Multipliers on Besov spaces

It is proved in this paper that the characteristic function of the half-space is not a multiplier for the pair (B _pq ^1/p , B _p ^1/p ), 1<p<, 1<q . In addition, necessary and sufficient conditions are found for the validity of the inclusion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 36–50, 1984.     

Uncertainty principle and uncertainty relations

It is generally believed that the uncertainty relation q p1/2, where q and p are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW and the mean peak width w of a general wave function and show that the productW w is bounded from below if is the Fourier transform of . It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments.     

Recovery and recrystallization in AISI 321 steel under static conditions

Static softening of AISI 321 steel after cold and hot deformation characterizing the industrial thermomechanical treatment was studied by means of tensile tests and TEM. The deformation temperature, the strain and the grain size were the main parameters determining the final softening. The results can be applied for optimization of the solution annealing.     

Two-jet production inp\bar p collisions

The production of two quark/gluon jets in \(p\bar p\) collisions is analyzed. We determine the cross section dependence on the transverse momentum, the rapidities, and on the two-jet invariant mass, and we evaluate the sensitivity of the results on the theoretical input assumptions and the experimental cuts. We extrapolate these results into the TeV energy region.     

Electron correlations in hydrocarbon molecules

An extensive investigation is made of electron correlations in the ground state of hydrocarbon molecules. This is done by starting from a semiempirical self-consistent field (SCF) calculation. The interatomic correlations are studied by means of a previously developed local approach to the correlation problem. It is demonstrated that the various contributions to the interatomic correlation energy can be described by simple analytical expressions which depend on the type of bond as well as on the bond lengths and angles. The results are easily understood in physical terms. The intraatomic correlations are obtained from an atoms in molecules type of approach as elaborated by Lievin et al. It makes use of a population analysis of the ground-state wave function as well as of calculations for the C and H atoms. We have then a very simple, and as it turns out rather accurate calculational scheme at hand. The computational times involved are of the same order as those for the fast SCF programs. As an application of the theory we have calculated the correlation energy difference between naphthalene and azulene.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Polarized β emitters for NMR probes

The physical principles of atomic and nuclear polarization by the tilted-foil interaction as applied to the production of polarized emitters for NMR probes are discussed.     

Optical bistability produced by resonant Joule's heating of semiconductors

The thermal hysteresis of Joule's absorption of infrared radiation in then-type semiconductor magnetoplasma is analysed. Such bistability is connected with the temperature dependence of the relaxation time of free electrons, their density being constant. The resonant Joule's absorption bistability of the pumping infrared wave near a Langmuir resonance of free electrons is discussed as well as the hysteresis cross-modulation of an infrared probing wave by means of a pumping microwave. The possibilities of smooth detuning of the hysteresis regime due to a magnetic-field control and low energy thresholds of these regimes are illustrated for InSb thin films in relatively weak magnetic fieldsH1–2 kG.     

Synthesen in der Pyridazin-Reihe, 26. Mitt.:

Zusammenfassung Es wird über die Synthese von verschiedenen methylsubstituiertens-Triazolo[4,3—b]pyridazinen berichtet. Außerdem wurdens-Triazolo[4,3—b]pyridazin und seine 7-Methyl- und 6-Chlor-Derivate der homolytischen Methylierung unterworfen, die Reaktionsgemische gaschromatographisch auf einzelne Methyl-s-triazolo[4,3—b]pyridazine aufgetrennt und die Verbindungen identifiziert.

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Syntheses of pyridazines, XXVI: Synthesis and homolytic methylation of s-triazolo[4.3—b]pyridazines

The syntheses of some methyl substituteds-triazolo[4,3—b]-pyridazines are reported.s-Triazolo[4.3—b]pyridazine and its 7-methyl and 6-chloro analogs were submitted to homolytic methylations and the obtained reaction mixtures were separated by gas chromatography into particular components which were then identified.