Competing kinetic pathways in the bromine addition to allylic ethers in 1,2‐dichloroethane: Opposite temperature effects

The kinetics of the electrophilic bromination of three allylic ethers in a nonprotic solvent, 1,2‐dichloroethane, has been investigated. Two of them followed a prevalent second‐order pathway, while the third one exhibited a classical, clean third order. The second‐order pathway in the first two olefins is attributed to electrophilic assistance of the ethereal oxygen to the attacking bromine molecule. In the molecular bromination of 2,4‐cis‐dimethyl‐8‐oxabicyclo[3.2.1]‐6‐octen‐3‐cis‐ol, opposite temperature dependences were found for the two different kinetic pathways. An exoergonic process for the second‐order reaction was explained by the lesser stability of the bromiranium–bromide ionic intermediate, compared to the bromiranium–tribromide in the third‐order profile. © 2007 Wiley Periodicals, Inc. 39: 197–203, 2007     

Synthesis of pyrazolo[4,5-d]- and pyrazolo[4,5-c][1]benzazepine derivatives. IV

Following our reports on synthetic tricyclic analogues of antitumor anthramycin the synthesis of some isomers pyrazolo[4,5-d]- and pyrazolo[4,5-c][1]benzazepine derivatives is reported.     

Domino reactions of 4,5-dicyanopyridazine with dihydroheterocycles: synthetic and mechanistic features

The title pyridazine 1 was found to react with both 2,3-dihydrofuran (2) and 3,4-dihydro-2H-pyran (9) to give the tetracyclic skeletons 5-8 and the phthalonitrile 12 through the intermediates 4 and 10, respectively. A more complex mechanism was ascertained for the reaction of 1 with the pyrroline 14 which, under suitable conditions, afforded the bicyclic derivative 19 as the predominant product; selective elaborations of this species into the 5,6-dicyanoindoles 22 and 23 are reported.     

Tricyclic heteroaromatic systems. 5H-1,2,4-triazolo[5,1-c][1,4]benzodiazepine

The synthesis of the new tricyclic heteroaromatic system 5H-1,2,4-triazolo[5,1-c][1,4]benzodiazepine, diazaanalogue of 5H-pyrrolo[2,1-c][1,4]benzodiazepine, which is the common feature of some antitumor antibiotics, is reported. The structure of the new tricyclic system and of some of its key intermediates is assigned by means of nuclear magnetic resonance studies.     

The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices

A bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n ²), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n ²) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one.     

Furstenberg Transformations on Cartesian Products of Infinite-Dimensional Tori

We consider in this note Furstenberg transformations on Cartesian products of infinite-dimensional tori. Under some appropriate assumptions, we show that these transformations are uniquely ergodic with respect to the Haar measure and have countable Lebesgue spectrum in a suitable subspace. These results generalise to the infinite-dimensional setting previous results of H. Furstenberg, A. Iwanik, M. Lemanzyk, D. Rudolph and the second author in the one-dimensional setting. Our proofs rely on the use of commutator methods for unitary operators and Bruhat functions on the infinite-dimensional torus.     

An approximate waves-bordering algorithm for adaptive finite elements analysis

In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equations that updates recursively and stops when the norm of the residual has gone under a user-defined threshold. This revised version was published online in June 2006 with corrections to the Cover Date.     

Search of single long-period oscillations in the daily temperatures

Summary Long-period oscillations have been searched in the time series of the daily minimum, mean and maximum temperatures measured in Modena, Italy, during the years 1869–1976. By assuming only one oscillation present, the amplitude and its statistical uncertainty have been estimated by means of a fitting procedure which takes into account the stochastic variability of the daily temperatures. The period of the long-term oscillations has been chosen to be an integer number of years (from 2 up to 36). This choice and the fit performed over a suitable number of years (the maximum possible multiple of the period) ensure a numerical stable solution and a negligible correlation between the long-period oscillation and the annual and seasonal oscillations present in the time series. The instrumental uncertainty of the long-period amplitude has been also evaluated. Within the overall uncertainty, no reliable evidence exists on single long-period oscillations.

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Riassunto Sono state cercate oscillazioni singole a lungo periodo nella serie temporale formata dalle temperature minime, medie e massime, misurate giornalmente a Modena durante gli anni 1869–1976. Nell'ipotesi di un'unica oscillazione sono state stimate l'ampiezza dell'oscillazione e la sua incertezza statistica mediante un procedimento di approssimazione che teneva conto della variazione stocastica delle temperature giornaliere. Come periodo delle oscillazioni a lungo termine si è scelto un numero intero di anni compreso fra 2 e 36. L'approssimazione è stata effettuata su un numero di anni che era il massimo multiplo del periodo compatibile con i dati disponibili. Con tali scelte le soluzioni risultano numericamente molto stabili. Inoltre le correlazioni fra i diversi parametri stimati in ciascuna approssimazione risultano trascurabili. è stato anche valutato l'effetto dell'errore sistematico di misure sull'ampiezza dell'oscillazione a lungo periodo. Dai risultati non emergono prove affidabili sull'esistenza di oscillazioni singole a lungo termine entro la risoluzione statistica e sistematica del presente studio.

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Резюме Проводится поиск осцилляций с большим периодом во временной последователвности суточных минимальных, средних и максимальных температур, измеренных в Модене, Италии, в течение 1869–1976 г. г. Предполагал, что существует только одна осцилляция, оценивается амплитуда и статистическая неопределенность, оспользуя процедуру подгонки, которая учитывает стохастическое изменение суточных температур. Период продолжителяной осцилляции выбирается равным целому числу лет (от 2 до 36). Этот выбор и проведенная подгонка соответствующего числя лет (максимально возможное кратное периоду) обеспечивают численное устойчивое решение и позволяйт пренебречь корреляцией между осцилляцией с большим периодом и ежегодными и сезонными осцилляциями, присутствующми во временной последовательности. Оценивается инструментальная неопределенность амплитуды осцилляции с большим периодом. С учетом полной неопределенности не обнаружено нодежного подтверждения отдельных осцилляциь с большим периодом.

     

Tracer element injection into PDX tokamak for spectral line identification and localized doppler temperature measurement

Magnetic dipole lines in ScXIII-XVII and resonance lines of ScXVIII-XIX were observed and identified. Advantages of ion thermometry by means of tracer element injection are described.