Adiabatic Theorems for Quantum Resonances

We study the adiabatic time evolution of quantum resonances over time scales which are small compared to the lifetime of the resonances. We consider three typical examples of resonances: The first one is that of shape resonances corresponding, for example, to the state of a quantum-mechanical particle in a potential well whose shape changes over time scales small compared to the escape time of the particle from the well. Our approach to studying the adiabatic evolution of shape resonances is based on a precise form of the time-energy uncertainty relation and the usual adiabatic theorem in quantum mechanics. The second example concerns resonances that appear as isolated complex eigenvalues of spectrally deformed Hamiltonians, such as those encountered in the N-body Stark effect. Our approach to study such resonances is based on the Balslev-Combes theory of dilatation-analytic Hamiltonians and an adiabatic theorem for nonnormal generators of time evolution. Our third example concerns resonances arising from eigenvalues embedded in the continuous spectrum when a perturbation is turned on, such as those encountered when a small system is coupled to an infinitely extended, dispersive medium. Our approach to this class of examples is based on an extension of adiabatic theorems without a spectral gap condition. We finally comment on resonance crossings, which can be studied using the last approach.     

Nonlinear differential equations with Caputo fractional derivatives in the class of monotonic functions

A fixed point theorem is established to prove the existence of a global solution to some fractional differential equations involving the Caputo derivatives under a, not necessarily small, growth condition on the nonlinearity.     

Preparation and characterizations of amorphous nanostructured SiC thin films by low energy pulsed laser deposition

Amorphous silicon carbide (SiC) thin films were deposited on silicon substrates by pulsed laser ablation at room temperature. Thicknesses and surface morphology of the thin films were characterized using optical profilers, atomic force and field emission scanning electron microscopy. Nanohardnes, modulus and scratch resistance properties were determined using XP nanoindenter. The results show that crack free, smooth and nanostructured thin films can be deposited using low laser energy densities.     

A test apparatus for measuring the biaxial strength of brittle materials

Experimental Techniques -     

Mossbauer, infrared and magnetic susceptibility studies of iron sodium borate glasses doped by sulphur

The affect of sulphur on the structural properties of iron sodium diborate glasses having the composition {(100−x)Na₂B₄O₇+xFe₂O₃}+yS, where x=0.05, 0.15 and 0.25 mol% and Y=0, 2.5 and 5 wt% was studied by infrared, Mossbauer spectroscopy and magnetic susceptibility measurements. It was found that, for samples having 5 mol% Fe₂O₃ and free from sulphur, the iron ions are present in both Fe²⁺ and Fe³⁺ states and also 92% of the total iron enters the glass network as a glass former. The ratio of Fe³⁺/Fe²⁺ increases with increasing the iron content for sulphur-free samples and others containing sulphur. This ratio also decreases with increasing the sulphur content. The magnetic susceptibility was found to decrease with increasing the sulphur content. Also, the increase of Fe₂O₃ content led to a less symmetrical environment of Fe³⁺ ions and vice versa for the Fe²⁺ environment.     

LC Simultaneous Determination of Thioctic Acid, Benfotiamine and Cyanocobalamin in Thiotacid Compound Capsules

A simple, selective, sensitive, precise, simultaneous liquid chromatographic analysis of capsules containing thioctic acid, benfotiamine and cyanocobalamin was described. Good chromatographic separation was achieved using a Zorbax C18 (4.6 cm × 250 mm, 5 μm) and a mobile phase consisting of acetonitrile–phosphate buffer pH 3.5 (15:85, v/v) at a flow rate of 0.9 mL min^?1. The ultraviolet detector was set a wavelength of 280 nm. Thioctic acid, benfotiamine and cyanocobalamin were eluted at 2.869, 3.752 and 13.689 min, respectively. The linear ranges for thioctic acid, benfotiamine and cyanocobalamin were 30–180, 4–24 and 0.025–0.150 μg mL^?1, respectively. The recoveries of thioctic acid, benfotiamine and cyanocobalamine in pharmaceutical preparation were all greater than 98% and their relative standard deviations were less than 2.0%. The limits of detection were 2.57, 0.19 and 0.003 μg mL^?1 for thioctic acid, benfotiamine and cyanocobalamin, respectively.     

First principles calculation of field emission from carbon nanotubes with nitrogen and boron doping

We investigate the field emission properties of nitrogenated and boronated carbon nanotubes using time-dependent density functional theory, where the wave function propagation is performed using the Crank–Nicholson algorithm. We extract the current–voltage characteristics of the emitted electrons from nanotubes with different doping configurations. We found that boron doping alone either impedes, or slightly enhances, field emission. Nitrogen generally enhances the emission current, and the current is sensitive to the location of the nitrogen dopant in the nanotube. Doping with both nitrogen and boron will generally enhance emission, and the closer the nitrogen dopant is to the tip, the higher is the emitted current. The emitted charge cloud from nitrogen-doped carbon nanotubes, however, diffuse more than that from pristine ones, our simulations show the emergence of a branching structure from the charge cloud, which suggests that nitrogenated carbon nanotubes are less convenient for use in precision beam applications.     

Synthesis and characterization of Mg-doped ZnO hollow spheres

Mg-doped ZnO nanoparticles were synthesized by a simple chemical method at low temperature with Mg:Zn atomic ratio from 0 to 7%. The synthesis process is based on the hydrolysis of zinc acetate dihydrate and magnesium acetate tetrahydrate were heated under refluxing at 65 °C using methanol as a solvent. X-ray diffraction analysis reveals that the Mg-doped ZnO crystallizes in a wurtzite structure with crystal size of 5–12 nm. These nanocrystals self-aggregated themselves into hollow spheres of size of 800–1100 nm. High resolution transmission electron microscopy images show that each sphere is made up of numerous nanoparticles of average diameter 5–11 nm. The XRD patterns, SEM and TEM micrographs of doping of Mg in ZnO confirmed the formation of hollow spheres indicating that the Mg²⁺ is successfully substituted into the ZnO host structure of the Zn²⁺ site. Furthermore, the UV–Vis spectra and photoluminescence (PL) spectra of the ZnO nanoparticles were also investigated. The band gap of the nanoparticles can be tuned in the range of 3.36–3.55 eV by the use of the dopants.