Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.     

Integrating across Pascal's triangle

Sums across the rows of Pascal's triangle yield n² while certain diagonal sums yield the Fibonacci numbers which are asymptotic to ?n where ? is the golden ratio. Sums across other diagonals yield quantities asymptotic to cn where c depends on the directions of the diagonals. We generalize this to the continuous case. Using the gamma function, we generalize the binomial coefficients to real variables and thus form a generalization of Pascal's triangle. Integration over various families of lines and curves yields quantities asymptotic to cx where c is determined by the family and x is a parameter. Finally, we revisit the discrete case to get results on sums along curves.     

Acoustic metamaterial with negative density

We fabricated a one-dimensional acoustic metamaterial with negative effective density using an array of very thin elastic membranes. We observed acoustic equivalence of the plasma oscillation at ωc=735 Hz. The metamaterial was opaque in the frequency range from 0 to 735 Hz, and was transparent above 735 Hz. We report direct observation of negative acceleration in this acoustic medium below 735 Hz. The frequency characteristics of the metamaterial have the same form as that of metals with negative permittivity. We also provide a simple theory to explain the experimental results.     

Electronic structure and optical absorption spectra of CdSe covered with ZnSe and ZnS epilayers

Using the first-principles methods we compute the electronic structure and the absorption spectra for a wurtzite CdSe (0001) slab covered with zincblende ZnSe and ZnS epilayers. For each structure we compute the DOS and the imaginary part of the dielectric function. We find that the semiconductor passivation shifts the ‘near Fermi-level’ states of the bare CdSe slab down to lower energy levels. The migration suggests the decrease of surface effects and energy loss. We observe the substantial reduction of the abnormal peaks in the absorption spectra of the bare CdSe slab, which seems to be a consequence of the DOS migration. This is consistent with the experimental results that a proper passivation enhance the luminescence efficiency. We also study the case that the epilayer surface is terminated with PH₃ and find the PH₃ passivation also reduces the surface state to some extent.     

Enhanced strain relaxation induced by epitaxial layer growth mode of MgO thin films

Growth of MgO films on silicon substrate was conducted by KrF excimer pulsed-laser ablation system. Two kinds of growth mode were revealed in situ by reflection high energy electron diffraction. It was found that the layer growth mode of MgO thin films could remarkably reduce the misfit strain originated from the different lattice constant and thermal expansion coefficiency between MgO films and Si. An enhanced strain relaxation was discovered for MgO films, which were grown with the layer growth mode, in the film thickness range of 40-100 nm. The value of critical thickness for the formation of misfit dislocation agrees well with the calculated one. This exceptional phenomenon should be ascribed to the layer growth mode of epitaxial MgO films.     

Wave emission from heterogeneities opens a way to controlling chaos in the heart

The effectiveness of chaos control in large systems increases with the number of control sites. We find that electric field induced wave emission from heterogeneities (WEH) in the heart gives a unique opportunity to have as many control sites as needed. The number of pacing sites grows with the amplitude of the electric field. We demonstrate that WEH has important advantages over methods used in clinics, and opens a new way to manipulate vortices in experiments, and potentially to radically improve the clinical methods of chaos control in the heart.     

Extreme red shifted SERS nanotags

Surfaced enhanced Raman scattering (SERS) nanotags operating with 1280 nm excitation were constructed from reporter molecules selected from a library of 14 chalcogenopyrylium dyes containing phenyl, 2-thienyl, and 2-selenophenyl substituents and a surface of hollow gold nanoshells (HGNs). These 1280 SERS nanotags are unique as they have multiple chalcogen atoms available which allow them to adsorb strongly onto the gold surface of the HGN thus producing exceptional SERS signals at this long excitation wavelength. Picomolar limits of detection (LOD) were observed and individual reporters of the library were identified by principal component analysis and classified according to their unique structure and SERS spectra.