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).     

Can Crude Oil Exploration Influence the Phytochemicals and Bioactivity of Medicinal Plants? A Case of Nigerian Vernonia amygdalina and Ocimum gratissimum

The Nigerian Niger-Delta crude oil exploration often results in spills that affect indigenous medicinal plant biodiversity, likely changing the phytochemical profile of surviving species, their bioactivity or toxicity. In crude oil-rich Kokori and crude oil-free Abraka, classic examples of indigenous plants occupying the medicine-food interface include Vernonia amygdalina (VAL) and Ocimum gratissimum leaves (OGL). These plants are frequently utilised during pregnancy and in anaemia. To date, no scientific investigation has been reported on the potential changes to the phytochemical or bioactivity of the study plants. To discuss the similarities and dissimilarities in antisickling bioactivity and phytochemicals in VAL and OGL collected from Kokori (VAL-KK and OGL-KK) and Abraka (VAL-AB and OGL-AB), in silico, in vitro and comparative UPLC-QTOF-MS analysis was performed. Nine unique compounds were identified in OGL-KK, which have never been reported in the literature, while differences in antisickling potentials were observed in VAL-KK, OGL-KK and, VAL-AB, OGL-AB. Our findings show that VAL-AB and OGL-AB are richer and more diverse in phytochemicals and displayed a slightly higher antisickling activity than VAL-KK and OGL-KK. Ligand-based pharmacophore modelling was performed to understand the potential compounds better; this study may provide a basis for explaining the effect of crude oil spills on secondary metabolites and a reference for further research.     

Regge Models of Proton Diffractive Dissociation Based on Factorisation and Structure Functions

Recent results by the authors on proton diffractive dissociation (single, double and central) in the low-mass resonance region with emphasis on the LHC kinematics are reviewed and updated. Based on the previous ideas that the contribution of the inelastic proton–Pomeron vertex can be described by the proton structure function, the contribution of the inelastic Pomeron–Pomeron vertex appearing in central diffraction is now described by a Pomeron structure function.     

Towards Photochromic Azobenzene-Based Inhibitors for Tryptophan Synthase

Light regulation of drug molecules has gained growing interest in biochemical and pharmacological research in recent years. In addition, a serious need for novel molecular targets of antibiotics has emerged presently. Herein, the development of a photocontrollable, azobenzene-based antibiotic precursor towards tryptophan synthase (TS), an essential metabolic multienzyme complex in bacteria, is presented. The compound exhibited moderately strong inhibition of TS in its E configuration and five times lower inhibition strength in its Z configuration. A combination of biochemical, crystallographic, and computational analyses was used to characterize the inhibition mode of this compound. Remarkably, binding of the inhibitor to a hitherto-unconsidered cavity results in an unproductive conformation of TS leading to noncompetitive inhibition of tryptophan production. In conclusion, we created a promising lead compound for combatting bacterial diseases, which targets an essential metabolic enzyme, and whose inhibition strength can be controlled with light.     

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.