On a differential-algebraic problem

The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.     

Preparation, Structure, and Thermal Decomposition of Co(II) Complexeswith 2,3- and 2,5-Dichlorobenzoic Acid and Imidazole

 The reaction products of Co(II)-2,3- and -2,5-dichlorobenzoate with imidazole (1, 2; CoL ₂⋯2imdċ2H₂O, L=C₇H₃Cl₂O, imd=imidazole) were characterized by their spectroscopic and thermochemical properties. The compounds crystallize in the monoclonic system with space group = P2₁/c, a=13.848(3), b=12.841(3) ?, c= 7.064(2) ?, β=98.12 °, V=1243.5(4) ?³, Z=2 for 1 and space group =P2₁/n, a=13.293(3), b= 6.964(2), c=13.800(3) ?, β=108.92(3) °, V=1208.6(4) ?³, Z=2 for 2. The complexes lose their crystal water in one step at 333 K and subsequently decompose to CoO with intermediate formation of Co₃O₄.     

Bicyclic [b]‐heteroannulated pyridazine derivatives. 9. cyclization reactions of 4,4‐dimethyl‐ and 4‐phenyltetrahydropyridazine‐3,6‐dione 3‐hydrazones with esters of keto dicarboxylic acids

Bis(ethoxycarbonyl)alkylidene derivatives 4 and 5 of the respective title hydrazones were obtained in the reactions with diethyl oxomalonate, diethyl oxosuccinate, diethyl 2‐oxoglutarate, and diethyl oxalo‐propionate as mixtures of geometric isomers with high predominance of one of them. On heating at 160‐200° without any solvent or on refluxing in ethanol 4 cyclized to yield the corresponding pyri‐dazino[6, 1‐c]triazines 6 , whereas heating of 5 gave, depending on the chain length, the corresponding pyra‐zolylpyridazines 8b and 8d or the pyridazinylpyridazine 8c . X‐ray analysis was used to determine the structures of 6 and 8 ; the unit cell of 6c was found to accommodate 16 molecules representing four conforma‐tional varieties. The different behavior of 4 and 5 in the cyclization reactions was interpreted in terms of the tautomeric equilibrium which was shifted towards the enamine form in 4 , and towards the imine form, in 5 . Transmission of a long‐range chirality effect in 4d and 5a‐d manifested itself in the ¹H nmr spectra as the magnetic non‐equivalence of the CH₂ protons in one or both ester ethyl groups.     

Electrical properties of TiO<Subscript>2</Subscript>: equilibrium vs dynamic electrical conductivity

The present work reports semiconducting properties of high purity TiO₂ determined in the gas/solid equilibrium, as well as during controlled heating and cooling in the range 300–1,273 K. The activation energy of the electrical conductivity is considered in terms of the activation enthalpy of the formation of ionic defects and the activation enthalpy of the mobility of electronic defects. These data, determined from the dynamic electrical conductivity experiments, are compared to the electrical conductivity data determined in equilibrium. It is shown that only the equilibrium electrical conductivity data for high-purity TiO₂ are well defined. It is shown that the activation energy of the electrical conductivity determined in equilibrium differs substantially from that for the dynamic electrical conductivity data during cooling and heating. It is concluded that the formation enthalpy term determined from the dynamic conductivity data is determined by the heating/cooling rate rather than materials’ properties.     

Von der Reaktion zwischen Arsenit und Permanganat in schwefelsauren L?sungen

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