Product numerical range in a space with tensor product structure

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.     

Weak intermolecular interactions in gas-phase nuclear magnetic resonance

Gas-phase nuclear magnetic resonance (NMR) spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO(2) dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D(2)-rare gas systems is considered.     

Total synthesis of a CD-ring: side-chain building block for preparing 17-epi-calcitriol derivatives from the Hajos-Parrish dione

An efficient synthesis of the key building block for 17-epi-calctriol from the Hajos-Parrish dione involving a sequence of diastereoselective transformation of the azulene core and the side-chain construction is presented.     

Ring-expanded bicyclic β-lactams: a structure-chiroptical properties relationship investigation by experiment and calculations

In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic β-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the β-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240-215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic β-lactams with the nonplanar amide chromophore only.     

Stabilization effect of potential antioxidants on the thermooxidative stability of styrene–butadiene rubber

Effects of several heterocyclic compounds containing nitrogen, trisubstituted amines and diamines and molecules based on N,N,N′,N′,N′′,N′′-substituted-[1,3,5]triazine-2,4,6-triamine in preventing thermooxidative degradation of styrene–butadiene rubber (SBR) have been studied using non-isothermal DSC measurements. The aim of this study was to determine and compare the stabilizing effect of individual compounds and to select the structures with the best antioxidative properties. In order to compare the stabilizing effect of the compounds, induction periods and protection factors have been calculated. The treatment of the experimental data was carried out using a method based on a non-Arrhenian temperature function. The results show that better antioxidative properties can be assigned to heterocyclic compounds. On the other hand, molecules containing triazine structures exhibited only negligible stabilizing effect on SBR at lower temperatures and even destabilizing effect at higher temperatures.     

Steady-state photoinduced absorption of CdSe/CdS octapod shaped nanocrystals

Colloidal branched nanocrystals have been attracting increasing attention due to evidence of an interesting relationship between their complex shape and charge carrier dynamics. Herein, continuous wave photoinduced absorption (CW PIA) measurements of CdSe/CdS octapod-shaped nanocrystals are reported. CW PIA spectra show strong bleaching due to the one-dimensional (1D) CdS pod states (480 nm) and the zero-dimensional (0D) CdSe core states (690 nm). The agreement with previously reported ultrafast pump-probe experiments indicates that this strong bleaching signal may be assigned to state filling. Additional bleaching features at 520 and 560 nm are characterized by a longer lifetime and are thus ascribed to defect states, localized at the pod-core interface of the octapod, showing that some of the initially photogenerated carriers get quickly trapped into these long-lived defect states. However, we remark that a relevant part of electrons remain untrapped: this opens up the opportunity to exploit octapod shaped nanocrystals in photovoltaics applications, as electron acceptor materials, considering that several efficient hole extracting materials are already available for the realization of a composite bulk heterojunction.     

A multifaceted approach to hydrogen storage

The widespread adoption of hydrogen as an energy carrier could bring significant benefits, but only if a number of currently intractable problems can be overcome. Not the least of these is the problem of storage, particularly when aimed at use onboard light-vehicles. The aim of this overview is to look in depth at a number of areas linked by the recently concluded HYDROGEN research network, representing an intentionally multi-faceted selection with the goal of advancing the field on a number of fronts simultaneously. For the general reader we provide a concise outline of the main approaches to storing hydrogen before moving on to detailed reviews of recent research in the solid chemical storage of hydrogen, and so provide an entry point for the interested reader on these diverse topics. The subjects covered include: the mechanisms of Ti catalysis in alanates; the kinetics of the borohydrides and the resulting limitations; novel transition metal catalysts for use with complex hydrides; less common borohydrides; protic-hydridic stores; metal ammines and novel approaches to nano-confined metal hydrides.     

Weak law of large numbers for iterates of random-valued functions

Aequationes mathematicae - Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ , a complete and separable metric space X with the $$ \sigma $$ -algebra $$ {\mathcal {B}} $$ of all its...     

From biased coin to any discrete distribution

Periodica Mathematica Hungarica - In this note we construct an algorithm generating any discrete distribution with an arbitrary coin (and, as a result, with arbitrary initial distribution). The...     

A Comparison of the Experimental and ab Initio Values of theO NMR Chemical Shifts in the Carbonyl Group

New experimental and theoretical results are presented for the NMR shielding of oxygen in the carbonyl group. The experimental values clearly demonstrate that the solvent effects are very significant. The new results for the chemical shifts are in better agreement than the previous literature data with the corresponding ab initio values calculated for isolated molecules.