2,144 research outputs found
Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group
A local classification of all Poisson-Lie structures on an
infinite-dimensional group of formal power series is given. All
Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of
are also classified.Comment: 11 pages, AmSTeX fil
Hamiltonian type Lie bialgebras
We first prove that, for any generalized Hamiltonian type Lie algebra ,
the first cohomology group is trivial. We then show that
all Lie bialgebra structures on are triangular.Comment: LaTeX, 16 page
Lie bialgebras of generalized Witt type
In a paper by Michaelis a class of infinite-dimensional Lie bialgebras
containing the Virasoro algebra was presented. This type of Lie bialgebras was
classified by Ng and Taft. In this paper, all Lie bialgebra structures on the
Lie algebras of generalized Witt type are classified. It is proved that, for
any Lie algebra of generalized Witt type, all Lie bialgebras on are
coboundary triangular Lie bialgebras. As a by-product, it is also proved that
the first cohomology group is trivial.Comment: 14 page
The Chemical and Electronic Structure of the Neutral Flavin Radical as Revealed by Electron Spin Resonance Spectroscopy of Chemically and Isotopically Substituted Derivatives
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65670/1/j.1432-1033.1970.tb00277.x.pd
Phase-Locked Spatial Domains and Bloch Domain Walls in Type-II Optical Parametric Oscillators
We study the role of transverse spatial degrees of freedom in the dynamics of
signal-idler phase locked states in type-II Optical Parametric Oscillators.
Phase locking stems from signal-idler polarization coupling which arises if the
cavity birefringence and/or dichroism is not matched to the nonlinear crystal
birefringence. Spontaneous Bloch domain wall formation is theoretically
predicted and numerically studied. Bloch walls connect, by means of a
polarization transformation, homogeneous regions of self-phase locked
solutions. The parameter range for their existence is analytically found. The
polarization properties and the dynamics of walls in one- and two transverse
spatial dimensions is explained. Transition from Bloch to Ising walls is
characterized, the control parameter being the linear coupling strength. Wall
dynamics governs spatiotemporal dynamical states of the system, which include
transient curvature driven domain growth, persistent dynamics dominated by
spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising
walls.Comment: 27 pages, 16 figure
A robust, scanning quantum system for nanoscale sensing and imaging
Controllable atomic-scale quantum systems hold great potential as sensitive
tools for nanoscale imaging and metrology. Possible applications range from
nanoscale electric and magnetic field sensing to single photon microscopy,
quantum information processing, and bioimaging. At the heart of such schemes is
the ability to scan and accurately position a robust sensor within a few
nanometers of a sample of interest, while preserving the sensor's quantum
coherence and readout fidelity. These combined requirements remain a challenge
for all existing approaches that rely on direct grafting of individual solid
state quantum systems or single molecules onto scanning-probe tips. Here, we
demonstrate the fabrication and room temperature operation of a robust and
isolated atomic-scale quantum sensor for scanning probe microscopy.
Specifically, we employ a high-purity, single-crystalline diamond nanopillar
probe containing a single Nitrogen-Vacancy (NV) color center. We illustrate the
versatility and performance of our scanning NV sensor by conducting
quantitative nanoscale magnetic field imaging and near-field single-photon
fluorescence quenching microscopy. In both cases, we obtain imaging resolution
in the range of 20 nm and sensitivity unprecedented in scanning quantum probe
microscopy
Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators
Previous studies of lasers and nonlinear resonators have revealed that the
polarisation degree of freedom allows for the formation of polarisation
patterns and novel localized structures, such as vectorial defects. Type II
optical parametric oscillators are characterised by the fact that the
down-converted beams are emitted in orthogonal polarisations. In this paper we
show the results of the study of pattern and defect formation and dynamics in a
Type II degenerate optical parametric oscillator for which the pump field is
not resonated in the cavity. We find that traveling waves are the predominant
solutions and that the defects are vectorial dislocations which appear at the
boundaries of the regions where traveling waves of different phase or
wave-vector orientation are formed. A dislocation is defined by two topological
charges, one associated with the phase and another with the wave-vector
orientation. We also show how to stabilize a single defect in a realistic
experimental situation. The effects of phase mismatch of nonlinear interaction
are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including
movies, can be obtained from
http://www.imedea.uib.es/Nonlinear/research_topics/OPO
A thin layer angiogenesis assay: a modified basement matrix assay for assessment of endothelial cell differentiation
BACKGROUND: Basement matrices such as Matrigel™ and Geltrex™ are used in a variety of cell culture assays of anchorage-dependent differentiation including endothelial cell tube formation assays. The volumes of matrix recommended for these assays (approximately 150 μl/cm(2)) are costly, limit working distances for microscopy, and require cell detachment for subsequent molecular analysis. Here we describe the development and validation of a thin-layer angiogenesis (TLA) assay for assessing the angiogenic potential of endothelial cells that overcomes these limitations. RESULTS: Geltrex™ basement matrix at 5 μl/cm(2) in 24-well (10 μl) or 96-well (2 μl) plates supports endothelial cell differentiation into tube-like structures in a comparable manner to the standard larger volumes of matrix. Since working distances are reduced, high-resolution single cell microscopy, including DIC and confocal imaging, can be used readily. Using MitoTracker dye we now demonstrate, for the first time, live mitochondrial dynamics and visualise the 3-dimensional network of mitochondria present in differentiated endothelial cells. Using a standard commercial total RNA extraction kit (Qiagen) we also show direct RNA extraction and RT-qPCR from differentiated endothelial cells without the need to initially detach cells from their supporting matrix. CONCLUSIONS: We present here a new thin-layer assay (TLA) for measuring the anchorage-dependent differentiation of endothelial cells into tube-like structures which retains all the characteristics of the traditional approach but with the added benefit of a greatly lowered cost and better compatibility with other techniques, including RT-qPCR and high-resolution microscopy. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12860-014-0041-5) contains supplementary material, which is available to authorized users
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