ON THE RATE OF CONVERGENCE OF BEZIER VARIANT OF SZASZ—DURRMEYER OPERATORS

In the present paper, we introduce Szasz-Durrmeyer-Bezier operators M.,.(f,x) , which generalize the Szasz-Durrmeyer operators. Here we obtain an estimate on the rate of convergence of Mn,a(f,x) for functions of bounded variation. Our result extends and improves that of Sahai and Prasad and Gupta and Pant.     

Asymptotic approximation of functions and their derivatives by Müller’s Gamma operators

We obtain the complete asymptotic expansion of the image functions of Müller’s Gamma operators and of their derivatives. All expansion coefficients are explicitly calculated. Moreover, we study linear combinations of Gamma operators having a better degree of approximation than the operators themselves. Using divided differences we define general classes of linear combinations of which special cases were recently introduced and investigated by other authors.     

The experimental structure of199Au and the interacting boson-fermion model

Gamma rays of¹⁹⁹Au obtained after double neutron capture in¹⁹⁷Au were measured at the ILL high flux reactor. A level scheme up to 1770 keV excitation energy is established. The result is compared with IBFM and Boson-Fermion-Symmetry calculations.     

On the theory of collective motion in nuclei. III. From Hamiltonian dynamics to vortex-free fluidity

It is assumed that the Hamiltonian for collective motion in nuclei is invariant under the orthogonal group O(n, $\text{R}$). For degenerate orbits in phase space it is shown that the classical Hamiltonian equations reduce to the equations of a vortex-free fluid with a velocity field determined by independent equations of motion.     

Elliptic flow of thermal photons in relativistic nuclear collisions

We predict the transverse momentum (p(T)) dependence of elliptic flow of thermal photons for Au + Au collisions at the BNL Relativistic Heavy Ion Collider. We model the system hydrodynamically, with a thermalized quark-gluon plasma at early times followed by hadronization and decoupling. Photons are emitted throughout the expansion history. Contrary to hadron elliptic flow, which increases monotonically with p(T), the elliptic flow nu2(p(T)) of thermal photons is predicted to first rise and then fall again. Photon elliptic flow at high p(T) reflects the quark momentum anisotropy at early times when it is small, while at low p(T) it mirrors the large pion momentum anisotropy during the late hadronic emission stage. An interesting structure is predicted at intermediate p(T) approximately 0.4 GeV/c, where photon elliptic flow reflects the momenta and the (compared to pions) reduced nu2 of heavy vector mesons in the late hadronic phase.     

Potential-induced structure transitions in self-assembled monolayers: ethanethiol on Au(1 0 0)

We have characterized the structural behaviour of ethanethiol self-assembled monolayers (SAMs) on Au(1 0 0) in 0.1 M H₂SO₄ as a function of electrode potential, using in-situ scanning tunneling microscopy (STM). After modification of the Au(1 0 0) electrode in an ethanolic solution of ethanethiol, STM images in air reveal a disordered thiol adlayer and a surface that is covered by 25% of monoatomic high gold islands, which originate from lifting of the (hex) reconstruction during thiol adsorption. In contrast to alkanethiol SAMs on Au(1 1 1), no vacancy islands are seen on the Au(1 0 0) surface. After contact of the SAM-covered Au(1 0 0) electrode with 0.1 M H₂SO₄ under potential control, two different structures are observed, depending on the potential range positive or negative of +0.3 V vs. SCE. In both cases the emerging ordered structures are quadratic, their unit cells being rotated by 45° with respect to the main crystallographic axes of the substrate. However, the ordered structure at negative potentials is more densely packed than the one at positive potentials, and in addition the surface reveals an almost 50% coverage of monoatomic high gold islands. The structure of the SAM changes reversibly with the electrode potential, the long range order gradually decreasing with each transition. Concomittant with this structure transition monoatomic deep holes are created when the potential is stepped from the cathodic to the anodic region. The experimental observations are rationalized by a high mobility of the gold thiolate moiety, causing the surface density of the SAM-covered gold to change drastically with potential.     

Probing the out-of-plane distortion of single point defects in atomically thin hexagonal boron nitride at the picometer scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.     

Effect of addition of a non-equidiffusional reactant to an equidiffusional diffusion flame

A Burke–Schumann (flame-sheet) formulation is developed for diffusion flames between a fuel and oxidiser with Lewis numbers of unity, subject to addition to the fuel and/or oxidiser stream of a different reactant for which the Lewis number differs from unity. This formulation is applied to laminar counterflow diffusion-flame experiments, reported here, in which hydrogen was added to either methane–nitrogen mixtures or oxygen–nitrogen mixtures at normal atmospheric pressure, with both feed streams at normal room temperature. Experimental conditions were adjusted to fix selected values of the stoichiometric mixture fraction and the adiabatic flame temperature, and the strain rate was increased gradually, maintaining the momentum balance of the two streams, until extinction occurred. At the selected sets of values, the strain rate at extinction was measured as a function of the hydrogen concentration in the fuel or oxidiser stream. The ratio of the fraction of the oxidiser flux that consumes hydrogen to the fraction that consumes fuel was calculated from the new Burke–Schumann formulation, and it was found that, within experimental uncertainty, the ratio of the extinction strain rate with hydrogen addition to that without was the same at any given value of this oxygen flux ratio, irrespective of whether the hydrogen was added on the fuel or oxidiser side. This experimental result was also in close agreement with computational predictions employing detailed chemistry. These results imply that differences in detailed hydrogen concentration profiles within the reaction zone have little or no influence on the chemical kinetics of extinction when the stoichiometric mixture fraction, the adiabatic flame temperature, and the proportion of oxygen that consumes the added fuel are fixed. This same correspondence may be expected to apply for other fuels and additives.     

Conical surface structures on model thin-film electrodes and tape-cast electrode materials for lithium-ion batteries

A computationally-effective approach for calculating the electromechanical behavior of SWNTs and MWNTs of the dimensions used in nano-electronic devices has been developed. It is a mixed finite element–tight-binding code carefully designed to realize significant time saving in calculating deformation-induced changes in electrical transport properties of the nanotubes. The effect of the MWNT diameter and chirality on the conductance after mechanical deformation was investigated. In case of torsional deformation, results revealed the conductance of MWNTs to depend strongly on the diameter, since bigger MWNTs reach the buckling load under torsion much earlier, their electrical conductivity changes more easily than in small diameter ones. For the same outer diameter, zigzag MWNTs are more sensitive to twisting than armchair MWNTs since the hexagonal cells are oriented in such a way that they oppose less resistance to the buckling deformations due to torsion. Thus small diameter armchair MWNTs should work better if used as conductors, while big diameter zigzag MWNTs are more suitable for building sensors.     

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.