Hilbert–Schmidt Hankel Operators with Anti-holomorphic Symbols on Complex Ellipsoids

On a complex ellipsoid in ${\mathbb{C}^n}$ C n , we show that there is no nonzero Hankel operator with an anti-holomorphic symbol that is Hilbert–Schmidt.     

Computation of ionization and various excited state energies ofhelium and helium‐like quantum dots

In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium‐like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree‐Fock Roothaan (HFR). The results are in a good agreement with literature results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Statistical ward continuity

Recently, it has been proved that a real-valued function defined on an interval $A$ of R, the set of real numbers, is uniformly continuous on $A$ if and only if it is defined on $A$ and preserves quasi-Cauchy sequences of points in $A$. In this paper we call a real-valued function statistically ward continuous if it preserves statistical quasi-Cauchy sequences where a sequence $\left({\alpha }_k\right)$ is defined to be statistically quasi-Cauchy if the sequence $\left(\Delta {\alpha }_k\right)$ is statistically convergent to 0. It turns out that any statistically ward continuous function on a statistically ward compact subset $A$ of R is uniformly continuous on $A$. We prove theorems related to statistical ward compactness, statistical compactness, continuity, statistical continuity, ward continuity, and uniform continuity.     

Tauberian conditions for Cesàro summability of integrals

In this paper we generalize some classical type Tauberian theorems given for Cesàro summability of integrals.     

Synthesis and Characterization of Some Novel Higher C,N-Diphenyl Nitrones,Isoxazolines, and Mercaptobenzimidazoles as Oleochemicals

Abstract

Some novel long-chain nitrones, isoxazolines, and (1H-benzo[d]-imidazol-2-ylthio) derivatives were synthesized. Nitrones, N-{4-[2-(tetradecylthio)acetoxy]benzylidene}aniline oxide, and N-[4-(12-oxo-2,5,8,11-tetraoxadocosan-22-yloxy)benzylidene]aniline oxide were prepared via the reaction of β-phenylhydroxylamine with the corresponding aromatic aldehydes. The isoxazolines were prepared from undec-10-en-1-ol and benzonitrile-N-oxide which was generated in situ. The 1H-benzo[d]-imidazol-2-ylthio derivatives were synthesized via the replacement reaction of ω-bromo esters and 2-mercaptobenzimidazole.     

Semi-guided plane wave reflection by thin-film transitions for angled incidence

The non-normal incidence of semi-guided plane waves on step-like or tapered transitions between thin film regions with different thicknesses, an early problem of integrated optics, is being reconsidered. As a step beyond the common effective index picture, we compare two approaches on how this problem can be tackled—at least approximately—by nowadays readily available simulation tools for integrated optics design. Accepting the scalar approximation, using an ansatz of harmonic field dependence on the position along the interface, the 3-D problem reduces to a 2-D Helmholtz problem, for guided wave input and transparent-influx boundary conditions, with an effective permittivity that depends on the incidence angle. Alternatively, one complements the structure with a second mirrored interface, such that the 2-D cross section of a wide multimode rib waveguide emerges. Constraints for transverse resonance then permit to translate the propagation constants of its polarized modes into discrete samples of the phase changes experienced by an in-plane guided wave upon total internal reflection at the sidewalls.     

Investigations on stabilities and intermolecular interactions of different naphthalene derivatives dimers by using B3LYP and M06-2X density functional calculations

In this paper, the stabilities and hydrogen bond interactions of 4-chloro-1-naphthol, 1-hydrox-ynaphthalene and 1,4-dihydroxynaphthalene dimers have been theoretically investigated by means of study on binding energies with nonlocal hybrid three-parameter Lee-Yang-Parr, B3LYP, and M06-class functional calculations. Calculations on dimers aim to provide as a test of the efficacy of M06 calculations for intermolecular interaction calculations and more strongly bound systems. For hydroxyl- and halo-substituted derivatives of naphthalene, total electronic energies, their correction for the zero point vibrational energies with some calculated thermodynamic properties and their relative differences are together in order to discuss the rotamer structures. Static (hyper) polarizabilities and the electric dipole moments, frontier molecular orbital energy gaps and the relationships between them have been interpreted. Generally, they are seen that the calculated geometric parameters and spectral results were in a good agreement with the corresponding experimental data.     

Separation and quantification of the urinary enantiomers of 2-hydroxyglutaric acid by capillary electrophoresis with capacitively coupled contactless conductivity detection: Application to the diagnosis of D- and L-2-hydroxyglutaric aciduria

2-hydroxyglutaric aciduria is an inherited neurometabolic disorder with two major types: D-2-hydroxyglutaric aciduria and L-2-hydroxyglutaric aciduria. An easy and fast capillary electrophoresis system combined with a capacitively coupled contactless conductivity detection method was developed for the enantioseparation and determination of D- and L-2-hydroxyglutaric acid in urine. D- and L-2-hydroxyglutaric acids were separated using vancomycin as the chiral selector. The optimal separation conditions for enantiomers were achieved by the use of a buffer containing 50 mM 4-(N-morpholino) butane sulfonic acid solution (pH 6.5), an electroosmotic flow modifier (0.001% [w/v] polybrene), and 30 mM vancomycin as chiral selector. The analysis time was 6 min under optimal conditions. The optimized and validated method was successfully implemented for quantifying D- and L-2-hydroxyglutaric aciduria in patients’ urine, without any pretreatment step. The linearity of the method was determined to be in the range of 2–100 mg/L for D- and L-2-hydroxyglutaric acid in urine. The precision (relative standard deviation%) was obtained at about 7%. For D- and L-2-hydroxyglutaric acids, the limits of detection were 0.567 and 0.497 mg/L, respectively.     

On the biological properties of alkynyl phosphine gold(i) complexes

Golden times for metal-based drugs? Alkynyl triphenylphosphine gold(I) complexes display interesting biological properties and show high potential for future drug development. They are strong inhibitors of the enzyme thioredoxin reductase, trigger antiproliferative effects in tumor cells, and influence tumor cell metabolism, mitochondrial respiration, and angiogenesis in zebrafish embryos.