The Eigenstructure of Operators Linking the Bernstein and the Genuine Bernstein–Durrmeyer operators

We study the eigenstructure of a one-parameter class of operators ${U_{n}^{\varrho}}$ of Bernstein–Durrmeyer type that preserve linear functions and constitute a link between the so-called genuine Bernstein–Durrmeyer operators U _n and the classical Bernstein operators B _n . In particular, for ${\varrho\rightarrow\infty}$ (respectively, ${\varrho=1}$ ) we recapture results well-known in the literature, concerning the eigenstructure of B _n (respectively, U _n ). The last section is devoted to applications involving the iterates of ${U_{n}^{\varrho}}$ .     

Molecular structures and electronic transitions of 3,6-diphenyl-1,2-dithiin and its radical cation: a spectroelectrochemical and DFT study

One-electron oxidation of 3,6-diphenyl-1,2-dithiin yields the corresponding radical cation. The product is stable at low temperatures and can be distinguished by a triplet EPR signal. Cyclic voltammetric, UV-vis spectroelectrochemical, and DFT studies were performed to elucidate its molecular structure and electronic properties. Time-dependent DFT calculations reproduce appreciably well the UV-vis spectral changes observed during the oxidation. The results reveal a moderately twisted structure of the 1,2-dithiin heterocycle in the radical cation.     

Molecular beams with a tunable velocity

The merging of molecular beam methods with those of accelerator physics has yielded new tools to manipulate the motion of molecules. Over the last few years, decelerators, lenses, bunchers, traps, and storage rings for neutral molecules have been demonstrated. Molecular beams with a tunable velocity and with a tunable width of the velocity distribution can now be produced, and are expected to become a valuable tool in a variety of physical chemistry and chemical physics experiments. Here we present a compact molecular beam machine, capable of producing 3D spatially focused packets of state-selected accelerated or decelerated molecules.     

The Genuine Bernstein–Durrmeyer Operators Revisited

We present some direct and inverse results for the approximation by the genuine Bernstein–Durrmeyer operators U _n . We also consider iterates of U _n and discuss some convergence results towards the corresponding semigroup. Using the eigenstructure of the operators U _n we give new proofs of some known qualitative results and obtain new quantitative estimates concerning the convergence of iterates towards the semigroup.     

From Hardcore Bosons to Free Fermions with Painlevé V

We calculate zero temperature Green’s function, the density–density correlations and expectation values of a one-dimensional quantum particle which interacts with a Fermi-sea via a δ-potential. The eigenfunctions of the Bethe-Ansatz solvable model can be expressed as a determinant. This allows us to obtain a compact expression for the Green’s function of the extra particle. In the hardcore limit the resulting expression can be analyzed further using Painlevé V transcendents. It is found that depending on the extra particles momentum its Green’s function undergoes a transition of that for hardcore Bosons to that of free Fermions.     

Mixed conducting polymers on ion-conducting sensor glasses – charge transfer in the system polymer/glass

Mixed ion/electron conducting polymer layers based on polypyrrole have been used as internal reference electrodes in all-solid-state pH glass electrodes. The effect of the nature and composition of the polymer used and of the deposition technique applied on the performance of the resulting sensor has been studied. For this purpose, crucial sensor properties, e.g. parameters of the calibration function, response behaviour and complex impedance, have been determined experimentally at room temperature. The results show that several properties studied remained nearly uninfluenced by changes of the polymer composition. The zero potential point of the calibration line was found to be the most sensitive parameter. Principally, almost all mixed conducting polymers used seems to result in a stable charge transfer in the system polymer/glass.     

ChemInform Abstract: Metastable Isonitrosyl Structure of the Nitroprusside Anion Confirmed by Nuclear Inelastic Scattering.

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