Bound-State Solutions of the Klein-Gordon Equation for the Generalized <Emphasis Type="Italic">PT</Emphasis>-Symmetric Hulthén Potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. PACS numbers: 03.65.Fd, 03.65.Ge     

Structural and Optical Properties of Zinc Nitride Films Prepared by Pulsed Filtered Cathodic Vacuum Arc Deposition

Polycrystalline zinc nitride films are deposited on Coming 7059 glass substrates by pulsed filtered cathodic vacuum arc deposition （PFCVAD）. The crystallographic structure is studied by means of x-ray diffraction. These measurements show that all the films are crystallized in the cubic structure, in a preferred orientation along the （332） and （631） directions. Weak XRD signal shows small crystallites distributed in an amorphous tissue. A small improvement of crystallinity is observed with annealing. Optical parameters such as absorption, energy band gap, Urbach tail, extinction coefficients have been determined. The Urbach tail energy is decreased with annealing at 500℃ for one hour. Energy band gap values are found to be increased by annealing.     

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov–Bohm potentials as special cases. The results are in exact agreement with other methods.     

Enantioselective synthesis of cyclic, quaternary oxonitriles

Quaternary oxonitriles are stereoselectively generated from the union of five-, six-, and seven-membered 2-chloroalkenecarbonitriles with chiral alcohols via a Claisen rearrangement. The strategy rests on a new conjugate addition-elimination of allylic alkoxides to 2-chlorocycloalkenecarbonitriles to afford substituted 2-alkoxyalkenenitriles. Subsequent thermolysis unmasks a cyclic oxonitrile while selectively forming a new quaternary center with enantiomeric ratios typically greater than 9:1. The overall alkylation strategy addresses the challenge of enantioselectively generating hindered, quaternary centers while simultaneously installing ketone, nitrile, and olefin functionalities.     

Novel and Stereospecific Synthesis of (2S)‐3‐(2,4,5‐Trifluorophenyl)propane‐1,2‐diol from D‐Mannitol

A stereospecific synthesis of (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol from D ‐mannitol has been developed. The reaction of 2,3‐O‐isopropylidene‐D ‐glyceraldehyde with 2,4,5‐trifluorophenylmagnesium bromide gave [(4R)‐2,2‐dimethyl‐1,3‐dioxolan‐4‐yl](2,4,5‐trifluorophenyl)methanol in 65% yield as a mixture of diastereoisomers (1 : 1). The Ph₃P catalyzed reaction of the latter with C₂Cl₆ followed by reduction with Pd/C‐catalyzed hydrogenation gave (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol with >99% ee and 65% yield.     

On Semi-Slant $${\varvec{\xi ^\perp }}$$-Riemannian Submersions

The aim of the present paper is to define and study semi-slant \(\xi ^\perp \)-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant \(\xi ^\perp \)-Riemannian submersions, semi-invariant \(\xi ^\perp \)-Riemannian submersions and slant Riemannian submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such submersions are mentioned.     

Dielectrophoretic assembly of grain-boundary-free 2D colloidal single crystals

Dielectrophoresis (DEP) force-assisted assembly of a colloidal single photonic-crystal monolayer in a microfluidic chamber was demonstrated. Negative DEP force with a high-frequency AC electric field induced the compression of colloidal microspheres to form a colloidal crystal domain at the center of a hexapolar-shaped electrode. While typical assembly by monotonic DEP force forms multicrystalline domains containing crystal defects, repetitions of the DEP/relaxation cycle significantly facilitated crystal growth of 10μm monodispersed polystyrene microspheres, allowing a grain-boundary-free single-crystal monolayer domain of ca. 200μm in size. Microsphere size as well as size distribution affected the formation of the single-crystal domain. A simple method was used to immobilize the single-crystal domain on the glass substrate without losing its crystallinity.     

Bound state energies for the exponential cosine screened Coulomb potential

The energy eigenvalues of bound states of an electron in the general exponential cosine screened Coulomb potential are obtained using the shifted 1/N expansion method. The energies for the states from 1s to 8k are calculated from six to eight significant figures. The energy eigenvalues for the 1s, 2s – 2p, 3s – 3d, and 4s – 4f states are also presented as a function of the screening parameter λ. Results are compared with the ones obtained by other workers. The agreement reduces roughly for large λ. It is also observed that the convergence of the expansion series increases remarkably asl increases.