The Generalized Chazy Equation from the Self-Duality Equations

It is shown that classically known generalizations of the Chazy equation and Darboux–Halphen system are reductions of the self-dual Yang–Mills (SDYM) equations with an infinite-dimensional gauge algebra. The general ninth-order Darboux–Halphen system is reduced to a Schwarzian equation which governs conformal mappings of regions with piecewise circular sides. The generalized Chazy equation is shown to correspond to special mappings where either the triangles are equiangular or two of the angles are π/3.     

Beta-branching fraction of117Cd isomers and it branching of117mIn

Using radiochemical and gamma spectrometric technique the branching fractions in the beta decay of¹¹⁷Cd isomers and the internal transition branching of^117mIn have been established. The beta branching fraction of^117gCd^117gIn was obtained as 0.86±0.06 and the value of^117mCd^117gIn was found to be less than 1%. The internal transitin branching and the isomer cross-section ratio were obtained as 0.31±0.02 and 0.197±0.002, respectively. From the measured isomer cross-section ratio the spin cut-off parameter was evaluated, which agreed with the value reported in the literature.     

Deterministic lot-sizing for coordinated families of production/inventory items

Coordination of order placing points, in a multi-item environment, becomes desirable as it reduces the set-up costs and eases the problem of order-control implementation. Because of the computational complexities most of the analysis in the literature is confined to single families of items. In this paper, we establish the basic property of item consecutiveness for the multi-family situation which facilitates a shortest-path formulation of optimal families. We also develop an efficient algorithm for lot size computations of a single family to be incorporated in the shortest-path model.     

Nocturnal absorption of radio waves due to the ionisation produced by X-rays from Sco X-1 and Tau X-1 in the lower ionosphere

The night-time attenuation of LF radio waves of frequency 164 kHz transmitted from Tashkent and received at Ahmedabad has been found to have a sidereal time variation which is associated with the transits of the X-ray stars Sco X-1 and Tau X-1. Using the full-wave admittance method of Barron and Budden for calculating the intensity and polarisation of LF radio waves reflected from ionosphere during night-time when the atmosphere is irradiated by X-rays from Sco X-1 and Tau X-1, the attenuation of 164 kHz waves transmitted from Tashkent and received at Ahmedabad, has been calculated and compared with the observed results. The agreement is reasonably satisfactory.     

The mechanisms of the acid-catalysed dissociation of tris-β-diketonatoruthenium(III) complexes

Summary The reactions of four -diketonatoruthenium(III) complexes in the presence of HNO₃ andp-MeC₆H₄SO₃H in the 45° and 57° range were followed spectrophotometrically in Me₂COH₂O mixtures. Dissociation of Ru(acac)₃ follows [H⁺]-dependent and [H⁺]²-dependent paths, whereas the bzac and F₃acacF₃ complexes follow only the [H⁺]-dependent path. The bzbz (Dibenzoylmethanate) complex is inert. Protonation of the bound ligand leads to its rupture from the metal ion. The bzac complex is kinetically more inert than the acac complex, because of extra stability arising from interaction of the (bzac) benzene ring with the pseudo-aromatic diketonate ring of the complex. Considering the kinetic labilities, the complexes may be arranged in the order Ru(F₃acacF₃)₃>Ru(acac)₃>Ru(bzac)₃>Ru(bzbz)₃.Activation parameters for [H⁺] dependent path are: H ₁ 86.5±7, 69±5, 121±7 kJ mol^–1, S ₂ –52±10, –107±10, 57±8 JK^–1 mol^–1 for acac, bzac and F₃acacF₃ complexes respectively and H ₂ 67±5 kJ mol^–1, S ₂ –92±8 JK^–1 mol^–1 for the acac complex only.     

Magnetic properties of transition metal ion cubic 5T2 terms in axial ligand fields

The theory of magnetic anisotropy and susceptibility is worked out for cubic ⁵T₂ terms, the degeneracy of which is partially lifted by a ligand field component of axial symmetry as well as by spin-orbit coupling. Matrix elements are calculated by application of the method of Abragam and Pryce to a set of M.O. based wave-functions. The anisotropy in covalency of the metal-ligand bond and in spin-orbit coupling is taken into account. Numerical values of principal magnetic moments, P and P , are calculated as function of kT/, /, and .The theoretical results are employed in a rigorius analysis of existing single crystal magnetic data on high-spin iron(II) compounds. For (NH₄)₂Fe(SO₄)₂·6 H₂O, =–100 cm^–1, =1070 cm^–1 and =0.8 to 0.6 is obtained. For FeSiF₆·6 H₂O, =–80 cm^–1, =–760cm^–1 at 77.3K and –580 cm^–1 between 20.4 and 1.57K, and 0.7 is derived. No unique fit is possible for K₂Fe(SO₄)₂·6 H₂O. The data are reproduced to better than ±1% in most cases. The limitations of the approach are stressed.

