Exact asymptotic behavior of singular values of a class of integral operators

We find an exact asymptotic formula for the singular values of the integral operator of the form , a Jordan measurable set) where and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T.     

Spectral properties of the operator of Riesz potential type

For the operator of the Riesz potential type we estimate the second term in the asymptotic behavior of the spectrum and find its ``regularized' trace.

     

Pattern formation by spatially incoherent light in a nonlinear ring cavity

Modulation instability and pattern formation by spatially incoherent light is investigated experimentally in a nonlinear ring cavity using a photorefractive strontium barium niobate crystal as the nonlinear medium. A step-like threshold for the onset of pattern formation is observed experimentally for the case of high optical feedback. When compared to the case without feedback, this threshold is shifted towards smaller nonlinearities and a significant increase of the modulation degree of the obtained patterns is obtained. Our measurements also show that, above threshold, the dominating spatial frequency of the patterns decreases monotonically with both increasing nonlinearity and increasing feedback. PACS 42.65.Tg; 42.65.Sf; 89.75.Kd     

Integral Operators Induced by the Fock Kernel

We study the L ^p boundedness and find the norm of a class of integral operators induced by the reproducing kernel of Fock spaces over . Dostanić is partialy supported by MNZZS Grant N°ON144010, Zhu is partially supported by the US National Science Foundation.     

<Emphasis Type="Italic">p</Emphasis>-Adic probability logics

This paper represents an comprehensive overview of the results from three papers where we developed several propositional logics for reasoning about p-adic valued probability.Each of these logics is a sound, complete and decidable extension of classical propositional logic.     

Observation of staggered surface solitary waves in one-dimensional waveguide arrays

The observation of nonlinear staggered surface states at the interface between a substrate and a one-dimensional self-defocusing nonlinear waveguide array is reported. Launching of staggered input beams of different power in the first channel of the array results in formation of localized structures in different channels. Our experimental results are confirmed numerically.     

Analysis of Polymer Dynamics by NMR Modulated Gradient Spin Echo

NMR modulated gradient spin echo method, which allows the quantification of polymer segmental displacement via the measurement of the velocity autocorrelation, requires the formulation of theoretical predictions in the frequency domain in order to test their validity. We worked out the velocity autocorrelation spectrum of the segmental motion according to the Rouse and the tube/reptation model to compare it to the experimental results obtained by the new NMR technique. The analysis of polybutadiene shows the segmental velocity autocorrelation spectrum typical for the reptation-like motion of polymer in a “tube”. The measurement of bulk water indicates a kind of Rouse motion in a network of hydrogen bonds.