The hydrogen molecule in an arbitrarily oriented magnetic field

Summary The modifications induced by a magnetic field of arbitrary direction and intermediate strength (i.e not larger than 2.35·10⁵ tesla, the ?atomic tesla?) on the lowest singlet and triplet energy states of the hydrogen molecule are studied. Using a linear combination of products of field-modified atomic orbitals, it is found that increasing the field strength the depth of the singlet energy well increases and the equilibrium internuclear distance decreases, yielding more rigid and localized nuclear vibrations. For sufficiently strong fields perpendicular to the internuclear axis, the triplet state exhibits a bonding behaviour. An explanation of the above results is given in terms of the field-modified electronic-charge distributions in the internuclear region. Based on the thesis submitted by S. Basile to the University of Palermo for graduation in Physics.     

Siloxane-Based Nanobuilding Blocks by Reaction Between Silanediol and Trifunctional Silicon Alkoxides

The preparation of nanostructured organic-inorganic materials by assembling of nanobuilding blocks allows controlling the extent of phase interaction, which in its turn governs structure-properties relationships. We present here the synthesis of siloxane-based nanobuilding blocks prepared by reacting diphenylsilanediol with vinyltriethoxysilane and triethoxysilane. The reaction products were obtained by non-hydrolytic condensation between silanediol and ethoxide groups in inert atmosphere, in the presence of pyridine, triethylamine or butyl lithium. Different synthetic conditions were examined by means of ATR-FTIR and NMR spectroscopies, showing the formation of siloxane bonds. In the case of triethoxysilane the reaction carried out in the presence of pyridine leads to Si–H bond preservation in the final product. Air stable products with improved Si–O–Si hydrolytic stability can be obtained by removal of the base after the reaction completion. The condensation products can be described as a mixture of siloxane rings involving difunctional and trifunctional silicon units.     

Optimal and one-complemented subspaces

Let X be a real Banach space and let V ⊂ X be a closed linear subspace. In [4, Prop. 5] it has been proven that if X is strictly convex, reflexive and smooth and V is an optimal subset of X then V is one-complemented in X. In this note we would like to extend this result to non-smooth Banach spaces. In particular, we show that any existence subspace of c,c _o and l ₁ is one-complemented. Also some results concerning non-smooth Musielak-Orlicz sequence spaces equipped with the Luxemburg norm will be presented. The first author was supported by Polish State Committee for Scientific Research Grant KBN 1 PO3A O10 26. Authors’ addresses: Grzegorz Lewicki, Department of Mathematics, Jagiellonian University, 30-059 Kraków, Reymonta 4, Poland; Giulio Trombetta, Department of Mathematics, University of Calabria, 87036 Arcavacata di Rende, Cosenza, Italy     

5nsec Dead time multichannel scaling system for Mössbauer spectrometer

A PC programmable and fast multichannel scaling module has been designed to use a commercial Mössbauer spectrometer. This module is based on a 10$ single chip 8 bits microcomputer (MC6805) and on a 35$ fast ALU, which allows a high performance and low cost system. The module can operate in a stand-alone mode. Data analysis are performed in real time display, on XT/AT IBM PC or compatibles. The channels are ranged between 256 and 4096, the maximum number of counts is 2³²?1 per channel, the dwell time is 3 μsec and the dead time between channels is 5 nsec. A friendly software display the real time spectrum and offers menues with different options at each state.     

Diastereoselective total synthesis of (+)-13-stemarene by fourth generation methods: a formal total synthesis of (+)-18-deoxystemarin

The problem of constructing diastereoselectively the C/D ring system of stemarane diterpenes from a bicyclo[2.2.2]octane intermediate was solved resulting in very simple synthesis of (+)-13-stemarene 1. The obtaining of the latter represents also a formal synthesis of (+)-18-deoxystemarin 2. In the key step, the epimeric mixture 10, dissolved in toluene, was converted by the action of TsOH into (+)-stemar-13-en-15-one 28.     

