Riesz Basis of Eigenvectors for Analytic Families of Operators and Application to a Non-symmetrical Gribov Operator

In the present paper, we are mainly concerned with the existence of a Riesz basis related to the Gribov operator

$$\begin{aligned} A^{*2}A^2+\varepsilon (A^* A + A^* (A + A^* )A), \end{aligned}$$

where \(\varepsilon \in \mathbb {C}\); while A is the annihilation operator and \(A^*\) is the creation operator verifying \([A, A^*] = I.\) Through a specific growing inequality, we extend this problem to a theoretical one and we study the invariance of the closure, the comportment of the spectrum as well as the existence of Riesz basis of generalized eigenvectors.

     

A lariat‐functionalized copper(II) di­imine–dioxime complex

The dimeric title copper(II) complex, diaqua‐1κO,2κO‐bis[3,9‐dimethyl‐6‐(2‐pyridyl­methyl)‐4,8‐di­aza­undeca‐3,8‐di­ene‐2,10‐dione dioximato(1?)]‐1k⁴N²,N⁴,N⁸,N¹⁰;1:2κ⁵O²:N²,N⁴,N⁸,N¹⁰‐dicopper(II) diperchlorate, [Cu₂(C₁₇H₂₄N₅O₂)₂](ClO₄)₂, crys­tallizes with one Cu atom in a square‐pyramidal environment and the other Cu atom displaying a distorted octahedral coordination. In each case, the four N atoms in the core of the ligand (two imine and two oxime N atoms) form the base of the pyramid, with a water mol­ecule at an apex. The two parts of the dimer are linked by an interaction [2.869 (2) Å] between one of the Cu atoms and one of the oxime O atoms coordinated to the second Cu atom, and also by a hydrogen bond between the apical water mol­ecule on the second Cu atom and the pyridyl N atom from the coordination sphere of the first Cu atom. The pyridyl N atoms of the lariat arms are not coordinated to either of the Cu atoms. Thus, this potentially pentadentate ligand is only tetradentate when coordinated to Cu^II.     

On ηα-groups and fields

Let :=. The following are known: two -sets of power are isomorphic. Let >0. Two ordered divisible Abelian groups that are -sets of power are isomorphic, two real closed fields that are -sets of power are isomorphic. The following is shown: (1) there exist 2 nonisomorphic ordered Abelian groups (respectively ordered fields) that are -sets of power ; (2) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) of power all having the same order type; (3) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) that are -sets having the same order type.     

Hydrothermal Syntheses of NiO−GO Nanocomposite on 3D Nickel Foam as a Support for Pt Nanoparticles and its Superior Electrocatalytic Activity towards Methanol Oxidation

In this project, Pt/NiO?GO nanocatalyst is grown on nickel foam (NF) and, its catalytic activity towards electrochemical oxidation of methanol in acidic media is studied. The first step is devoted to the synthesis of NiO?GO support by a hydrothermal method. Then Pt nanoparticles (～34.3 nm) are electrodeposited on this supporting material. Hydrothermal and electrochemical deposition conditions are optimized. Surface of modified NF was inspected for physical characterization and Chemical composition by some techniques such as field emission scanning electron microscopy (FESEM), energy‐dispersive X‐ray spectra (EDS), and X‐ray diffraction (XRD). In the electrochemical section, the catalytic performance of Pt/NiO?GO/NF towards methanol oxidation is investigated by cyclic voltammetry and chronoamperometry measurements. The electrochemical impedance spectroscopy (EIS) is elected to deliberate charge transfer resistance on the catalyst surface. Mass activity, electrochemical surface area (ECSA) and durability of prepared catalysts are compared with commercial Pt/C. Deliberations prove the superiority of Pt/NiO?GO/NF towards methanol oxidation in acidic media. The Superior quality of synthesized nanocatalyst that is attributed to the synergetic effect of the NiO?GO support material and Pt nanoparticles, indicate that Pt/NiO?GO/NF can be successfully used as the anode in the direct methanol fuel cell (DMFC).     

Essential spectra of operator matrices and applications

The main goal of this paper is to give a characterization of Wolf, Schechter, and Browder essential spectra of (2 × 2) matrix operator on a Banach space. Furthermore, we apply the obtained results to transport equations. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of a selective fluorimetric technique for rapid trace determination of zinc using 3-hydroxyflavone

A sensitive and a selective spectrofluorimetric method have been developed for the rapid determination of trace levels of zinc. The method is based on complex formation between zinc and 3-hydroxyflavone (3HF), which displays an intense emission signal around 478 nm. The analytical performance of the method was examined by considering the factors that affect the complex formation such as pH, mole ratio of the metal and solvent type. The optimum conditions for the complex formation were metal to ligand stoichiometric ratio of 1:1 at pH 7.5 with 0.1 M Tris buffer. Under these conditions the detection limit attained was 1.5 ppb. The method was appropriately validated and yielded relative standard deviations of less than 2% (n = 5), which was considered acceptable. It was successfully applied to the trace determination of zinc in drinking water, hair shampoo and pharmaceutical samples.     

