Hydrogen bonding interactions between indole and benzenoid-pi-bases

The NH-pi interactions of indole with benzene, naphthalene, phenanthrene, toluene, m-xylene, and mesitilene, in carbon tetrachloride solutions, have been studied by Fourier transform infrared spectroscopy. The experiments, carried out on the NH stretching band of indole, prove the formation of 1:1 complexes in which the NH bond of indole is engaged. The NH frequency shifts are independent of the number of rings in the base, but they progressively increase as the electron density is enhanced by methylation. The association constants increase with the increase of both, the number of rings and the methyl groups on the base. At higher base concentrations, further shifts on the free NH and associated bands indicate the formation of 1:2 complexes, which suggest hybride NH-pi and van der Waals interactions between one indole ring and two benzene acceptor molecules.     

Simple and condensed β-lactams-I : The application of diketene in β-lactam synthesis. The synthesis and functional group manipulations of diethyl 3-acetyl-4-oxoazetidine-2,2-dicarboxylates

Acylation of the N-substituted diethyl aminomalonates 3a–3d with diketene furnished the ring tautomers 6a–6d of the expected acetoacetyl derivatives 5. By treatment with iodine and sodium ethoxide compounds 6a–6d are smoothly converted into the β-lactam derivatives 2a–2d. Deethoxycarbonylation of the ethylene ketals 7a–7d of the latter furnishes mixtures of the corresponding diastereomeric monoesters 8 and10. The ethoxycarbonyl groups of the trans esters 8 are more reactive than those of the cis isomers 10. This permits, under appropriate conditions, selective alkaline hydrolysis and NaBH₄ reduction of the trans esters 8 in the presence of the cis esters 10. Reduction of the cis ester 10c under more forceful conditions furnishes the trans hydroxymethyl derivative 11c.     

Radiotracer method for the study of the radiolysis of aqueous solutions of pyruvic acid

The purpose of this work is to study the radiolytic behavior of aqueous solutions of¹⁴C-pyruvic acid (oxygen-free). Several parameters were varied such as radiation dose, pH, etc. Gas chromatography, mass spectrometry and high performance liquid chromatography were used extensively for the analysis of radiolytic products. The more abundant product was dimethyltartaric acid. Other products identified were acetic, lactic, succinic, malonic and tricarballylic acids, acetaldehyde, carbon dioxide, and hydrogen. The yields of these products were influenced by the irradiation dose, concentration of the target compound and pH of the solution.     

Some regularity properties of algorithms and additive functions with respect to them

Summary The paper deals with the behaviour of the so-called algorithms with respect to interval filling sequences A connection is established between the uniquely representable points and the continuity points of the algorithms; also strong continuity properties on monotonic algorithms are proved. Finally the results are applied to additive functions. The theorems extend some former results by the authors, by I. Kátai and by A. Járai.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

On the maximal number of certain subgraphs inK r -free graphs

Given two graphsH andG, letH(G) denote the number of subgraphs ofG isomorphic toH. We prove that ifH is a bipartite graph with a one-factor, then for every triangle-free graphG withn verticesH(G) H(T ₂(n)), whereT ₂(n) denotes the complete bipartite graph ofn vertices whose colour classes are as equal as possible. We also prove that ifK is a completet-partite graph ofm vertices,r > t, n max(m, r – 1), then there exists a complete (r – 1)-partite graphG* withn vertices such thatK(G) K(G*) holds for everyK _r -free graphG withn vertices. In particular, in the class of allK _r -free graphs withn vertices the complete balanced (r – 1)-partite graphT _r–1(n) has the largest number of subgraphs isomorphic toK _t (t < r),C ₄,K _2,3. These generalize some theorems of Turán, Erdös and Sauer.Dedicated to Paul Turán on his 80th Birthday     

Axiomatic foundations of quantum physics: Critiques and misunderstandings. Piron's question-proposition system

Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the aim of clarifying their true significance, taking Piron's approach as conceptual framework. In particular, we deal with the following topics: the wrong identification of Piron's questions and Mackey's questions, and some curious alleged empirical consequences; the role of propositions as suitable equivalence classes of questions, their partial order structure, and the paradoxical consequences of the erroneous assignment to questions of some lattice properties involving propositions; the logical and the empirical purport of some negative theorems; the standard Hilbert space model of the theory and the consequent metaphysical disasters related to some identifications, which are peculiar of this model. A controversy between Foulis-Piron-Randall and Hadjisavvas-Thieffine-Mugur-Schächter is analyzed on the basis of the proposed Hilbert space model (in which Piron's questions are realized by Hilbertian effects, i.e., linear bounded operatorsF such that which clarify the different point of views. As an example, we treat the unsharp localization operators inL ₂().     

Exact solution of the Boltzmann equation in the homogeneous color conductivity problem

An exact solution of the Boltzmann equation for a binary mixture of colored Maxwell molecules is found. The solution corresponds to a nonequilibrium homogeneous steady state created by a nonconservative external force. Explicit expressions for the moments of the distribution function are obtained. By using information theory, an approximate velocity distribution function is constructed, which is exact in the limits of small and large field strengths. Comparison is made between the exact energy flux and the one obtained from the information theory distribution.