Additive results for the Drazin inverse of block matrices and applications

In this paper, we consider the Drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu [H. Yang, X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011) 1412-1417]. As an application we give some new representations for the Drazin inverse of a block matrix.     

Effects of a parallel magnetic field on the metal-insulator transition in a dilute two-dimensional electron system

The temperature dependence of conductivity sigma(T) of a two-dimensional electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a metal-insulator transition at a critical electron density n(c)(0), and dsigma/dT>0 in the metallic phase. At low fields ( B < or approximately equal to 2 T), n(c) increases as n(c)(B)-n(c)(0) proportional, variant Bbeta ( beta approximately 1), and the zero-temperature conductivity scales as sigma(n(s),B,T = 0)/sigma(n(s),0,0) = f(B(beta)/delta(n)), where delta(n) = [n(s)-n(c)(0)]/n(c)(0) and n(s) is electron density, as expected for a quantum phase transition. The metallic phase persists in fields of up to 18 T, consistent with the saturation of n(c) at high fields.     

Gaussian-induced rotation in periodic photonic lattices

We numerically investigate time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices. We demonstrate the relation between such rotation and less confined discrete solitonic solutions.     

Determination of the soil-to-grass transfer of 137Cs and its relation to several soil properties at various locations in Serbia

Transfer coefficients of (137)Cs from soil to grass were determined for the terrain around the city of Kragujevac in central Serbia. Mass activity concentrations of (137)Cs in soil and grass samples were determined with a high-purity Ge-detector (HPGe). The activity concentration at the depth of 20 cm was found to be in the range of 14.92-124.05 Bq kg(-1), whereas the activity in grass for the same location was in the range of 4.60-84.95 Bq kg(-1). Transfer factors (TFs) were in the range of 0.07 up to 1.94. Dependences of TFs on different soil characteristics were presented graphically. Weak dependences were determined between them. Absalom's model was used to predict TFs based on soil characteristics: pH value, contents of clay, exchangeable potassium and humus. A comparison of measured and predicted values from Absalom's model is shown graphically. It has been found that Absalom's model might be carefully used for the prediction of (137)Cs in grass for specific regions.     

On the Quantum KPRV Determinants for Semisimple and Affine Lie Algebras

Let g be a semisimple or affine Lie algebra and U _q (g) its quantized enveloping algebra. Extending earlier work, the KPRV determinant for an admissible integrable U _q (g) module V relative to a parabolic subalgebra pg is defined and shown to be nonzero. These determinants had previously been evaluated for g semisimple and p a Borel subalgebra. The present results can be used to extend this to g affine as will be shown in a subsequent publication.For a parabolic subalgebra the evaluation of these determinants is much more difficult. For appropriate overalgebras of the primitive quotients of the enveloping algebra U(g) defined by one-dimensional representations of p, these determinants had been calculated for g semisimple. However the quantum case is interesting because it is unnecessary to pass to overalgebras and besides for U(g):g affine, it is not even clear how these determinants should be defined. Here for g semisimple, the degrees of the determinants are computed and shown to depend on being the same type of functions as in the enveloping algebra case; yet in a different fashion. Some special cases (in type A ₄) are computed explicity. Here, as in the Borel case, the determinants take a remarkably simple form and notably can be expressed as a product of linear factors. However compared to the enveloping algebra case one finds additional factors corresponding to what are called quantum zeros and whose origin remains unknown.     

Solid phase extraction and HPLC determination of veterinary pharmaceuticals in wastewater

This work focuses on the application of SPE-HPLC analysis of important veterinary pharmaceuticals from different classes in highly complex wastewater matrix. The pharmaceutical investigated included three sulfonamides (sulfamethazine, sulfadiazine and sulfaguanidine), a sulfonamide synergist (trimethoprim), a tetracycline (oxytetracycline), a fluoroquinolone (enrofloxacine) and a β-lactame (penicillin G/procaine). The method involves pre-concentration and clean-up by solid phase extraction (SPE) using Oasis HLB extraction catridges. Final analysis of the selected pharmaceutical compounds was carried out by high-performance liquid chromatography (HPLC) coupled with diode array detector (DAD). Recoveries were ranged from 68.3 to 97.9% with relative standard deviation below 8.4%. Only for sulfaguanidine low recovery was obtained. Limits of quantification were in the range 1.5-100 μg/L depending on pharmaceutical. The described method was applied to the determination of pharmaceuticals in wastewater samples from pharmaceutical industry.     

Re-nnd generalized inverses

In this paper, we give some necessary and sufficient conditions for the existence of Re-nnd and nonnegative definite {1,3}$\{1,3\}$- and {1,4}$\{1,4\}$-inverses of a matrix A∈C^n×n$A\in {\mathbb{C}}^{n\times n}$ and completely described these sets. Moreover, we prove that the existence of nonnegative definite {1,3}$\{1,3\}$-inverse of a matrix A   is equivalent with the existence of its nonnegative definite {1,2,3}$\{1,2,3\}$-inverse and present the necessary and sufficient conditions for the existence of Re-nnd {1,3,4}$\{1,3,4\}$-inverse of A.     

Disorder-induced localization of light near edges of nonlinear photonic lattices

We investigated the influence of edges and corners on the Anderson localization of light in disordered two-dimensional photonic lattices that are optically induced in nonlinear saturable photorefractive media. A systematic quantitative study of gradual transition from corner to bulk Anderson localization in truncated two-dimensional photonic lattices was carried out. We analyzed numerically the localization at several corners and edges of the square and triangular photonic lattices and compared them with the localization in bulk medium. We found that, for strong disorder, corners and edges effectively suppress Anderson localization, as compared to the bulk, but to a varying degree.