a theory is presented for the dispersion relations of the nonlinear phonon-polaritons arising when phonons are coupled to the electromagnetic waves in multilayered structures of nonlinear materials. the calculations are applied to a multilayered structure consisting of a thin film surrounded by semi-infinite bounding media where each layer may have a frequency dependent dielectric function and ...

We design a sublinear Fourier sampling algorithm for sparse off-grid frequency recovery.

We prove that there is no class-dual for almost all sublinear models on graphs.

The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increa...

We present a general non-oscillation criterion for a second order two-term scalar nonlinear differential equation in the spirit of a classic result by Atkinson [1]. The presentation is simpler than most and can serve to unify many such criteria under one common theme that eliminates the need for specfic techniques in each of the classical cases (sublinear, linear, and superlinear). As is to be ...

Inspired by recent construction of high-rate locally correctable codes with sublinear query complexity due to Kopparty, Saraf and Yekhanin (2010) we address the similar question for locally testable codes (LTCs). In this note we show a construction of high-rate LTCs with sublinear query complexity. More formally, we show that for every , ρ > 0 there exists a family of LTCs over the binary field...

Any algorithm for finding a pattern of length k in a string of length n must examine at least n k + of the characters of the string in the worst case. By considering the pattern 00 0, we prove that this is the best possible result. Therefore there do not exist pattern matching algorithms whose worst-case behavior is "sublinear" in n (that is, linear with constant less than one), in contrast wit...

the volterra model is widely used for nonlinearity identification in practical applications. in this paper, we employed volterra model to find the nonlinearity relation between electroencephalogram (eeg) signal and the noise that is a novel approach to estimate noise in eeg signal. we show that by employing this method. we can considerably improve the signal to noise ratio by the ratio of at le...