Approximation of solutions of operator-differential equations by operator polynomials

We prove theorems that characterize the classes of functions whose best approximations by algebraic polynomials tend to zero with given order. We construct approximations of solutions of operator-differential equations by polynomials in the inverse operator. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1506–1516, November, 1998.     

Computational Study of Cage Like (ZnO)12 Cluster Using Hybrid and Hybrid Meta Functionals

Density Functional Theory employing hybrid and M06 functionals in combination with three different basis sets is used to calculate the ground state of a cage like (ZnO)₁₂ nanocluster which has been consistently reported as the more stable cluster for its particular size. B3LYP and B3PW91 hybrid functionals combined with 6‐31+G*, Lanl2dz and SDD basis sets are employed to treat the ZnO molecular system. Alternatively, three M06 functionals in combination with three basis sets are employed in the nanostructure calculations. Results obtained by treating ZnO sodalite cage nanocluster with M06 functionals demonstrated comparable quality to results obtained with hybrid functionals. Within this study, efficient theoretical DFT methods with the widely known hybrid and the recently created M06 meta‐hybrid functionals are employed to study nanostructured ZnO. Our resulting parameters provide a fresh approach performance wise on the different theoretical methods to treat transition metal nanostructures, particularly, ZnO nanoclusters geometry and electronic structure.     

Recent advances in DNA sequencing by capillary and microdevice electrophoresis

A number of significant improvements in the electrophoretic performance and design of DNA sequencing devices have culminated in the introduction of truly industrial grade production scale instruments. These instruments have been the workhorses behind the massive increase in genomic sequencing data available in public and private databases. We highlight the recent progress in aspects of capillary electrophoresis (CE) that has enabled these achievements. In addition, we summarize recent developments in the use of microfabricated devices for DNA sequencing that promise to bring the next leap in productivity.     

Systematic study of field and concentration effects in capillary electrophoresis of DNA in polymer solutions

A systematic study of the separation of double-stranded DNA in hydroxypropylcellulose (HPC) with a molecular mass of 10⁶ was undertaken, using a variety of concentrations (from 0.1 to 1%) and different electric fields (from 6 to 540 V/cm). The data show that a high polymer concentrations (0.4%) and low fields, the separation mechanism is similar to that occurring in gels. The results are in good agreement with theoretical models, and in particular with a recently proposed theory for gels with a pore size smaller than the persistence length of DNA. For more dilute solutions and high fields, however, the separation pattern cannot be explained by existing theories. The existence of an original mechanism was confirmed by the direct observation of the conformation of double-stranded DNA molecules in the polymer solution by fluorescence videomicroscopy. Practical conclusions for the capillary electrophoretic separation of duplex DNA are drawn.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazole monoxides

Conjugated organic heterocycles are systems of growing interest in materials science in view of the potential applications in fields such as electronics, photonics, sensors, or corrosion protection. The study of their molecular properties serves as a model for the prediction of the behavior of potentially conductive oligomers and polymers. A detailed analysis of isomeric thiadiazole monoxide molecules has been done using Hartree–Fock and local (SVWN) and nonlocal (BLYP, B3LYP) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecules has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness, and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 105–115, 2001     

Observation of trielectronic recombination in Be-like Cl ions

Recombination involving the core excitation of two electrons, which may be termed trielectronic recombination, has been experimentally identified for the first time. Using Cl13+ ions circulating in the TSR heavy-ion storage ring, we have observed surprisingly strong low-energy trielectronic recombination resonances, comparable to the dielectronic process. At higher electron-ion collision energies, trielectronic recombination is suppressed due to the autoionization of the triply excited intermediate state into excited final states. The formation of the intermediate state depends sensitively on configuration mixing, making trielectronic recombination a challenge to atomic-structure calculations.     

Deep-core dielectronic-capture resonances in the electron-impact ionization of heavy atomic ions

Experimental measurements and theoretical calculations are carried out for the electron-impact ionization of Sm(12+). The low energy region of the single ionization cross section for Sm(12+) is found to be dominated by contributions from the indirect process of excitation autoionization. At about 1.0 keV strong resonance features are found in the experimental crossed-beam measurements performed in scan mode at high resolution. Theoretical calculations confirm that the high energy experimental features are due to deep-core dielectronic capture followed by sequential double Auger decay. The discovery of these unusual high energy resonances in single and multiple ionization opens the door for future systematic studies of how heavy atomic ions with deep inner-shell vacancies achieve final stabilization.     

Time-dependent close-coupling calculations of dielectronic capture in He

We report on the first time-dependent close-coupling calculation of dielectronic capture into a doubly excited state of a two-electron atom. An incoming electron is represented by a Gaussian wave packet which collides with singly ionized helium in its ground state. The close-coupling equations describe the propagation of the total compound wave function on a two-dimensional radial lattice. By projecting this wave function onto a doubly excited state of neutral helium, we can determine the probability amplitude for dielectronic capture into one of these states and the subsequent autoionization from it.     

Theoretical assessment of antioxidant property of polyproponoid and its derivatives

Structural Chemistry - Derivatives of parent molecules possess similar structural activity which makes them to be the topic of equal interest. In the present work, a naturally occurring acid...