Strong-field multiphoton ionization of hydrogen. TheS-matrix treatment of the elementary process

Summary A theoretical model is presented to treat the elementary act of strong-field multiphoton ionization of atoms when the electron continuum final-state distribution is important. It is based on theS-matrix formalism and treats the final-state electron-radiation interaction in an essentially nonperturbative way. Selected numerical calculations concern the ionization of hydrogen atoms and include differential and total cross-sections of several multiphoton channels as a function of the laser intensity. Good, qualitative agreement with the experimental observations is found for values of the field intensity which are not critical with respect to the simplifications adopted in constructing the theoretical model. It applies particularly to the use of an ideal model for the laser field. Significant departure from observations is instead found when the implications of the ideal laser model play a critical role, as occurs at channel inversion and suppression. It is concluded that the theoretical treatment to be completely satisfactory needs essentially to incorporate a more realistic laser model such as a multimode one.

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Riassunto Si presenta un modello teorico per il processo elementare della ionizzazione multifotonica di atomi da parte di un forte campo laser quando diventa importante la distribuzione degli stati finali del continuo dell'elettrone. Il modello si fonda sul formalismo della matriceS e tratta l'interazione elettrone-radiazione nello stato finale in modo non perturbativo. I calcoli numerici qui riportati si riferiscono alla ionizzazione di atomi d'idrogeno e includono sezioni d'urto totali e differenziali per diversi canali multifotonici in funzione dell'intensità del laser. Si trova un accordo qualitativo con i dati sperimentali per valori dell'intensità del campo che non sono critici rispetto alle semplificazioni adottate nella costruzione del modello teorico. Un significativo distacco dai dati sperimentali si ha quando le implicazioni del modello di laser ideale giocano un ruolo critico, come si ha per l'inversione e la scomparsa dei canali. Si conclude che il trattamento teorico per essere completamente soddisfacente necessita dell'introduzione di un modello di laser piú realistico, quale, ad esempio, quello a molti modi.

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Резюме Предлагается теоретическая модель для рассмотрения элементарного акта многофотонной ионизации атомов в сильном поле, когда распределение электронных непрерывных конечных состояний является существенным. Подход базируется на формализмеS-матрицы и взаимодействие электронов в конечном состоянии с полем излучения рассматривается непертурбационным образом. Численные вычисления касаются ионизации атомов водорода и включают дифференциальные и полные поперечные сечения для некоторых многофотонных каналов, как функции интенсивности лазерного излучения. Получено хорошее качественное согласие с экспериментальными результатами для значений интенсивности поля, которые не являются критическими по отношению к упрощениям, используемым при конструировании теоретической модели. Используется идеальная модель для лазерного поля. Обнаружено существенное отклонение от экспериментальных результатов в тех случаях, когда имеет место инверсия и подавление каналов. Делается вывод, что теоретический подход становится удовлетворительным, если используется более реалистическая модель лазера, как например, многомодовая модель.

     

Hybrid Siloxane-Based Nano Building Blocks for Optical Applications: Optimization of the Synthetic Procedures by Spectroscopic Analysis

Diphenylsilanediol (DPDO) reacts with triethoxysilane (TREOS) in anhydrous conditions and in the presence of pyridine, to form complex mixtures of linear and cyclic condensation products which were identified by ²⁹Si NMR and ATR/FTIR spectroscopies. The distribution of products can be varied by modifying the reaction conditions. Spectroscopic analysis allowed to identify the optimal reagents ratio and concentration for the production of hetero-condensation products minimizing the number of residual –OH groups whose presence would affect the performance of optical waveguides based on the synthesised nano building blocks.     

Compactness and Vitali’s compactness criterion in vector-valued F-seminormed function spaces

Results of compactness for vector-valued F-seminormed function spaces and a general Vitali’s compactness criterion under the W-property are exhibited.

     

On Boundary Conditions for Wedge Operators on Radial Sets

We present a theorem about calculation of fixed point index for k-ψ-contractive operators with 0 ≤ k < 1 defined on a radial set of a wedge of an infinite-dimensional Banach space. Then, results on the existence of eigenvectors and nonzero fixed points are obtained.