An oscillation criterion for discrete trigonometric systems

In this paper, we investigate oscillation properties of discrete trigonometric systems whose coefficients matrices are simultaneously symplectic and orthogonal. The main result generalizes a necessary and sufficient condition of non-oscillation of trigonometric systems proved by M. Bohner and O. Do?lý (J. Differential Equations 163 (2000), pp. 113–129) in the case when the block in the upper right corner of the coefficient matrix is symmetric and positive definite. Now, we present this oscillation criterion for an arbitrary trigonometric system. The obtained results are applied to formulate a necessary and sufficient condition for non-oscillation of even-order Sturm–Liouville difference equations.     

The number of edges of radius-invariant graphs

The eccentricity e(υ) of vertex υ is defined as a distance to a farthest vertex from υ. The radius of a graph G is defined as r(G) = {e(u)}. We consider properties of unchanging the radius of a graph under two different situations: deleting an arbitrary edge and deleting an arbitrary vertex. This paper gives the upper bounds for the number of edges in such graphs. Supported by VEGA grant No. 1/0084/08.     

Electrophoretic methods for analysis of urinary polypeptides in IgA-associated renal diseases

We evaluated the utility of SDS-PAGE/Western blot and CE coupled with MS (CE-MS) for detection of urinary polypeptide biomarkers of renal disease in patients with IgA-associated glomerulonephritides. In a reference cohort of 402 patients with various renal disorders and 207 healthy controls, we defined CE-MS patterns of renal damage and IgA nephropathy (IgAN). In a blinded analysis of a separate cohort of patients with IgAN (n = 10), Henoch-Schoenlein purpura (HSP) with nephritis (n = 10), and IgA-associated glomerulonephritis due to hepatitis C virus (HCV)-induced cirrhosis (n = 9), and healthy controls (n = 12), we compared SDS-PAGE/Western blot and CE-MS against clinical urinalysis for detection of urinary proteins/polypeptides. Urinalysis indicated proteinuria for 50, 90, and 33% of patients, respectively, and for none of the healthy controls. SDS-PAGE/Western blot showed urinary polypeptides abnormality for 90, 80, and 67% of patients, respectively, and for none of the healthy controls. CE-MS indicated a Renal Damage Pattern in 80, 80, and 100 of patients, respectively, and in 17% of healthy controls, with the more specific IgAN Pattern in 90, 90, and 1%, respectively, and in none of the healthy controls. Based on differences in CE-MS patterns, the disease mechanisms may differ among various IgA-associated glomerulonephritides. These exploratory findings should be evaluated in a prospective study with contemporaneous renal biopsy and urinary testing. If validated, it may be feasible to adapt the CE-MS methodology to develop novel tests to detect renal injury at earlier stages, assess clinical manifestations, and monitor responses to therapy in patients with IgA-associated renal diseases.     

Ternary Hybrid γ‐Fe2O3/CrVI/Amine Oxidase Nanostructure for Electrochemical Sensing: Application for Polyamine Detection in Tumor Tissue

Dichromate binds to surface‐active maghemite nanoparticles (SAMNs) to form a stable core–shell nanostructures (SAMN@Cr^VI). The hybrid was characterized by Mössbauer spectroscopy, high‐angle annular dark‐field imaging, electron energy‐loss spectroscopy, and electrochemical techniques, which revealed a strong interaction of dichromate with the nanoparticle surface. Electrochemical characterization showed lower charge‐transfer resistance, better electrochemical performance, and more reversible electrochemical behavior with respect to naked SAMNs. Moreover, SAMN@Cr^VI is an excellent electrocatalyst for hydrogen peroxide reduction. Furthermore, an enzyme, namely, bovine serum amine oxidase (BSAO: EC 1.4.3.6), was immobilized on SAMN@Cr^VI by self‐assembly to give a ternary hybrid nanostructured catalyst for polyamine oxidation (SAMN@Cr^VI‐BSAO). SAMN@Cr^VI‐BSAO was applied for the development of a reagentless, fast, inexpensive, and interference‐free polyamine biosensor, which was successfully exploited for the discrimination of tumorous tissue from healthy tissue in human crude liver extracts.     

Synthesis of electron energy loss spectra for the quantification of detection limits.

