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 $^{87}$Rb spin-1 Bose-Einstein condensate to the $1_\mathrm{g} (P_{3/2}) v = 152$ 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