Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.

Layer-by-layer multilayer films self-assembled from a rare-earth-containing poly-oxometalate Na-9[Eu(W5O18)(2)] and poly (allylamine hydrochloride) and their photoluminescent properties

Ultrathin multilayer films of a rare-earth-containing polyoxometalate Na-9[Eu(W5O18)(2)] (EW) and Poly (allyamine hydrochloride) (PAH) have been prepared by layer-by-layer self-assembly from dilute aqueous solutions. The fabrication process of the EW/PAH multilayer films was followed by UV-vis spectroscopy and ellipsometry, which show that the deposition process is linear and highly reproducible from layer to layer. An average EW/PAH bilayer thickness of ca. 2.1 nm was determine,by ellipsometry. In addition, the scanning electron microscopy (SEM) image of the EW/PAH film indicates that the film sufface is relatively uniform and smooth. The photoluminescent properties of these films were also investigated by fluoresence spectroscopy.

Photoluminescent organic-inorganic composite films layer-by-layer self-assembled from the rare-earth-containing polyoxometalate Na-9[EuW10O36] and poly(allylamine hydrochloride)

Photoluminescent organic-inorganic composite films incorporating the rare-earth-containing polyoxometalate Na-9[EuW10O36] (EW) and poly(allylamine hydrochloride) (PAH) have been prepared by the layer-by-layer self-assembly method. UV-vis spectroscopy and ellipsometry were used to follow the fabrication process of the EW/PAH composite films. The experimental results show that the deposition process is linear and highly reproducible from layer to layer. An average EW/PAH bilayer thickness of ca. 2.1 nm was determined by ellipsometry. In addition, scanning electron microscopy and atomic force microscopy images of the EW/PAH composite films indicate that the film surface is relatively uniform and smooth. The photoluminescent properties of these films were investigated by fluorescence spectroscopy.

Ultrafine polystyrene nanofibers prepared by electrospinning

Ultrafine polystyrene (PS) nanofibers were prepared via the simple electrospinning technique. Uniform and smooth PS nanofibers were obtained with adding the organic salt BTEAC into the PS solutions and adjusting the concentration of PS solutions. Without the addition of BTEAC, PS fibers with few beads could be achieved with a PS mass fraction of 20%, and the average diameter of the fibers was 280 nm. The addition of the organic salt BTEAC could lower the critical concentration for the fiber formation and reduce the amount of beads on the fibers. Unltrafine PS fibers without any beads were obtained with a PS mass fraction of 10% and an ionic salt mass fraction of 0.5%. The average diameter of the fiber was successfully reduced to 100 nm. The influence of the salt concentration on the morphology and diameter of the PS fibers was also investigated. The viscosity and surface tension changes were measured with changing the concentration of BTEAC. The results show that the changes were so small that these factors could be ignored. It was suggested that variations of the fiber diameter should be mainly resulted from the changes of conductivity and conformation of the polymer chain as the concentration of BTEAC is varied.

Ultra-wideline 14N solid-state NMR as a method for differentiating polymorphs: glycine as a case study

Nitrogen-14 solid-state NMR (SSNMR) is utilized to differentiate three polymorphic forms and a hydrochloride (HCl) salt of the amino acid glycine. Frequency-swept Wideband, Uniform Rate, Smooth Truncated (WURST) pulses were used in conjunction with Carr-Purcell Meiboom-Gill refocusing, in the form of the WURST-CPMG pulse sequence, for all spectral acquisitions. The ¹⁴N quadrupolar interaction is shown to be very sensitive to variations in the local electric field gradients (EFGs) about the ¹⁴N nucleus; hence, differentiation of the samples is accomplished through determination of the quadrupolar parameters CQ and ηQ, which are obtained from analytical simulations of the ¹⁴N SSNMR powder patterns of stationary samples (i.e., static NMR spectra). Additionally, differentiation of the polymorphs is also possible via the measurement of ¹⁴N effective transverse relaxation time constants, T^eff2(¹⁴N). Plane-wave density functional theory (DFT) calculations, which exploit the periodicity of crystal lattices, are utilized to confirm the experimentally determined quadrupolar parameters as well as to determine the orientation of the ¹⁴N EFG tensors in the molecular frames. Several signal-enhancement techniques are also discussed to help improve the sensitivity of the ¹⁴N SSNMR acquisition method, including the use of selective deuteration, the application of the BRoadband Adiabatic INversion Cross-Polarization (BRAIN-CP) technique, and the use of variable-temperature (VT) experiments. Finally, we examine several cases where ¹⁴N VT experiments employing Carr-Purcell-Meiboom-Gill (CPMG) refocusing are used to approximate the rotational energy barriers for RNH3⁺ groups.

Properties of DLC films deposited by an oxyacetylene flame

Diamond-like carbon (DLC) films were obtained by spinning a tungsten carbide substrate at a high speed using an oxyacetylene flame. The films deposited at a typical experimental condition of substrate temperature of 810 degrees C, rotation of 600 rpm and 3 h deposition time, exhibited an uniform, very smooth, hard and glassy surface covering the entire exposed face of the substrate. These films were identified as DLC by their characteristic broad Raman spectra centered at 1554 cm(-1) and micro-Vicker's hardness > 3400 kg mm(-2). For substrate temperatures < 800 degrees C the film started losing the uniform glassy surface and the hardness deteriorated. For temperatures > 950 degrees C the film was still hard and shiny, but black in color. DLC films were also obtained in a wide range of speeds of rotation (300-750 rpm), as long as the temperature remained close to 850 degrees C. (C) 1999 Elsevier B.V. S.A. All rights reserved.

Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Approximation of Lipschitz Mappings

2000 Mathematics Subject Classification: 46B03

MOVPE growth and characterization of Al(Ga)N and InAlN/AlGaN quantum wells for UV LED applications

The study of III-nitride materials (InN, GaN and AlN) gained huge research momentum after breakthroughs in the production light emitting diodes (LEDs) and laser diodes (LDs) over the past two decades. Last year, the Nobel Prize in Physics was awarded jointly to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura for inventing a new energy efficient and environmental friendly light source: blue light-emitting diode (LED) from III-nitride semiconductors in the early 1990s. Nowadays, III-nitride materials not only play an increasingly important role in the lighting technology, but also become prospective candidates in other areas, for example, the high frequency (RF) high electron mobility transistor (HEMT) and photovoltaics. These devices require the growth of high quality III-nitride films, which can be prepared using metal organic vapour phase epitaxy (MOVPE). The main aim of my thesis is to study and develop the growth of III-nitride films, including AlN, u-AlGaN, Si-doped AlGaN, and InAlN, serving as sample wafers for fabrication of ultraviolet (UV) LEDs, in order to replace the conventional bulky, expensive and environmentally harmful mercury lamp as new UV light sources. For application to UV LEDs, reducing the threading dislocation density (TDD) in AlN epilayers on sapphire substrates is a key parameter for achieving high-efficiency AlGaNbased UV emitters. In Chapter 4, after careful and systematic optimisation， a working set of conditions, the screw and edge type dislocation density in the AlN were reduced to around 2.2×108 cm-2 and 1.3×109 cm-2 , respectively, using an optimized three-step process, as estimated by TEM. An atomically smooth surface with an RMS roughness of around 0.3 nm achieved over 5×5 µm 2 AFM scale. Furthermore, the motion of the steps in a one dimension model has been proposed to describe surface morphology evolution, especially the step bunching feature found under non-optimal conditions. In Chapter 5, control of alloy composition and the maintenance of compositional uniformity across a growing epilayer surface were demonstrated for the development of u-AlGaN epilayers. Optimized conditions (i.e. a high growth temperature of 1245 °C) produced uniform and smooth film with a low RMS roughness of around 2 nm achieved in 20×20 µm 2 AFM scan. The dopant that is most commonly used to obtain n-type conductivity in AlxGa1-xN is Si. However, the incorporation of Si has been found to increase the strain relaxation and promote unintentional incorporation of other impurities (O and C) during Si-doped AlGaN growth. In Chapter 6, reducing edge-type TDs is observed to be an effective appoach to improve the electric and optical properties of Si-doped AlGaN epilayers. In addition, the maximum electron concentration of 1.3×1019 cm-3 and 6.4×1018 cm-3 were achieved in Si-doped Al0.48Ga0.52N and Al0.6Ga0.4N epilayers as measured using Hall effect. Finally, in Chapter 7, studies on the growth of InAlN/AlGaN multiple quantum well (MQW) structures were performed, and exposing InAlN QW to a higher temperature during the ramp to the growth temperature of AlGaN barrier (around 1100 °C) will suffer a significant indium (In) desorption. To overcome this issue, quasi-two-tempeature (Q2T) technique was applied to protect InAlN QW. After optimization, an intense UV emission from MQWs has been observed in the UV spectral range from 320 to 350 nm measured by room temperature photoluminescence.

Novel P(3HB) Composite Films Containing Bioactive Glass Nanoparticles for Wound Healing Applications

Bioactive glass (BG) is considered an ideal material for haemostasis as it releases Ca2+ ions upon hydration, which is required to support thrombosis. In this study the effect of the presence of the BG nanoparticles in P(3HB) microsphere films on the structural properties, thermal properties and biocompatibility of the films were studied. The nanoscaled bioactive glass with a high surface area was also tested for its in vitro haemostatic efficacy and was found to be able to successfully reduce the clot detection time. In an effort to study the effect of the roughness induced by the formation of HA on the cellular functions such as cell adhesion, cell mobility and cell differentiation, the composite films were immersed in SBF for a period of 1, 3 and 7 days. From the SEM images the surface of the P(3HB)/n-BG composite microsphere films appeared fairly uniform and smooth on day 1, however on day 3 and day 7 a rough and uneven surface was observed. The presence of HA on the composite microsphere films on day 3 and day 7 influenced the surface roughness of the films. However, when the P(3HB)/n-BG composite microspheres with enhanced surface roughness were tested for biocompatibility, reduced amount of protein adsorption and cell adhesion were observed. This study thus revealed that there is an optimal surface roughness for the P(3HB) microsphere films for increased cell adhesion, beyond which it could be deleterious for cell adhesion and differentiation.

Comment on "Another look at the uniform rope sliding over the edge of a smooth table"

Comment on "Another look at the uniform rope sliding over the edge of a smooth table"

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.