive GW that brings more concentrated energy and
consists of different GW components broadly covering low-, intermediate- and
high-frequency bands simultaneously. These features might underlie interesting
electromagnetic(EM) response to these GWs generated by the CSs. In this paper,
with novel results and effects, we firstly calculate the analytical solutions
of perturbed EM fields caused by interaction between impulsive cylindrical GWs
(would be one of possible forms emitted from CSs) and background celestial high
magnetic fields or widespread cosmological background magnetic fields, by using
rigorous Einstein - Rosen metric. Results show: perturbed EM fields are also in
the impulsive form accordant to the GW pulse, and asymptotic behaviors of the
perturbed EM fields are fully consistent with the asymptotic behaviors of the
energy density, energy flux density and Riemann curvature tensor of
corresponding impulsive cylindrical GWs. The analytical solutions naturally
give rise to the accumulation effect which is proportional to the term of
distance^1/2, and based on it, we for the first time predict potentially
observable effects in region of the Earth caused by the EM response to GWs from
the CSs.Comment: 34 pages, 12 figure
A statistical method (cross-validation) for bone loss region detection after spaceflight.
Astronauts experience bone loss after the long spaceflight missions. Identifying specific regions that undergo the greatest losses (e.g. the proximal femur) could reveal information about the processes of bone loss in disuse and disease. Methods for detecting such regions, however, remains an open problem. This paper focuses on statistical methods to detect such regions. We perform statistical parametric mapping to get t-maps of changes in images, and propose a new cross-validation method to select an optimum suprathreshold for forming clusters of pixels. Once these candidate clusters are formed, we use permutation testing of longitudinal labels to derive significant changes
Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control
Sampled-data analysis and harmonic balance analysis are applied to analyze
switching DC-DC converters under constant on-time control. Design-oriented
boundary conditions for the period-doubling bifurcation and the saddle-node
bifurcation are derived. The required ramp slope to avoid the bifurcations and
the assigned pole locations associated with the ramp are also derived. The
derived boundary conditions are more general and accurate than those recently
obtained. Those recently obtained boundary conditions become special cases
under the general modeling approach presented in this paper. Different analyses
give different perspectives on the system dynamics and complement each other.
Under the sampled-data analysis, the boundary conditions are expressed in terms
of signal slopes and the ramp slope. Under the harmonic balance analysis, the
boundary conditions are expressed in terms of signal harmonics. The derived
boundary conditions are useful for a designer to design a converter to avoid
the occurrence of the period-doubling bifurcation and the saddle-node
bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications
on August 10, 2011; Manuscript ID: CTA-11-016
Lateral shift of the transmitted light beam through a left-handed slab
It is reported that when a light beam travels through a slab of left-handed
medium in the air, the lateral shift of the transmitted beam can be negative as
well as positive. The necessary condition for the lateral shift to be positive
is given. The validity of the stationary-phase approach is demonstrated by
numerical simulations for a Gaussian-shaped beam. A restriction to the slab's
thickness is provided that is necessary for the beam to retain its profile in
the traveling. It is shown that the lateral shift of the reflected beam is
equal to that of the transmitted beam in the symmetric configuration.Comment: 14 pages, 4 figure
- …