Constructing fixed rank optimal estimators with method of best recurrent approximations

We propose a new approach which generalizes and improves principal component analysis (PCA) and its recent advances. The approach is based on the following underlying ideas. PCA can be reformulated as a technique which provides the best linear estimator of the fixed rank for random vectors. By the proposed method, the vector estimate is presented in a special quadratic form aimed to improve the error of estimation compared with customary linear estimates. The vector is first pre-estimated from the special iterative procedure such that each iterative loop consists of a solution of the unconstrained nonlinear best approximation problem. Then, the final vector estimate is obtained from a solution of the constrained best approximation problem with the quadratic approximant. We show that the combination of these techniques allows us to provide a new nonlinear estimator with a significantly better performance compared with that of PCA and its known modifications.     

Single freezing and triple melting of micrometre-scaled (NH4)2SO4/H2O droplets

Atmospheric aerosol droplets containing NH(4)(+) and SO(4)(2-) ions are precursors of cirrus ice clouds. However, the low-temperature phase transformation of such droplets is not understood yet. Here we show for the first time that micrometre-scaled (NH(4))(2)SO(4)/H(2)O droplets produce one freezing event but three melting events which are the melting of (i) pure ice, (ii) eutectic ice/(NH(4))(2)SO(4), and (iii) eutectic ice/(NH(4))(3)H(SO(4))(2). We also find that the melting of ice/(NH(4))(3)H(SO(4))(2) consists of two eutectic melting events, presumably ice/letovicite-II and ice/letovicite-III.     

DN‐Scattering of a plane wave by wedges

We continue our study of a nonstationary scattering by wedges. In this paper we consider nonstationary scattering of plane waves by a ‘hard–soft’ wedge. We prove the uniqueness and existence of a solution to the corresponding DN‐Cauchy problem in appropriate functional spaces. We also give the explicit form of the solution and prove the Limiting Amplitude Principle. Copyright © 2011 John Wiley & Sons, Ltd.     

Projection Method for Cauchy Problem for an Operator-Differential Equation

In the current paper, we study a projection method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in a Hilbert space. The projection subspaces are linear spans of eigenvectors of an operator similar to A(t). It is assumed that the operators A(t) and K(t) are sufficiently smooth. Error estimates for the approximate solutions and their derivatives are obtained. The application of the developed method for solving the initial boundary value problems is given.     

Polar nanoregions in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> (PMN): insights from a supercell approach

We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.     

Asymptotic Estimates for the p-Laplacian on Infinite Graphs with Decaying Initial Data

Potential Analysis - We consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for...     

Spatially inhomogeneous enhancement of fluorescence by a monolayer of silver nanoparticles

Near-field scanning optical microscopy (NSOM) was applied to study the effect of a two-dimensional array of silver nanoparticles on the spatial distribution and magnitude of fluorescence signal enhancement for a monolayer of Rhodamine 6G (Rh6G). Twenty polyelectrolyte monolayers were deposited between the nanoparticles and the dye by a layer-by-layer deposition technique resulting in a 15-20 nm separation cushion, necessary to minimize the fluorescence signal quenching. The fluorescence signal in NSOM images was found to be distributed inhomogeneously as small (100-200 nm in diameter) fluorescent clusters with typically 5-30 times higher fluorescence intensities than a sample without nanoparticles. The position and relative intensity of the clusters was found to be dependent on the excitation wavelength, suggesting that the enhancement originates from the nanoparticle surface plasmon resonance.     

UV resonance Raman spectroscopy probes the localization of tryptophan‐containing antimicrobial peptides in lipid vesicles

In this work we employed UV resonance Raman spectroscopy with 229 nm excitation to study two tryptophan‐containing antimicrobial peptides with a broad‐spectrum activity against Gram‐positive and Gram‐negative bacteria: lactoferricin B (LfB, RRWQWRMKKLG) and pEM‐2 (KKWRWWLKALAKK). UV resonance Raman spectra of both peptides are dominated by tryptophan bands. Raman spectra of LfB and pEM‐2 in D₂O and 2,2,2‐trifluoro ethanol (TFE) have been measured and used to identify the hydrogen‐bond strength marker bands W6 and W17. The tryptophan doublet, W7, at 1340 and 1360 cm⁻¹ was used to detect an increase in the hydrophobicity of Trp environment in TFE. The spectra of LfB in complex with model cell membranes composed of zwitterionic dipalmitoylglycero‐phosphocholine (DPPC) or anionic dipalmitoyglycero‐phosphoglycerol (DPPG) lipid vesicles revealed a more hydrophobic Trp environment in DPPG, suggesting stronger interactions between the cationic peptide and anionic model cell membrane. Copyright © 2008 John Wiley & Sons, Ltd.     

On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering

The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab.