Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs

In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method.     

Highly selective PVC-membrane electrodes based on Co(II)-Salen for determination of nitrite ion.

A cobalt(II) derivative was used as a suitable ionophore for the preparation of a polymeric membrane nitrite-selective electrode. The electrode reveals a Nemstian behavior over a very wide NO2- ion concentration range (1.0 x 10(-6)-1.0 x 10(-1) M) and a very low detection limit (5.0 x 10(-7) M). The potentiometric response is independent of the pH of solution in the pH range 4.0-9.5. The electrode shows advantages such as low resistance, fast response and, most importantly, good selectivity relative to a wide variety of inorganic and organic anions. In fact, the selectivity behavior of the proposed NO2- ion-selective electrode shows great improvements compared to the previously reported electrodes for nitrite ion. The proposed electrodes could be used for at least 2 months without any significant changes in potentials. The electrode was successfully applied to the determination of nitrate ion concentrations in sausage and milk samples.     

Spectroscopic studies of biologically active organotin(IV) derivatives of 2-[N-(2,4,6-tribromophenylamido]propanoic acid

Herein we describe the synthesis and characterization of compounds having the formulae R₂SnL₂ and R₃SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and ¹H, ¹³C, ¹¹⁹Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results.     

1,1‐Organoboration of bis(trimethylstannyl)ethyne with trimethylsilyl‐ and dimethylsilyl‐dialkylboryl‐substituted alkenes: organometallic‐substituted allenes

The reactions of bis(trimethylstannyl)ethyne, Me₃Sn–C?C–SnMe₃ ( 4 ), with trimethylsilyl‐ or dimethylsilyl‐dialkylboryl‐substituted alkenes 1 – 3 afford organometallic‐substituted allenes 5 , 6 and 8 , 9 in high yield. In the case of (E)‐2‐trimethylsilyl‐3‐diethylboryl‐2‐pentene ( 1) , a butadiene derivative 7 could be detected as an intermediate prior to rearrangement into the allene. All reactions were monitored by ²⁹Si and ¹¹⁹Sn NMR, and the products were characterized by an extensive NMR data set (¹H, ¹¹B, ¹³C, ²⁹Si, ¹¹⁹Sn NMR). Copyright © 2003 John Wiley & Sons, Ltd.     

Ca(NO3)2•4H2O-catalysed Biginelli Reaction: One-pot Synthesis of 1,2,3,4-Tetrahydropyrimidin-2-ones/pyrimidine-2-thiones under Solvent-free Conditions

The synthesis of 1,2,3,4-dihydropyrimidinone/thione derivatives was achieved in good to excellent yields using calcium(II) nitrate as catalyst to promote the Biginelli three-component condensation reaction from a diversity of aromatic aldehydes, β-keto compounds and urea or thiourea. The reaction was carried out under solvent-free conditions.     

Solid-liquid extraction and preconcentration of trace nickel using 2-nitroso-1-naphthol-4-sulfonic acid (Nitroso-S) and TDBA onto benzophenone and determination by atomic absorption spectrometry.

Nickel was quantitatively retained by 2-nitroso-1-naphthol-4-sulfonic acid (Nitroso-S) and tetradecyldimethylbenzylammonium chloride (TDBA Cl) onto benzophenone in the pH range 5.0-6.0 from large volumes of aqueous solutions of various samples. After filtration, each solid mass consisting of a nickel complex and benzophenone was dissolved with 5 ml of dimethylformamide (DMF) and the metal was determined by atomic absorption spectrometry (AAS). About 0.6 microg of nickel could be concentrated from 200 ml of an aqueous sample, where its concentration was as low as 3.0 ng/ml. Eight replicate determinations of 2.5 microg/ml of nickel in the final DMF solution gave a mean absorbance of 0.112 with a relative standard deviation of 1.9%. The sensitivity for 1% absorption was 98 ng/ml. The interference of a number of anions and cations was studied and the developed optimized conditions were utilized for the trace determination of nickel in various alloys and biological samples.     

Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO

We have found that the gold nanoparticles on the ITO substrates might be considered promising materials for circularly polarized light-induced linear electrogyration (EG). The maximal achieved value of the EG susceptibility described by third-order axial tensor caused by probe circularly polarized light at a wavelength of 1060 nm was equal to about 13 deg/mm at pulsed electric field strength 30.0 V/cm with a duration of about 1 ms. We have revealed that the maximal EG coefficient is achieved for the samples possessing maximal resistivity. The investigated composites possess long-lived EG grating which decreases by not more than 12% after 120 min of laser treatment. Applying a non-circular pump light leads to the diminishing of the observed EG.     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.