On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhy Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.     

Ferri-spin glass nature of spinel ferrites Gax Fe1−x Ni Cr O4

Mössbauer measurements in mixed spinel ferrite Ga_x Fe_1–x Ni Cr O₄ (0x0.8), carried out between 4.2 and 298°K, show the presence of entropic spins in this system. Recent Monte Carlo calculations /4/ have predicted the presence of such spins in a frustrated spin glass lattice.     

Thermal decomposition kinetics of thiophene-2-carboxaldehyde thiosemicarbazone complexes of nickel(II) and palladium(II)

The thermal analysis of Ni(II) and Pd(II) complexes with thiophene-2-carboxaldehyde thiosemicarbazone have been studied using TG technique. Their decompositions are subjected to critical evaluation using the equations of Coats-Redfern, Horowitz-Metzger and modified Horowitz-Metzger and the kinetic parameters (non-isothermal method) have been evaluated for each step of decomposition by the method of weighted least-squares.     

Weak Wiener–Ditkin sets

A weak form of Wiener–Ditkin set is introduced and some of its properties are studied. As a consequence, a weak form of C-set-S-set problem has come up.     

One-step transformation of tricyclopentabenzene (trindane, C(15)H(18)) to bicyclo(10.3.0)pentadec-1(12)ene- 2,6,7,11-tetrone (C(15)H(18)O(4)) and its aldol product, 12-hydroxy-16-oxatetracyclo(10.3.1.0.(1,5)0(7,11))hexadec-7(11)ene-2,6-dione (C(15)H(18)O(4))

[reaction: see text] Ozonolysis of 1 largely results in 2 and 3, having features similar to several classes of natural products. The retention of the C(15) pericycle suggests preference for the cleavage of pi-bonds endo to the cyclopentane ring. This unique property of trindane offers opportunities for synthesis of complex natural products from this hydrocarbon that can be made in quantity by acid-catalyzed trimerization of cyclopentanone.     

Can Helical Peptides Unwind One Turn at a Time? ‐ Controlled Conformational Transitions in α,β2,3‐Hybrid Peptides

Unfolding of helical trans‐β^2,3‐hybrid peptides with (α–β)_nα composition, when executed by increasing solvent polarity or temperature, proceeded in a systematic manner with the turns unwinding sequentially; C‐terminal region of these peptides were first to unwind and the process propagated towards N terminus with more and more β residues equilibrating from the gauche to the anti rotameric state across C_α?C_β. This is evidenced by clear change in their C_βH signal splitting, ³J_CαH–CβH values, and sequential disappearance of i,i+2 NOEs.     

Thermal decomposition kinetics of potassium iodate

The rate and kinetics of the thermal decomposition of potassium iodate (KIO₃) has been studied as a function of particle size, in the range 63?C150???m, by isothermal thermogravimetry at different temperatures, 790, 795, 800 and 805?K in nitrogen atmosphere. The theoretical and experimental mass loss data are in good agreement for the thermal decomposition of all samples of KIO₃ at all temperatures studied. The isothermal decomposition of all samples of KIO₃ was subjected to both model-fitting and model-free (isoconversional) kinetic methods of analysis. It has been observed that the activation energy values are independent of the particle size. Isothermal model-fitting analysis shows that the thermal decomposition kinetics of all the samples of KIO₃ studied can be best described by the contracting cube equation.     

Thermal decomposition kinetics of polymeric complexes of copper(II) and mercury(II) with N,N′-bis(dithiocarboxy)piperazine

The thermal decomposition behaviour of polymeric complexes of Cu(II) and Hg(II) with N,N-bis(dithiocarboxy)piperazine is investigated in air by thermogravimetric (TG), derivative thermogravimetric (DTG) and differential thermal analysis (DTA) techniques. The kinetic parameters (non-isothermal method) for their decomposition have been evaluated by graphical as well as by least-squares methods. The equations of Coats-Redfern, Freeman-Carroll and Horowitz-Metzger have been applied. The results indicate that the values ofE,A and S obtained by these three different methods agree well. It was also found that the decomposition of these metal chelates follow first-order kinetics.

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Zusammenfassung Mittels TG, DTG und DTA wurde das thermische Zersetzungsverhalten von Polymerkomplexen aus Cu(II) bzw. Hg(II) mit N,N-Bis(dithiocarboxy)piperazin an Luft untersucht. Für ihre Zersetzung (nichtisotherme Methode) wurden die kinetischen Parameter sowohl graphisch als auch durch Methoden mit den kleinsten Fehlerquadraten ermittelt. Dabei wurden die Gleichungen von Coats-Redfern, Freeman-Carroll und von Horowitz-Metzger angewendet. Alle drei Verfahren zeigen übereinstimmende Resultate fürE, A undS. Es wurde weiterhin gefunden, daß diese Metallchelate einer Reaktion erster Ordnung unterliegen.

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The authors are thankful to Prof. C. G. R. Nair, Head of the Department of Chemistry, University of Kerala and Dr. M. P. Kannan, Department of Chemistry, University of Calicut for some helpful discussions.