A linear multistep numerical integration scheme for solving systems of ordinary differential equations with oscillatory solutions

In ^[1], a set of convergent and stable two-point formulae for obtaining the numerical solution of ordinary differential equations having oscillatory solutions was formulated. The derivation of these formulae was based on a non-polynomial interpolant which required the prior analytic evaluation of the higher order derivatives of the system before proceeding to the solution. In this paper, we present a linear multistep scheme of order four which circumvents this (often tedious) initial preparation. The necessary starting values for the integration scheme are generated by an adaptation of the variable order Gragg-Bulirsch-Stoer algorithm as formulated in ^[2].     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Nuclear structure effect in internal conversion of the 166 kev hinderedM1 transition in139La

The internal conversion coefficients were calculated for the 165.853 keV 5/2⁺7/2⁺ hindered transition in ₅₇ ¹³⁹ La using the new computer program NICC for conversion coefficients of all atomic shells. The algorithm employed in this code is described. The analysis of precise experimental data yielded the nuclear penetration parameter=4.2±0.8. This value was found to be in accord with theoretical estimates and to correspond to the Nilsson deformation parameter=–0.056±0004 of the¹³⁹La nucleus. Using the Nilsson wave functions for above the mixing ratio ² = N(E2)/N(M1) was determined to be less than 8.10^–5, which supports the assumption of a pureM1 multipolarity of this transition.Presented at the 26th All-Union Conference on Nuclear Spectroscopy and Nuclear Structure (February 1976, Baku, USSR).We are obliged to Dr. B. N.Subba Rao for the communication of his value for the investigated transition.     

A measurement of the lifetimes of Ξ0 and Λ hyperons

The mean lifetimes of the Λ and Ξ⁰ hyperons have been measured in a short neutral beam at the CERN Proton Synchrotron. Λ and Ξ⁰ decays have been identified by measuring their decay products in a magnetic spectrometer and in a lead glass hodoscope. The experimental results, based on 53 000 Λ decays and 6300 Ξ⁰ decays are

From the result for τ_Ξ⁰ together with existing data on τ_Ξ^? we obtain a violation of the $\text{ΔI =}\text{1}\text{2}$ rule in non-leptonic Ξ decays.     

Development of fast atom bombardment mass spectral methods for the identification of carcinogen-nucleoside adducts

An analytical strategy using fast atom bombardment (FAB) ionization and tandem mass spectrometry has been developed to determine the molecular weight and major fragment ions, and to provide limited structural characterization of low picomole levels of carcinogen-nucleoside adducts. This strategy consists of three main components: (1) the sensitivity for analysis by FAB combined with mass spectrometry is increased via chemical derivatization; (2) the nucleoside adducts are selectively detected by using constant neutral loss scans; and (3) structurally characteristic fragments are obtained by using daughter ion scans. Trimethylsilyl derivatized arylamine-nucleoside adducts have been detected at levels as low as a few picomoles by using this approach. After experimental determination of the mass of the BH ₂ ⁺ fragment ion, daughter ion spectra have been used to probe the structure specificity associated with collision-activated decomposition of this fragment. With model C-8 substituted arylamine adducts [N-(deoxyguanosin-8-yl)-4-aminobiphenyl, N-(deoxyadenosin--yl)-4-aminobiphenyl, and N-(deoxyguanosin-8-yl)-2-aminofluorene], nucleoside-specific and carcinogen-specific fragmentation have been observed in daughter ion spectra.     

19-Electron arenecyclopentadienyl complexes of ruthenium

A series of are necyc lope ntadienyl complexes,i. e., [Ru(⁵-c₅R₅)(⁶- are ne)]⁺ (1, R= H, arene = C₆H₆; 2, R = Me, arme = C₆H₆; 3, R = H, arctic = C₆H₃Me₃; 4, R = Me, arene = C₆H₃Me₃; 5, R = H, arene = C₆Me₆; 6, R = Me, arene = C₆Me₆) was studied by cyclic voltammetry. These compounds are capable of both oxidation and reduction. The reduction potential values depend on the number of methyl groups in the complex. Reduction of benzene complexes I and 2 by sodium amalgam in THF leads to the formation of decomplexation products, the addition of hydrogen to benzene, and dimerization of the benzene ligands. Both chemical and electrochemical reductions of mesitylene complexes3 and4 result in dimeric products [(⁵-C₅R₅)Ru(-⁵;⁵-Me₃H₃C₆H₃Me₃)Ru(⁵-C₅R₅)] (14, R = H; 15, R = Me). The action of sodium amalgam on compound5 gives products of hydrogen addition to both hexamethylbenzene (17) and cyclopentadienyl (18) ligands along with the major product, the dimer [⁵-C₅H₅)Ru(-⁵; ⁵-Me₆C₆C₆Me₆)Ru(⁵-C₅H₅)] (16). In contrast to5, its permcthylated analog 6 is only capable of adding hydrogen to the hexamethylbenzene ligand.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1691–1697, July, 1996.     

Determination of kinetic parameters for the inhibitory effects of organic sulphides on an amperometric peroxide biosensor in non-aqueous media

The amperometric detection of some organic sulphides in non-aqueous media using a horseradish peroxidase modified platinum electrode is reported. The performance of the electrode is based on the inhibitory effect of sulphides on the activity of peroxidase. The electrode responds rapidly to micromolar concentrations of the sulphides with linearities extending up to 0.4, 0.25 and 0.8 mmol/dm(3) for thiourea, ethylenethiourea, and mercaptoethanol, respectively. The current as peroxide concentration approaches infinity in the absence of any inhibitor (I(max)), and the apparent inhibition constant (K'(i)) for each inhibitor were evaluated. I(max)/K'(i), i.e. the percentage inhibition of sensor response per millimolar of each inhibitor, was calculated and used as a measure of the performance of the sensor in the determination of the organic sulphides. From these values the sensitivity trend of the biosensor for the organic sulphides is ethylenethiourea > thiourea > mercaptoethanol. The kinetic effects of other operational parameters such as mediator concentration, water content of the solvent and working potential were also evaluated to assess analytical performance.     

Highly efficient transfer of chirality from macrocyclic conformation in the tandem oxy-Cope/Claisen/ene reaction

We report three highly stereoselective pericyclic reactions occurring in cascade leading to the synthesis of Decalins skeletons possessing two contiguous quaternary centers. The tandem reaction is triggered by an oxy-Cope rearrangement to create in situ a 10-membered ring enol ether macrocyle 6, which immediately rearranges via a Claisen [3,3] shift to the corresponding E-cyclodec-6-en-1-one 7. The latter spontaneously cyclizes via a transannular ene reaction to produce Decalin 5. Analysis of the mechanism with respect to the origin of the high diastereoselectivity of the tandem oxy-Cope/Claisen/ene reaction is presented.     

Multicapillary Chromatographic Columns

The possibilities for multicapillary tubes with channels 3–10 μm in diameter and a total number of channels of about 2 × 10⁵−10⁶ to be used as chromatographic columns are studied. It is shown that substances with a sufficiently high boiling point can be separated at temperatures of 20–30°C in 2–3 min with an efficiency of about 1500 theoretical plates per meter (300 theoretical plates for a 20-cm column). __________ Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 10, 2005, pp. 1075–1079. Original Russian Text Copyright ? 2005 by Rudenko, Shoromov, Kumakhov, Naida.