On the structure of a metastable phase in the lead-bismuth system

A new metastable phase is detected in liquisol-quenched (splat-cooled) lead-bismuth alloys. Its crystal structure of the new phase is established as tetragonal with a maximum of 48 atoms per unit cell and with the lattice parameters $\text{a = 9.931}\text{A}\text{?}\text{, c = 14.99}\text{A}\text{?}$ and c/a = 1.510.     

Dielectric dispersion and its temperature variation in calcite single crystals

The variation of dielectric constant and loss of calcite single crystals with frequency and temperature over wide ranges (10² to 2.4×10¹⁰c/s and ?193 to 450 °C) in two orientations of the crystal, namely, the electric field (i) parallel to the optic axis and (ii) perpendicular to the optic axis, has been studied and the results reported. The dielectric constant at 25 °C in both orientations (E‖, 7.8 andE⊥, 8.2) is frequency-independent. The dielectric loss shows a minimum in the 10⁵ to 10⁸ c/s region. Dielectric constant as a function of temperature exhibits two distinct regions: frequency-independent (?193 to 50 °C) and frequency-dependent (50 to 450 °C). The temperature variation of specific conductivity can be represented by a sum of two exponentials, e.g., \(\sigma = Ae^{ - E_1 /kT} + Be^{ - E_2 /kT}\) with the usual notation; the constants have different values in the two orientations. The intrinsic conductivity with larger activation energy (E‖ 0.91 eV andE⊥ 1.05 eV) is attributed to the movement of lattice vacancies in the crystal. The 15% larger value for the intrinsic activation energy alongE⊥ optic axis over the other orientation may be due to a probably large electrostatic interaction between the charge carriers and the lattice ions in this orientation.     

Über die Beziehung der Dielektrizitätskonstanten zur Oberflächenspannung und zur Viskosität

Zusammenfassung Es wird gezeigt, daß das Verhältnis der elektrischen Volumspolarisation zur vierten Wurzel der Oberflächenspannung für verschiedene Flüssigkeiten in einem großen Temperaturbereich bemerkenswert konstant ist. Ebenso konstant bleibt auch bei nicht assoziierten Flüssigkeiten das Verhältnis der elektrischen Volumspolarisation zur achten Wurzel der Viskosität. Die Natur der intermolekularen Kräfte wird kurz diskutiert.     

Modified Cyclodextrins as Enantioselective Hosts for Amino Acids

Two modified β‐cyclodextrins, H‐2 and H‐3 , having a flexible appended moiety were studied for the chiral discrimination of the enantiomers of various amino acids by means of fluorescence as signaling option. These hosts quenched the fluorescence intensities of amino acids upon binding. The d‐ enantiomers were better recognized by these hosts. The association constants (K_s) and enantioselectivity factors (α) of the host?guest complexes were calculated.     

Cathodic synthesis of 2-amino-2-propene-1-ones electrolytical studies on vinylazides,VII

The cathodic preparation of enamino ketones from enazidoketones has been generalised to include heteroaromatic and aliphatic derivatives. Mechanistically the role of different sites of protonation, either on N¹ of the N₃-group or on carbonyl depending on electrolysis potential and acid strength, apparent by product distribution, is clarified. Aldehydic groups are preferentially reduced compared to the vinylazide part. Purely aliphatic azidoketones yield conjugated dienes under reductive acetylation, which might be useful for cycloaddition reactions.Die kathodische Synthese von Enaminoketonen aus ungesättigten Azidoketonen wurde auf heteroaromatisch substituierte und auf rein aliphatische Derivate übertragen. Zum Reduktionsmechanismus wurde der Einfluß verschiedener Stellen der Protonierung (am N¹ der N₃-Gruppe bzw. an der Carbonylgruppe), abhängig von Potential und Säurestärke, untersucht. Aldehydische Gruppen als weitere funktionelle Gruppen im Enazid werden leichter als die Vinylazide reduziert. Die rein aliphatischen Enazidoketone ergeben bei reduktiver Acylierung konjugierte Diene.

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Elektrolytische Untersuchungen an Vinylaziden, 7. Mitt.: Kathodische Synthese von 2-Amino-2-propen-1-onen

     

Existence theorems for optimization problems concerning hyperbolic partial differential equations

Existence theorems are given for optimal control problems with partial integro-differential equations of hyperbolic type. A variety of conditions are given depending on whether (i) the cost functional is in the Lagrange form or Mayer form, (ii) the controls vary in a fixed compact set or variable but closed sets, (iii) the required solutions are generalized or usual, (iv) the defining equations are nonlinear or linear in the state variable or linear in the control, (v) the trajectories belong to the usual Sobolev classW _p ² ,p>1, or the special Sobolev classW _p ^* , 1?p?∞. Several examples are given to illustrate the above cases. Necessary conditions for some of these problems have been discussed in an earlier paper.