Gewöhnliche lineare Differentialgleichungen zweiter Ordnung mit Distributionskoeffizient

Zusammenfassung Läßt man in der gew. lin. Dgl. zweiter Ordnung einen Distributionskoeffizient zu, der Ableitung einerL _loc ² -Funktion ist, so existieren eindeutig festlegbare, stetige Lösungen derart, daß die in der Dgl. auftretenden Produkte definiert werden können. Mit einer Regularisierung des Distr.-Koeffizienten können die Lösungen durchC -Funktionen approximiert werden. Es wird der Sturmsche Vergleichssatz verallgemeinert. Hieraus und aus den Eigenschaften der mit zwei Basislösungen gebildeten Lösungskurve folgt die Gültigkeit des Ljapunovschen Satzes über die Eigenwertverteilung der verallgemeinerten Hillschen Dgl. mit positivem Distr.-Koeffizient, falls eine zusätzliche Bedingung erfüllt ist. Die vorliegende Arbeit enthält einige Ergebnisse meiner Dissertation [6] (weitere Resultate und Details finden sich dort).     

Proton-14N double resonance study of the structural phase transitions in the perovskite type layer compound (CH3NH3)2CdCl4

Using a proton-nitrogen double resonance technique we have determined the quadrupole coupling of¹⁴N in the room temperature orthorhombic (Cmca), the low temperature tetragonal (P4₂/ncm), and the monoclinic low temperature (P2₁/c) phases of (CH₃NH₃)₂CdCl₄. In all these phases all nitrogens are chemically equivalent demonstrating that the disorder in the orientations and H-bonding arrangements of the CH₃-NH₃ groups in theC m c a andP4₂/ncm phases is indeed dynamic and not static. In the monoclinic phase the¹⁴N quadrupole coupling constant equalse ² qQ/h=880 kHz and the asymmetry parameter is=0.20, wherease ² qQ/h=790 kHz,=0.1 in the tetragonal low temperature phase ande ² qQ/h=726 kHz,=0.21 in the room temperature orthorhombic phase. The observed increase in the¹⁴N quadrupole coupling constant on going from the orthorhombic phase to the tetragonal low temperature phase which is coupled with a simultaneous decrease in the asymmetry parameter can be understood in terms of a partial freezing in of the dynamic disorder in the C-N bond directions whereas the¹⁴N quadrupole coupling tensor in the monoclinic phase is characteristic of a frozen in C-N bond in a deformed lattice, where the N-H — Cl bonds are of different length.     

Fibrous Networks with Incorporated Macrocycles: A Chiral Stimuli‐Responsive Supramolecular Supergelator and Its Application to Biocatalysis in Organic Media

A new and versatile, crown ether appended, chiral supergelator has been designed and synthesized based on the bis‐urea motif. The introduction of a stereogenic center improved its gelation ability significantly relative to its achiral analogue. This low‐molecular‐weight gelator forms supramolecular gels in a variety of organic solvents. It is sensitive to multiple chemical stimuli and the sol–gel phase transitions can be reversibly triggered by host–guest interactions. The gel can be used to trap enzymes and release them on demand by chemical stimuli. It stabilizes the microparticles in Pickering emulsions so that enzyme‐catalyzed organic reactions can take place in the polar phase inside the microparticles, the organic reactants diffusing through the biphasic interface from the surrounding organic phase. Because of the higher interface area between the organic and polar phases, enzyme activity is enhanced in comparison with simple biphasic systems.     

Synthesis and Rearrangement of P‐Nitroxyl‐Substituted PIII and PV Phosphanes: A Combined Experimental and Theoretical Case Study

Low‐temperature generation of P‐nitroxyl phosphane 2 (Ph₂POTEMP), which was obtained by the reaction of Ph₂PH ( 1 ) with two equivalents of TEMPO, is presented. Upon warming, phosphane 2 decomposed to give P‐nitroxyl phosphane P‐oxide 3 (Ph₂P(O)OTEMP) as one of the final products. This facile synthetic protocol also enabled access to P‐sulfide and P‐borane derivatives 7 and 13 , respectively, by using Ph₂P(S)H ( 6 ) or Ph₂P(BH₃)H ( 11 ) and TEMPO. Phosphane sulfide 7 revealed a rearrangement to phosphane oxide 8 (Ph₂P(O)STEMP) in CDCl₃ at ambient temperature, whereas in THF, thermal decomposition of sulfide 7 yielded salt 10 ([TEMP‐H₂][Ph₂P(S)O]). As well as EPR and detailed NMR kinetic studies, indepth theoretical studies provided an insight into the reaction pathways and spin‐density distributions of the reactive intermediates.     

Possible acceleration of cosmic rays in a rotating system: Uehling-Uhlenbeck model

We illustrate the possible acceleration of cosmic rays passing through a kind of amplification channel (via diffusion modes of propagating plane-wave fronts) induced by a rotating system. Our analysis is mainly based on the quantum discrete kinetic model (considering a discrete Uehling-Uhlenbeck collision term), which has been used to study the propagation of plane (e.g., acoustic) waves in a system of rotating gases.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.