A Reverse of bessel’s inequality in 2-inner product spaces and some grüss type related results with applications

A reverse of Bessel’s inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given.     

A potential source of free radicals in iodine-based chemical oscillators

The iodide-peroxide system in an acidic medium was investigated as a potential source of free radicals in iodine-based chemical oscillators. The radicals were detected by EPR spin-trapping using spin-trap 5-(tert-butoxycarbonyl)-5-methyl-1-pyrroline N-oxide (BMPO), which forms stable spin-adducts with oxygen-centered radicals. The iodide-peroxide system is introduced as an easily available laboratory source of free radicals.     

Nonlinear spectral-spatial control and localization of supercontinuum radiation

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Characterizations of proximinal,semichebychevian and chebychevian subspaces in real normed spaces

A simple model optimal control problem for continuous casting with state-space constraints is approximated, as usual, by a penalty method and by a numerical discretization of the nonlinear heat equation. The convergence of the approximate problems directly to the original problem is proven under a stability criterion linking the penalty parameter with the discretization parameters. For this purpose, known discretization error estimates for the Stefan problem are extended for the case of time varying boundary conditions.     

Some general divergence measures for probability distributions

Summary General divergence measures for probability distributions are introduced and their main properties established. Connections with f-divergence corresponding to a convex function fare explored.     

Application of flammability limit criteria on non-ASTM standard equipment

Journal of Thermal Analysis and Calorimetry - Accurate data of flammability limits for flammable gases and vapors are needed to prevent fires and explosions. The flammability limit, which is the...     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

Infinitesimal Liouville Distributions for Teichmuller space

We consider an arbitrary Riemann surface X, possibly of infinitehyperbolic area. The Liouville measure of the hyperbolic metricdefines a measure on the space of geodesics of the universal covering of X. As we vary the Riemann surface structure,this gives an embedding from the Teichmuller space of X intothe Fréchet space of Hölder distributions on G. We show that the embedding is continuouslydifferentiable. In particular, we obtain an explicit integralrepresentation of the tangent map. 2000 Mathematics SubjectClassification 30F60, 32G15 (primary), 46F99 (secondary).     

Some Logical Implications of the Two Einstein Assumptions Used in His Analysis of Geometry on a Relativistically Rotating Disc

We show that with the help of the two well known Einstein assumptions used by him in the treatment of geometry on relativistically rotating disc, and elementary logical analysis only, two different and opposite models of rotating discs can be constructed: In one of them the disc, set rotating from the stationary state, changes neither its radius nor circumference, as measured from stationary inertial frame; while in the other both the radius and the circumference contract by the same Lorentz factor. We also show that one can construct discs whose contraction factors vary continuously from unity (no contraction) to the full Lorentz factor.