The rank of the covariance matrix of an evanescent field

Evanescent random fields arise as a component of the 2D Wold decomposition of homogeneous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the observed signal in the space-time adaptive processing (STAP) of airborne radar data. In this paper we derive an expression for the rank of the low-rank covariance matrix of a finite dimension sample from an evanescent random field. It is shown that the rank of this covariance matrix is completely determined by the evanescent field spectral support parameters, alone. Thus, the problem of estimating the rank lends itself to a solution that avoids the need to estimate the rank from the sample covariance matrix. We show that this result can be immediately applied to considerably simplify the estimation of the rank of the interference covariance matrix in the STAP problem.     

Simplified method for concentration of mitochondrial membrane protein complexes

Extracting and concentrating mitochondrial protein complexes from gel strips after blue native PAGE (BN‐PAGE) can be daunting tasks using the traditional methods, such as electroelution, passive diffusion and centrifugal concentration. We present a simplified gel electrophoresis method to concentrate mitochondrial protein complexes with excellent recovery rate. Mitochondrial complex I present in a long gel strip from BN‐PAGE can be easily concentrated into a 0.8 cm gel strip when a second BN‐PAGE is performed with a Y‐shaped gel and the addition of 0.01% n‐dodecyl β‐D ‐maltoside and 0.001% SDS in the cathode buffer. Once completed, the concentrated protein complex in the gel strip is ready for SDS‐PAGE or proteomic studies.     

On generalized harmonic number sums

We evaluate generalized harmonic number sums with parameter in terms of values of polylogarithm functions, and several examples are given. Instances of such sums occur in diverse areas including analytic number theory, and in calculations of high energy, nuclear, and atomic physics.     

Use of an internal control for matrix-assisted laser desorption/ionization time-of-flight mass spectrometry analysis of bacteria

A method to aid in the analysis of bacterial samples of unknown concentration by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry is demonstrated. It is shown that in MALDI analysis of bacteria, the intensities of resulting peaks in spectra are sensitive to the microbial concentration. At the high and low ends of the concentration range, no signal can be obtained, leaving very concentrated or very dilute samples indistinguishable. The addition of cytochrome c as an internal control allows the differentiation of these concentrated and dilute samples. The presence of the internal control causes only a 20% to 30% decrease in signal intensity when the bacterial concentration is optimum. However, the signal quality is improved when the internal control is added to some low concentrations of bacteria.     

Phase transitions of the first kind as radiation processes

Crystallization and vapor condensation are considered as the processes of sequential penetration of single atoms/molecules into condensate. In the course of these transitions the transitive radiation must be generated, which would carry away the liberated latent heat by photons of characteristic frequencies. The transient radiation is examined by the general Ginzburg-Frank theory. The emission of defined frequencies determined by the values of liberated latent heat is confirmed by analyses of several experiments of authors and other researchers.