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Zusammenfassung Die Theorie der magnetischen Anisotropie und der magnetischen SuszeptibilitÄt eines ⁵ T ₂ Grundterms im oktaedrischen Ligandenfeld wird für den Fall entwickelt, da\ die Entartung unter dem Einflu\ einer axial-symmetrischen Feldkomponente sowie der Spin-Bahn-Wechselwirkung teilweise aufgehoben ist. Eigenfunktionen werden auf der Grundlage der M.O.-Theorie aufgestellt, Matrixelemente mittels der Theorie von Abragam und Pryce ermittelt. Der Anisotropie der Metall-Ligand-Bindung sowie der Spin-Bahn-Kopplung wird Rechnung getragen. Numerische Werte für die magnetischen Hauptmomente P und P werden in AbhÄngigkeit von kT/, / und berechnet.Die Ergebnisse der Theorie werden für eine genaue Analyse der verfügbaren magnetischen Daten aus Messungen an Einkristallen magnetisch normaler Eisen(II)-Verbindungen verwendet. Für (NH₄)₂Fe(SO₄)₂·6 H₂O werden =–100 cm^–1, = 1070 cm^–1 und = 0,8 bis 0,6 erhalten. Für FeSiF₆·6 H₂O ergeben sich =–80 cm^–1, =–760 cm^–1 bei 77,3K und =–580 cm^–1 zwischen 20,4 und 1,57K sowie 0,7. Die experimentellen Daten können in den meisten FÄllen auf ±1% genau oder besser wiedergegeben werden. Bei K₂Fe(SO₄)₂·6 H₂O gelang keine eindeutige Bestimmung der theoretischen Parameter. Die Grenzen der vorliegenden Behandlung werden kritisch diskutiert.

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Résumé La théorie de l'anisotropie magnétique et de la susceptibilité magnétique est développée pour les termes cubiques ⁵ T ₂, dont la dégénérescence est partiellement levée par une composante à symétrie axiale du champ de ligandes ainsi que par le couplage spin-orbite. Les éléments de matrice sont calculés à l'aide de la méthode d'Abragam et Pryce employée sur un système M.O. des fonctions d'onde de base. On a pris en consideration l'anisotropie de la liaison entre le metal et le ligand et aussi du couplage spin-orbite. Les valeurs numériques des moments magnétiques principaux P et P sont calculées en fonction de kT/, /, et .Les résultats théoriques sont employés dans une analyse détaillée des données magnétiques disponibles sur monocristaux des composés ferreux spin-élevés. Pour (NH₄)₂Fe(SO₄)₂·6 H₂O on a obtenu =–100 cm^–1, =1070 cm^–1 et =0.8 à 0,6. Pour FeSiF₆·6 H₂O on a eu comme résultat =–80 cm^–1, =–760 cm^–1 à 77,3 K et =–580 cm^–1 entre 20,4 et 1,57K avec 0,7. Les valeurs expérimentales sont réprésentées dans la plupart de cas plus précises que ±1%. Au cas de K₂Fe(SO₄)₂·6 H₂O une détermination unique était impossible. Les limites de cette approximation sont discutées.

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Postdoctoral Fellow, Theoretical Chemistry, 1963–1964.     

Synthesis of pyrimidines from ketones using microwave irradiation

A simple, high yielding synthesis of pyrimidines from ketones in the presence of HMDS and formamide is described. Under microwave irradiation, heteroaromatic, aryl, aliphatic, and cyclic ketones cyclized to give pyrimidines in good yields.     

Synthesis, crystal structure and imine bond activation of a copper(II) Schiff base complex

A new copper(II) complex [Cu(HL)(ClO₄)](ClO₄) (1), where HL is a multidentate Schiff base N,N′-(2-hydroxypropane-1,3-diyl)bis(pyridine-2-aldimine), is prepared, structurally characterized by X-ray crystallography and its spectral and electrochemical properties studied. The complex forms a one-dimensional chain in the solid state structure in which the monomeric Cu(HL) units are linked by the perchlorate ligand. The complex has an axially elongated six coordinate geometry (4+2) with a CuN₄O₂ core in which the Schiff base ligand displays a tetradentate mode of bonding in the basal plane. The axial ligand is perchlorate with a significantly long Cu–O bond of ca. 2.6 Å. The one-electron paramagnetic complex displays a cyclic voltammetric response for the Cu(II)/Cu(I) couple at 0.01 V versus SCE in MeCN–0.1 M TBAP. The azomethine bond of the Schiff base in 1 on treatment with H₂O₂ undergoes oxidative conversion to form a bis(picolinato)copper(II) · dihydrate species through the formation of an amido intermediate as evidenced from the solution infrared spectral studies.     

Reaction between cis-diaquabisbiguanideruthenium(III) and hexathiocyanatochromium(III) ions in aqueous media. A mechanistic survey on the formation of a dinuclear bridged complex

The reaction between two complex species [Ru(BigH)₂(H₂O)₂]³⁺ and [Cr(SCN)₆]^3– has been investigated in aqueous medium in the pH range 4.00–6.10, and followed in the 21–40 °C range. Pseudo-first order rate constants were evaluated using the chromium complex in a ten-fold excess. The plot of k _obs versus pH has a bell shaped profile. From this and other evidence it was concluded that only the [Ru(BigH)₂(OH)(H₂O)]²⁺ form of the ruthenium complex is reactive under the experimental conditions, and forms the dinuclear complex [Ru(BigH)₂--(SCN)₂-Cr(NCS)₄]⁰. The rate constant for the dinuclear complex formation at 31 °C is (2.57 ± 0.05) × 10^–3 mol^–1 s^–1. H = 60 ± 2 kJ mol^–1 and S = 116 ± 10 J K^–1 mol^–1.