The integration of certain products of the multivariableH-function with a general class of polynomials

The authors present six general integral formulas (four definite integrals and two contour inegrals) for theH-function of several complex variables, which was introduced and studied in a series of earlier papers by H. M. Srivastava and R. Panda (cf., e.g., [25] through [29]; see also [14] through [18], [20], [24], [32], [34], [35], [37], and [38]). Each of these integral formulas involves a product of the multivariableH-function and a general class of polynomials with essentially arbitrary coefficients which were considered elsewhere by H. M. Srivastava [21]. By assigning suiatble special values to these coefficients, the main results (contained in Theorems 1, 2 and 3 below) can be reduced to integrals involving the classical orthogonal polynomials including, for example, Hermite, Jacobi [and, of course, Gegenbauer (or ultraspherical), Legendre, and Tchebycheff], and Laguerre polynomials, the Bessel polynomials considered by H. L. Krall and O. Frink [9], and such other classes of generalized hypergeometric polynomials as those studied earlier by F. Brafman [3] and by H. W. Gould and A. T. Hopper [8]. On the other hand, the multivariableH-functions occurring in each of our main results can be reduced, under various special cases, to such simpler functions as the generalized Lauricella hypergeometric functions of several complex variables [due to H. M. Srivastava and M. C. Daoust (cf. [22] and [23])] which indeed include a great many of the useful functions (or the products of several such functions) of hypergeometric type (in one and more variables) as their particular cases (see,e. g., [1], [10] and [39]). Many of the aforementioned applications of our integral formulas (contained in Theorems 1, 2 and 3 below) are considered briefly. Further usefulness of some of these consequences of Theorems 1 and 2 in terms of the classical orthogonal polynomials is illustrated by considering a simple problem involving the orthogonal expansion of the multivariableH-function in series of Jacobi polynomials. It is also shown how these general integrals are related to a number of results scattered in the literature. 0261 0262 V     

Interaction of chloroform with aniline, o-toluidine and N,N-dimethyl aniline

Heats of mixing aniline, o-toluidine, and N,N-dimethyl aniline with chloroform have been determined by an adiabatic calorimeter. The results have been examined for molecular interactions between them, and they indicate that aniline and o-toluidine are associated through hydrogen bonds. Enthalpy of bond formation in a 1:1 complex has also been determined.     

Organic solid-state reactions

The role of voids and cracks in solid-state reaction between 8-hydroxyquinoline and phthalic anhydride has been investigated. 8-hydroxyquinoline reacts with phthalic anhydride both in solution and in solid state, forming a 1:1 yellow-colored complex. X-ray diffraction studies prove that the complex obtained from the solid-state reaction is the same as that obtained from solution. Several techniques have been used to study the kinetics of the reaction in the solid state. Kinetic studies by capillary technique showed that surface migration is the mode of diffusion of reactant concerned. Dilatometric technique confirms the formation of cracks and voids in the systems and shows that the reaction is propagated through the channels.     

Syntheses of the first N-mono- and N,N'-dipolyfluoroalkyl-4,4'-bipyridinium compounds

Reactions of 4,4'-bipyridine (1) with excess of polyfluoroalkyl iodides (2a-d) at 100-110 degrees C, under neat conditions, led to the formation of monoquaternary salts (3a-d) in > 90% yields. Salts 3a-d were metathesized with LiN(SO2CF3)2 either in water or water/acetone mixtures to form ionic liquids (4a-d), respectively, in > 88% yields. When 1 was reacted with 2.5 equivalent of 2a-c in DMF at 110 degrees C, the diquaternary salts 5a-c were formed in > 85% yields. Alternatively, 5a-c were also synthesized by heating a mixture of 3a-c and 2a-c (1.25 equivalent) in DMF. The metathesis reaction of 5a-c with LiN(SO2CF3)2 produced dicationic ionic liquids (6a-c) in > 86% yield.     

Vinyl polymerization: Kinetics of Ce(IV)–acetophenone-initiated polymerization of acrylonitrile in acetic–sulfuric acid mixtures

The polymerization of acrylonitrile (M) initiated by the Ce(IV)–acetophenone (AP) redox pair has been studied in acetic–sulfuric acid mixtures in a nitrogen atmosphere. The rate of polymerization is proportional to [M]^3/2, [AP]^1/2 and [Ce(IV)]^1/2. The rate of disappearance of ceric ion,–R_Ce, is proportional to [AP], [M], and [Ce(IV)]. The effect of certain salts, solvent, acid and temperature on both the rates have been investigated. A suitable kinetic scheme has been proposed, and the composite rate constants k_p ²(k/k/_t) and k₀/k_i are reported.     

The chemistry of cyclic enaminoketones. III. Synthesis of bi- and tricyclic enaminoketones from enamine esters and nitriles

The cyclization of enamines derived from β-aminoesters and β-aminonitriles into bi- and tricyclic enaminoketones ( 6,9,13 and 24 ) has been investigated. The enamines derived from aminonitriles cyclize smoothly with magnesium perchlorate in benzene or toluene, whereas the enamines derived from aminoesters cyclize spontaneously during their formation. The scope and limitation of this process is discussed.     

Volumetric studies in oxidation-reduction reactions: Oxidation with chloramine-t. iodine monochloride method

Chloramine-T has been used as an oxidizing agent in hydrochloric acid medium' for the volumetric estimations of potassium iodide, hydrazine sulphate, arscnious oxide, stannous chloride, mercurous chloride, tartar-emetic, potassium thiocyanate and ferrous ammonium sulphate, using iodine monochloride as a catalyst and pre-oxidizer. Chloroform is used as an indicator. It is coloured pink owing to the liberation of iodine during the titration and becomes very pale yellow at the end-point because of the formation of iodine monochloride.     

Tracer diffusion of131I− ions in a few 1–2 electrolytes in agar gel

Tracer diffusion of¹³¹I^– ions is studied at different temperatures /20°C–50°C/ in 2.5% agar gel containing sodium and potassium sulphate solutions over a wide range of concentrations. The results are in qualitative agreement with the theoretical values in the concentration range 10^–6–10^–1M. Agar gel shows an obstruction effect to diffusional flow. The activation energy for tracer diffusion was found to be of the order of 16.3 kJ mol^–1.     

Kinetics of thermal dehydration of La(III) and Yb(III) complexes with ortho-vanillin oxime

The analysis of dehydration of the complexes, [La(C₈H₈NO₃)₃.2H₂O] and [Yb(C₈H₈NO₃)₃.3H₂O] for the evaluation of kinetic parameters (Z, E &S ^*) and mechanism of dehydration by non-isothermal methods are reported. The complexes decompose in three well defined steps involving random nucleation mechanism. First two steps involving the dehydration and the third step the loss of the ligand moiety. The intermediates formed during decomposition were found to be unstable for carrying out any significant studies.

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Zusammenfassung Zwecks Ermittlung der kinetischen Parameter (Z, E undS ^*) und des Mechanismus der Dehydratierung durch nichtisotherme Verfahren wird die Analyse der Dehydratierung der Komplexe [La(C₈H₈NO₃)₃·2H₂O] und [Yb(C₈H₈NO₃)₃·3H₂O] beschrieben. Die Komplexe zersetzen sich in drei gut definierten Schritten mit Random-Keimbildungsmechanismus. Die ersten zwei Schritte beinhalten die Dehydratierung, der dritte Schritt den Verlust der Liganden. Die wÄhrend der Zersetzung entstandenen Zwischenprodukte erwiesen sich für jegliche signifikante Untersuchung als zu unstabil.