We describe a method for predicting detection limits of minority elements in electron energy loss spectroscopy (EELS), and its implementation as a software package that gives quantitative predictions for user-specified materials and experimental conditions. The method is based on modeling entire energy loss spectra, including shot noise as well as instrumental noise, and taking into account all the relevant experimental parameters. We describe the steps involved in modeling the entire spectrum, from the zero loss up to inner shell edges, and pay particular attention to the contributions to the pre-edge background. The predicted spectra are used to evaluate the signal-to-noise ratios (SNRs) for inner shell edges from user-specified minority elements. The software also predicts the minimum detectable mass (MDM) and minimum mass fraction (MMF). It can be used to ascertain whether an element present at a particular concentration should be detectable for given experimental conditions, and also to quickly and quantitatively explore ways of optimizing the experimental conditions for a particular EELS analytical task. We demonstrate the usefulness of the software by confirming the recent empirical observation of single atom detection using EELS of phosphorus in thin carbon films, and show the effect on the SNR of varying the acquisition parameters. The case of delta-doped semiconductors is also considered as an important example from materials science where low detection limits and high spatial resolution are essential, and the feasibility of such characterization using EELS is assessed.     

Laser ablation generation of cluster ions from concentrated sulfuric and selenic acids

The generation and identification of novel homo- and hetero-polyacid clusters was achieved using a standard matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometer. The formation of several singly charged species was achieved via the interaction of a laser beam with concentrated sulfuric acid, selenic acid or their mixtures, applied on a graphite microcrucible. A higher yield of the species was observed in the negative detection mode, where sulfuric acid adducts HSO(4) (-) . mH(2)SO(4) (m = 0-3) and HSO(4) (-) . mH(2)SO(4) . SO(3) (m = 1, 2), and selenic acid adducts HSeO(4) (-), HSeO(4) (-) . X (X = SeO(3), H(2)SeO(4), 2SeO(3), H(2)SO(4) . SeO(3)) and NaSeO(4) (-). Y (Y = H(2)SeO(4), H(2)SeO(4). SeO(3), 2H(2)SO(4), H(2)SeO(4) . 2SeO(3), 2H(2)SeO(4) . SeO(3), 3H(2)SeO(4)), were identified. In the mass spectra of the mixture of acids, besides the homo-polyacidic adducts, eleven mixed species containing both sulfuric and selenic acid molecules or ions were identified, of which the heaviest was found to correspond to NaSeO(4) (-) . H(2)SeO(4) . 3SO(3). The stoichiometry of the species was confirmed using isotopic pattern modeling.     

Monte Carlo correction programme for PC

A Monte Carlo correction program for quantitative microanalysis on PC computer is introduced in this paper. The elastic scattering is described by the screened Rutherford cross section. Instead of computing the energy loss according to the actual path between two scatterings we have defined the Bethe inelastic cross section determined by the Bethe-slowing-down approximation. It is assumed that it causes no angular departure of the scattered electron. In the second model we took into account the angular dependence of inelastic scattering assuming that the primary electron interacts with quasi-free atom electrons. On the basis of these two models analytical Monte Carlo programmes were developed and experimentally tested on some oxide glass. Our results are fully comparable to those obtained by ten world microprobe laboratories using classical ZAF correction or Bence-Albee methods. We have found that introducing angular part of the inelastic cross section analytical results did not significantly change. All of our results were carried out for bulk specimens but extending it to layers is under the development.     

9,9′-Thiobis-(1,2,3,4,7,8-hexahydro-7-methyl-6H-pyrimido[1,6-a]pyrimidine-6,8-dione)

The 6-(3-hydroxypropylamino)-3-methylpyrimidine-2,4-dione (1) did not afford the expected 6-(3-chloro-propylamino)- derivative on reaction with thionyl chloride, but, instead, the pyrimidine rings were joined via a sulfur bridge to give 9,9′-thiobis(1,2,3,4,7,8-hexahydro-7-melnyl-6H-pyrimido[1,6-a]pyrirnidine-6,8-dione) ( 3 ). An identical 9,9′-thiobis- derivative 3 was obtained when reacting thionyl chloride with 1,2,3,4,7,8-hexahydro-7-methyl-6H-pyrimido[1,6-a]pyrimidine-6,8-dione ( 4 ). We suppose the sulfoxide- derivative 2 to be the intermediate of both routes: it underwent reduction to the final sulfide 3 in excess thionyl chloride.