Koplienko Spectral Shift Function on the Unit Circle

The note shows that, for every pair of contractions, a trace formula of Koplienko holds with a summable spectral shift function, see Theorem 1 below. This answers a question by F. Gesztesy, A. Pushnitski, B. Simon (see Zh Mat Fiz Anal Geom 4(1):63–107, 202, 2008, Open Question 11.2).     

Homogeneous nucleophilic radiofluorination and fluorination with phosphazene hydrofluorides

A series of phosphazenium hydrofluorides, P(1)(tBu)·[(18/19)F]HF, P(1)(tOct)·[(18/19)F]HF, P(2)(Et)·[(18/19)F]HF, and P(4)(tBu)·[(18/19)F]HF, was synthesized. The radioactive phosphazenium [(18)F]hydrofluorides were obtained by the one-step formation and trapping of gaseous [(18)F]HF with the respective phosphazene bases. The [(19)F] isotopomers were prepared from the corresponding phosphazene bases and Et(3)N·3HF. Under the design of experiment (DoE)-optimized conditions, P(2)(Et)·HF and P(4)(tBu)·HF fluorinated alkyl chlorides, bromides, and pseudohalides in 76-98% yield, but gave lower yields with iodides and electron-deficient arenes. DoE models showed that fluorination can be performed in glass vessels, and that the reactivity of P(2)(Et)·HF and P(4)(tBu)·HF is dominated by solvent polarity but is insensitive to water to at least 2 equiv. In contrast, P(1)(tBu)·HF and P(1)(tOct)·HF were unstable towards autofluorolysis. DFT calculations were performed to rationalize this finding in terms of diminished steric bulk, higher Parr's electrophilicity, and chemical hardness of P(1)(R)H(+). The corresponding radiofluorination reaction gave no valid DoE model but displayed similar substrate scope. High specific activity and excellent radiochemical yields with various pseudohalides (81-91%) suggest that the proposed radiofluorination methodology can complement the current [(18)F]KF/Kryptofix methods, particularly in the areas for which nonpolar reaction conditions are required.     

Pyrazolyc 3-hydroxychromones: Regulation of ESIPT reaction by the “flavonol-like” intramolecular hydrogen bonding to carbonyl group oxygen,which dominates over the “alternative” H-bond to heterocyclic nitrogen

Two isomeric pyrazole derivatives of 3-hydroxychromone (3HC) with and without the possibility of the multiple intramolecular hydrogen bonds formation were compared theoretically and experimentally with the aim to find out whether the excited state intramolecular proton transfer (ESIPT) reaction follows the traditional to the most of 3HCs “flavonol-like” direction towards the CO group oxygen or an “alternative” direction towards the heterocyclic nitrogen atom.Quantum-chemical modeling and comparative study of the experimental spectral parameters of the title compounds indicated the preferential realization of “flavonol-like” ESIPT to oxygen channel.The 3HC systems with the “alternative” intramolecular hydrogen bond to nitrogen were characterized as low fluorescent and practically unable to ESIPT with participation of the nitrogen containing heterocyclic unit.     

Rescue of an abasic hairpin ribozyme by cationic nucleobases: evidence for a novel mechanism of RNA catalysis

The hairpin ribozyme catalyzes a reversible phosphodiester cleavage reaction. We examined the roles of conserved nucleobases in catalysis using an abasic ribozyme rescue strategy. Loss of the active site G8 nucleobase reduced the cleavage rate constant by 350-fold while loss of A9 and A10 nucleobases reduced activity less than 10-fold. Certain heterocyclic amines restored partial activity when provided in solution to the variant lacking G8. Heterocyclic amines that were capable of rescue shared the exocyclic amine and cyclic amide in common with the Watson-Crick hydrogen bonding face of guanine. In contrast to the shallow pH dependence of unmodified ribozyme activity, rescue activity increased sharply with decreasing pH. These results support a novel model for RNA catalysis in which a cationic nucleobase contributes electrostatic stabilization to negative charge developing in the transition state.     

Refractive-index dispersion of glassy semiconductors in the pseudo-binary As2Se3–SbSI system

The bulk chalcogenide glasses in the pseudo-binary system (As₂Se₃)_100?x(SbSI)_x (with x = 20, 30, 50, 70 and 80 at.%) were prepared from high-purity elemental components by melt-quenching technique. It is a system with the variable ratio of classical amorphous compound As₂Se₃ and the molecule of antimony-sulphoiodide, SbSI, which in the monocrystal form is characterized as a ferroelectric. The refractive-index behaviour (magnitude and spectral dispersion) of investigated glasses was determined by the prism method and analyzed. To calculate and discuss the parameters of dispersion in the band gap region three different approaches were used (Cauchy, Sellmeier and Wemple–DiDomenico single-oscillator model). The comparison of the results shows good agreement between all applied models. It was found that the value of the refractive-index shows normal dispersion behaviour and increases with the increase of Sb (or SbSI) content in the investigated system, whereas the optical gap of these glasses E_g slightly decreases.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.