4,811 research outputs found
Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
We introduce the framework of path-complete graph Lyapunov functions for
approximation of the joint spectral radius. The approach is based on the
analysis of the underlying switched system via inequalities imposed among
multiple Lyapunov functions associated to a labeled directed graph. Inspired by
concepts in automata theory and symbolic dynamics, we define a class of graphs
called path-complete graphs, and show that any such graph gives rise to a
method for proving stability of the switched system. This enables us to derive
several asymptotically tight hierarchies of semidefinite programming
relaxations that unify and generalize many existing techniques such as common
quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov
functions. We compare the quality of approximation obtained by certain classes
of path-complete graphs including a family of dual graphs and all path-complete
graphs with two nodes on an alphabet of two matrices. We provide approximation
guarantees for several families of path-complete graphs, such as the De Bruijn
graphs, establishing as a byproduct a constructive converse Lyapunov theorem
for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has
gone through two major rounds of revision. In particular, a section on the
performance of our algorithm on application-motivated problems has been added
and a more comprehensive literature review is presente
Oro-Dental Health Status and Salivary Characteristics in Children with Chronic Renal Failure
Children suffering from decreased renal function may demand unique considerations regarding special oral and dental conditions they are encountered to. It is mentioned that renal function deterioration may affect the hard or soft tissues of the mouth. Having knowledge about the high prevalence of dental defects, calculus, gingival hyperplasia, modified salivary composition and tissue responses to the dental plaque may aid the physician and the dentist to help nurture the patient with chronic renal failure through the crisis, with an aesthetically satisfying and functioning dentition
Photoassociation spectroscopy of a Spin-1 Bose-Einstein condensate
We report on the high resolution photoassociation spectroscopy of a Rb
spin-1 Bose-Einstein condensate to the excited
molecular states. We demonstrate the use of spin dependent photoassociation to
experimentally identify the molecular states and their corresponding initial
scattering channel. These identifications are in excellent agreement with the
eigenvalues of a hyperfine-rotational Hamiltonian. Using the observed spectra
we estimate the change in scattering length and identify photoassociation laser
light frequency ranges that maximize the change in the spin-dependent
mean-field interaction energy.Comment: 5 pages, 4 figure
The synthesis, characterization and biological evaluation of a stable phosphorus ylide and an imidazole as novel compounds
A convenient one pot synthesis of two novel compounds including a stable phosphorus ylide and an imidazole from electron-poor acetylenes in fairly good yields by the condensation of triphenylphosphine and acetylene derivatives, in the presence of dimethyl thiourea from the 1:1:1 addition reactions is described. The structures of the synthesized compounds were characterized by IR, 1H-NMR, 13C-NMR and elemental analysis. The newly synthesized compounds were screened for antimicrobial on Staphylococcus aureus, Bacillus sublitis, Escherichia coli and Pseudomonas aeruginosa and antifungal activities on Candida albicans, patient isolate Candida glabrata and Candida krusei. The results showed that these compounds have activity against all the tested bacteria and fungi with a sufficient minimum inhibitory concentration. KEY WORDS: Phosphorus ylides, Electron-poor acetylenes, Imidazole, Antifungal, Antimicrobial Bull. Chem. Soc. Ethiop. 2014, 28(1), 137-141.DOI: http://dx.doi.org/10.4314/bcse.v28i1.1
Nonlocal communication with photoinduced structures at the surface of a polymer film
Nonlocal communication between two laser light beams is experimented in a
photochromic polymer thin films. Information exchange between the beams is
mediated by the self-induction of a surface relief pattern. The exchanged
information is related to the pitch and orientation of the grating. Both are
determined by the incident beam. The process can be applied to experiment on a
new kind of logic gates.Comment: 7 pages, 4 figures, 2 table
Quantum gravitational optics: Effective Raychaudhuri equation
Vacuum polarization in QED in a background gravitational field induces
interactions which {\it effectively} modify the classical picture of light
rays, as the null geodesics of spacetime. These interactions violate the strong
equivalence principle and affect the propagation of light leading to
superluminal photon velocities. Taking into account the QED vacuum
polarization, we study the propagation of a bundle of rays in a background
gravitational field. To do so we consider the perturbative deformation of
Raychaudhuri equation through the influence of vacuum polarization on photon
propagation. We analyze the contribution of the above interactions to the
optical scalars namely, shear, vorticity and expansion using the Newman-Penrose
formalism.Comment: 17 pages, 1 figure, RevTex format, Replaced with the published
versio
Multistate polarization addressing using one single beam in an azo polymer film
Peculiar light-matter interactions can break the rule that a single beam
polarization can address only two states in an optical memory device.
Multistate storage of a single beam polarization is achieved using self-induced
surface diffraction gratings in a photo-active polymer material. The grating
orientation follows the incident light beam polarization direction. The
permanent self-induced surface relief grating can be readout in real time using
the same laser beam.Comment: 11 pages,3 figure
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