Mean value estimates in lattice point theory

LetQ(u) be a positive definite quadratic form inr2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0b _j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid andP(x)=A(x)–V(x). Let . By introduction of a parameter we shall show how the treatment of estimates onP(x) and onM(x) can be unified.     

Lattice point theory in polyhedra

The exact order of the remainder term is determined in the formula for the number of lattice points in the region α₁∥u₁ + b₁∥ + α₂∥u₂ + b₂∥ + … + α_r∥u_r + b_r∥ ≤ x in dependence on the arithmetical properties of the coefficients α₁, α₂,…, α_r.     

Nanofibers of Semiconductor Oxides as Sensitive Materials for Detection of Gaseous Products Formed in Low-Temperature Pyrolysis of Polyvinyl Chloride

Nanofibers of semiconducting oxides SnO₂, ZnO, WO₃, produced by the electrospinning method, were tested as sensitive materials for detection of products formed in pyrolysis of polyvinyl chloride in conditions simulating the smoldering of electrically insulating materials upon occurrence of a short-circuit failure in electrical circuits. The method of thermal analysis with mass-spectroscopic determination of gaseous products demonstrated that, in pyrolysis of polyvinyl chloride in the temperature range 200–400°C corresponding to the invisible-smoke stage, the main component of the gas mixture being formed is HCl. It was shown that the materials synthesized can be used to develop gas sensors for early fire warning.     

Separation of PCR-ready DNA from dairy products using magnetic hydrophilic microspheres and poly(ethylene glycol)-NaCl water solutions

Carboxyl group-containing magnetic nonporous poly(2-hydroxyethyl methacrylate-co-glycidyl methacrylate) (P(HEMA-co-GMA)) and magnetic glass microspheres were used for the isolation of bacterial DNA. P(HEMA-co-GMA) microspheres were prepared by the dispersion polymerization in toluene/2-methylpropan-1-ol mixture in the presence of magnetite nanoparticles obtained by coprecipitation of Fe(II) and Fe(III) salts with ammonium hydroxide. Carboxyl groups were then introduced by oxidation of the microspheres with potassium permanganate. The most extensive DNA recovery was achieved at PEG 6000 concentrations of 12% or 16% and 2 M NaCl. The method proposed was used for bacterial DNA isolation from different dairy products containing Bifidobacterium and Lactobacillus cells. The presence of target DNA and the quality of isolated DNA were checked by polymerase chain reaction (PCR) amplification with specific primers.     

Friedel-Crafts alkylation of indoles with nitroalkenes catalyzed by Cu(Ⅱ)-imine complex

A series of new ligands L₁-L₇ were readily prepared in one step.Friedel-Crafts alkylation of indoles with nitroalkenes catalyzed by a novel Cu（Ⅱ）-L complex has been developed.The remarkable advantages of this reaction are mild reaction conditions,simple workup procedure,high yields of products and the use of ethanol as a green solvent.     

Effect of Bimetallic Pd/Pt Clusters on the Sensing Properties of Nanocrystalline SnO<Subscript>2</Subscript> in the Detection of CO

Nanocrystalline tin dioxide modified by Pd and Pt clusters or by bimetallic PdPt nanoparticles was synthesized. Distribution of the modifers on the SnO₂ surface was studied by high-resolution transmission electron microscopy and energy dispersive X-ray microanalysis with element distribution mapping. It was shown that the Pd/Pt ratio in bimetallic particles varies over a broad range and does not depend on the particle diameter. The effect of platinum metals on the reducibility of nanocrystalline SnO₂ by hydrogen was determined. The sensing properties of the resulting materials towards 6.7 ppm CO in air were estimated in situ by electrical conductivity measurements. The sensor response of SnO₂ modified with bimetallic PdPt particles was a superposition of the signals of samples with Pt and Pd clusters.     

New Advances in Catalytic Systems for Conversion of CH_4 and CO_2

One of the main goals for developing the C1 chemical industry is the direct conversion of methane and carbon dioxide to useful products. To realize this goal, researches on new catalytic systems are being globally focused. The exploration has been evolved from traditional heterogeneous catalysis into homogeneous catalysis. Coordinate complexes, biochemical and bionics, and photo- and electrochemical catalysis have been extensively studied in recent years. Tests in laboratories have verified for the direct conversion of CH4 to CH3OH that single-pass converstion of CH4 can reach over 70% in both Hg(II) salt and Pt(II) complex systems. The main problem of these systems is the obstacles involving reaction kinetics, so they must be solved before moving to pilot tests. Other catalytic systems discussed in the present article include explorations in the early stage. Among them, features of photo and enzymatic catalyst systems, such as mild reaction conditions, better selectivity and environmentally friendliness     

Immunomagnetic separation and detection of Salmonella cells using newly designed carriers

A new method for simultaneous determination of alkoxyethanols (2-methoxyethanol, 2-ethoxyethanol, 2-isopropoxyethanol, and 2-butoxyethanol) by high-performance liquid chromatography (HPLC) with fluorescence detection has been developed. The alkoxyethanols and an internal standard (2-phenoxyethanol) were derivatized by treatment with 1-anthroylnitrile to give the anthroyl esters. The esterification was completed in 30 min in the presence of quinuclidine as base catalyst at room temperature. After stopping the reaction, an aliquot of the final solution was injected into the HPLC. The resulting anthroyl esters of the alkoxyethanols and the internal standard were separated on a C18 reversed-phase column with acetonitrile-water-acetic acid (65:35:0.1, v/v) as the mobile phase and detected fluorimetrically at excitation and emission wavelengths of 360 nm and 460 nm, respectively. The detection limits of the derivatives as alkoxyethanols at a signal-to-noise ratio of 3 were in the range of 1-3 pg per injection. The minimal amounts of alkoxyethanols derivatized in the reaction mixture for derivatization to determine the limits of detection were approximately 0.5 ng. This HPLC method was applied to the determination of some of alkoxyethanols in the air of the workplace where the thinner containing alkoxyethanols was used for painting.     

Determination of neopterin, kynurenine, tryptophan and creatinine in human serum by high throuput HPLC

A new HPLC method for simultaneous determination of neopterin, creatinine, kynurenine and tryptophan in human serum was developed and validated. Monolithic stationary phase's technology (two monolithic columns RP-18e were connected with guard monolithic cartridge 4.6 mm × 50 mm + 3.0 mm × 100 mm and 4.6 × 10 mm) and special auto sampler for micro titration plates (samples are storage in dark cooled place protected against evaporation) were combined with easy sample preparation step. As mobile phase 15 mmol/L phosphate buffer at pH 4.50 was used. Neopterin and tryptophan were detected using fluorescent detection and kynurenine and creatinine were detected by diode-array detection. This method may be suitable for large sequences of samples in clinical research and routine practice.