Antibacterial,Antioxidant and Binding Studies of Some Novel Diaryl Sulphide Derivatives

Abstract

A series of novel acyclic and cyclic diaryl sulphides was synthesized from 2,2′-dithiobenzoic acid. The various diaryl sulphides were characterized by use of spectral (IR, ¹H and ¹³C NMR, ESI/MS) and elemental analyses. The antimicrobial activities of the compounds were evaluated in terms of their minimum inhibition concentration (MIC) against a panel of clinical isolates bacteria and were found to possess only moderate antimicrobial activities. N,N′-Bis(2-hydroxyphenyl)-2,2′-thiodibenzamide (13), exhibiting a hydroxy group at the phenyl ring, was the most active antimicrobial agent within the series, with MIC values of 0.05 mg mL^–1 and 10 mg mL^–1 against Staphylococcus aureus and Bacillus cereus, respectively. The antioxidant efficiency of the diaryl sulphides was determined by 2,2-diphenyl-1-picrylhydrazyl (DPPH) scavenging activity with 13 being the most active compound. The interaction of 2,2′-thiodibenzanilide, N,N′-bis(2-methylphenyl)-2,2′-thiodibenzamide, and N,N′-bis(2-hydroxyphenyl)-2,2′-thiobenzamide with guanine, glutamic acid, and urea were studied quantitatively with binding constants ranging from 1 × 10³ M^?1 to 2.7 × 10⁴ M^?1.     

Exploration of the reactivity of N2O5 with two Si(OH)4 monomers using electronic structure methods

The heterogeneous uptake of N₂O₅ on mineral dust particles may play an important role in the removal of nitrogen oxides from the atmosphere. However, the reaction of N₂O₅ with the mineral particles is not well understood. The reaction of N₂O₅ with two Si(OH)₄ monomers is explored using theoretical methods. This study represents a first step towards understanding the interaction of N₂O₅ with the hydroxyl groups of silica particles. Energies are calculated using MP2 single point calculations on the B3LYP optimized geometries and including B3LYP thermodynamic corrections. Four mechanisms are considered for the formation of two HNO₃ and one H₆Si₂O₇. The rate limiting activation barrier of the most favorable path is found to be 12.5 kcal mol^?1. This reaction appears to be more favorable than the hydrolysis of N₂O₅ with one water molecule. These results are in agreement with experimental observations, which show that N₂O₅ reacts with OH groups of Saharan dust to form nitrate. © 2012 Wiley Periodicals, Inc.     

Allylsilyl Propargyl Ethers as Substrates for Intramolecular Pauson–Khand Reactions

Silyl ethers that are synthesized by coupling a propargylic alcohol with an allylsilyl chloride are shown to undergo sulfide‐promoted Pauson–Khand reactions, affording bicyclic enones.     

High throughput method for the analysis of cetrizine hydrochloride in pharmaceutical formulations and in biological fluids using a tris(2,2'-bipyridyl)ruthenium(II)-peroxydisulphate chemiluminescence system in a two-chip device

A fast, economic and sensitive chemiluminescence (CL) method has been developed for the analysis of cetrizine hydrochloride (CET) in pharmaceutical formulations and in biological fluids. The CL method is based on the oxidation of tris(2,2′-bipyridyl)ruthenium(II) (Ru (bipy)₃²⁺) by peroxydisulphate in a two-chip device. Up to 180 samples can be analysed per hour, consuming only minute quantities of reagents. Three instrumental setups were tested to find the most economical, sensitive and high throughput setup. In the first setup, a continuous flow of sample and CL reagents was used, whereas in the second setup, a fixed volume (2 μL) of (Ru (bipy)₃²⁺) was introduced into a continuous infusion of peroxydisulphate and the sample. In the third design, a fixed volume of sample (2 μL) was injected while the CL reagents were continuously infused. Compared to the first setup, a 200% signal enhancement was observed in the third setup. Various parameters that influence the CL signal intensity, including pH, flow rates and reagent concentrations, were optimized. A linear response was observed over the range of 50 μg L⁻¹ to 6400 μg L⁻¹ (R² = 0.9959) with RSD values of 1.1% (n = 15) for 1000 μg L⁻¹. The detection limit was found to be 15 μg L⁻¹ (S/N = 3). The amount of consumed sample was only 2 μL, from which the detected amount of CET was found to be 6.5 × 10⁻¹⁴ mol. This procedure was successfully applied to the analysis of CET in pharmaceutical formulations and biological fluids.