Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators

Journal of Statistical Physics - Let V 0be a real-valued function on [0,∞) and V∈L 1([0,R]) for all R&;gt;0 so that H(V 0)=? $\frac{{d^2 }}{{dx^2 }}$ +V 0in L 2([0,∞))...     

The Mössbauer effect and collective motions in glass-forming liquids and polymeric networks

Glass-forming liquids, synthetic polymers and biopolymers share essential properties. Dynamic processes in these complex systems are characterized by cooperative motions with wide distributions of time scales, which manifest themselves in broad quasielastic lines in the Mössbauer spectrum. In this article, the application of the Mössbauer effect to the study of structural dynamics in complex systems is discussed.     

The Arrow of Time in the Equations of Motion

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized.     

L'acide hydroxylamine-O-sulfonique,réactif de choix pour la conversion d'aldéhydes en nitriles

Hydroxylamine-O-sulfonic acid: a convenient reagent for the conversion of aldehydes into nitriles . Hydroxylamine-O-sulfonic acid (HAS) proved to be an excellent reagent for the conversion of aliphatic, aromatic and heteroatomic aldehydes into nitriles. There, aldehydes in the form of suspension in HAS water solution, react rapidely to give the corresponding nitriles in high yield. Only with formylpyridines could the intermediate oxime-O-sulfonic acids be isolated.     

Transition metal nitrosyls as nitrosylation agents : II.Photo-nitrosylation of η5-C5H5V(CO)3L(L = CO,Pz3) by [Co(NO)2Br]2

η⁵-C₅H₅V(NO)₂CO is prepared in 40% yield by the photo-reaction between η⁵-C₅H₅V(CO)₄ and [Co(NO)₂Br]₂.η⁵-C₅H₅V(NO)₂CO reacts by an S_N1 mechanism with various phosphines PZ₃ to yield η⁵-C₅-H₅V(NO)₂PZ₃. The phosphine complexes are also obtained by photo-induced ligand interchange between η⁵-C₅H₅V(CO)₃PZ₃ and [Co(NO)₂Br]₂, or η⁵-C₅H₅V(CO)₄ and Co(NO)₂Br(PZ₃). In all cases, the main cobalt species formed is Co(NO)(CO)₃. While the one-bond vanadiumphosphorus coupling constants of most of the phosphine complexes are virtually the same (ca 410 Hz),the chemical shift values δ(⁵¹V) (?1328 to ?973 ppm rel. VOCl₃) decrease in the order PF₃ > CO > P(OR)₃ > P(alkyl)₃ > PPh₃ > PPh(NEt₂)₂, reflecting the decreasing π-acceptor ability of the ligands. δ(⁵¹V) also decreases in the series of alkylphosphines PR₃ (R = Me, Et, Prⁿ, Buⁱ, Prⁱ, BU^t) as the cone angle of PR₃increases.     

Verhalten von ng- und μg-Mengen biochemisch interessierender Amine bei Trennverfahren,wie Ionenaustausch-Chromatographie,Mitfällung und Extraktion

The behaviour of ng- and μg-amounts of amines of biochemical interest is compared. ng-amounts are co-precipitated from aqueous solutions with the tetraphenyloborates of potassium, ammonium and creatinine. A separation from potassium chloride, ammonium chloride and creatinine is achieved by extraction of the amines with methanol. The elution volumes of about 50 amines during ion-exchange chromatography using a weakly acidic resin are compared. A procedure has been elaborated by which the amines can be collected from urine.     

Coulometric titration of acids in non-aqueous solvents

Coulometric titrations of mineral acids, sulphonic acids, carboxylic acids, enols, imides and phenols have been carried out in t-butanol or in acetone with electrically generated tetrabutylammonium hydroxide. Either a potentiometric titration or a visual indicator end-point may be used. The amount of acid titrated ranges from 10 to 60 muequiv, and the precision and accuracy of the method are excellent.     

Untersuchungen zur Lithiierung und Substitution des HP[Si(t-Bu)2]2PH

Investigations on Lithiation and Substitution of HP[Si(t-Bu)₂]₂PH HP[Si(t-Bu)₂]₂PH 1 is monolithiated by reaction with LiPH₂ · DME or LiBu in toluene. The crystalline compound HP[Si(t-Bu)₂]₂PLi · 2 DME 2 can be isolated in DME. Reaction of 2 with Me₂SiCl₂ leads to HP[Si(t-Bu)₂]₂P? SiMe₂Cl 4 , ClMe₂Si? P[Si(t-Bu)₂]₂P? SiMe₂Cl 5 , HP[Si(t-Bu)₂]₂P? SiMe₂? P[Si(t-Bu)₂] ₂PH 6 . Isomerization by Li/H migration between 4 and 2 leads to the formation of 5 . Reaction of Li(t-Bu) with 1 or 2 yields LiP[Si(t-Bu)₂]₂PLi 3 by further lithiation. 3 could not be obtained purely, only in a mixture with 2 . These compounds favourably generate with t-BuPCl₂ in hexane Cl(t-Bu)P? P[Si(t-Bu)₂]₂P? P(t-Bu)Cl 9 , in THF HP[Si(t-Bu)₂]₂P? P(t-Bu)? P[Si(t-Bu)₂]₂ PH 12 (main product), 9 , H(t-Bu)P? P[Si(t-Bu)₂]₂P? P(t-Bu)Cl 10 , H(t-Bu)P? P[Si(t-Bu)₂]₂P? P(t-Bu)H 11 as well as HP[Si(t-Bu)₂]₂P? P(t-Bu)H 13 and HP[Si(t-Bu)₂]₂P? P(t-Bu)₂ 14 .