Numerical stability of fast cosine transforms

In this paper we consider the numerical stability of fast algorithms for discrete cosine transform (DCT) of type III and II, respectively. We show that various fast DCTs can possess a very different behaviour of numerical stability. By matrix factorizations we find that a complex fast DCT which is based mainly on a fast Fouier transform has a better numerical stability than a real fast DCT despite its larger arithmetical complexity. Numerical tests illustrate our theoretical results.     

Regularization in Sobolev Spaces with Fractional Order

We study the minimization of a quadratic functional where the Tichonov regularization term is an H ^s -norm with a fractional s > 0. Moreover, pointwise bounds for the unknown solution are given. A multilevel approach as an equivalent norm concept is introduced. We show higher regularity of the solution of the variational inequality. This regularity is used to show the existence of regular Lagrange multipliers in function space. The theory is illustrated by two applications: a Dirichlet boundary control problem and a parameter identification problem.     

Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of common fixed points of finite family of relatively quasi-nonexpansive mappings and set of common solutions of a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space is proved using the properties of generalized f-projection operator. Our results extend important recent results.     

Thed(7Li,p)8Li cross section nearE cm=0.61 MeV

The absolute cross sectionσ of thed(⁷Li,p)⁸Li reaction near theE _cm=0.61 MeV resonance has been measured using a⁷Li ion beam and a windowless gas target system filled with D₂ gas. The proton yield of the reaction and theβ-delayedα-activity of the residual nuclides⁸Li were observed both concurrently with the elastic scattering yield, relatingσ to the Rutherford scattering cross sectionσ _R. The resulting values,σ (fromp)=143.6±8.9 mb andσ (from⁸Li)=151±20 mb, lead to a weighted mean value ofσ=153±6 mb (x ²=2.26) including all available values andσ=146±5 mb (x ²=0.05) removing some values from the data set. The consequences for the expected flux of high-energy solar neutrinos are discussed.     

Nonlinear optical investigations of the dynamics of hydrogen interaction with silicon surfaces

Optical second-harmonic generation (SHG) from silicon surfaces may be resonantly enhanced by dangling-bond-derived surface states. The resulting high sensitivity to hydrogen adsorption combined with unique features of SHG as an optical probe has been exploited to study various kinetical and dynamical aspects of the adsorption system H₂/Si. Studies of surface diffusion of H/Si(111)7×7 and recombinative desorption of hydrogen from Si(111)7 × 7 and Si(100)2 × 1 revealed that the covalent nature of hydrogen bonding on silicon surfaces leads to high diffusion barriers and to desorption kinetics that strongly depend on the surface structure. Recently, dissociative adsorption of molecular hydrogen on Si(100)2×1 and Si(111)7×7 could be observed for the first time by heating the surfaces to temperatures between 550 K and 1050 K and monitoring the SH response during exposure to a high flux of H₂ or D₂. The measured initial sticking coefficients for a gas temperature of 300K range from 10^–9 to 10^–5 and strongly increase as a function of surface temperature. These results demonstrate that the lattice degrees of freedom may play a decisive role in the reaction dynamics on semiconductor surfaces.     

Laser-cooled and trapped atoms as a precision target for heavy ion beams

We report on the development of a novel precision target for atomic physics with heavy ion beams, which consists of extremely cold and well localized, laser-cooled lithium atoms in a magneto-optical trap. First experiments are in preparation to study the collisional losses from the trap caused by the ion beam. The experimental set-up and the laser system, using exclusively 670 nm diode lasers, are described.     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

Effect of implantation temperature on the blistering behavior of hydrogen implanted GaN

GaN epitaxial layers were implanted by 100 keV H⁺ ions at different implantation temperatures (LN₂, RT and 300 °C) with a fluence of 2.5×10¹⁷ cm^?2. The implanted samples were characterized using Nomarski optical microscopy, AFM, XRD, and TEM. Topographical investigations of the implanted surface revealed the formation of surface blistering in the as-implanted samples at 300 °C and after annealing at higher temperature for the implantation at LN₂ and RT. The physical dimensions of the surface blisters/craters were dependent on the implantation temperature. XRD showed the dependence of damage-induced stress on the implantation temperature with higher stress for the implantation at 300 °C. TEM investigations revealed the formation of a damage band in all the cases. The damage band was filled with large area microcracks for the implantation at 300 °C, which were responsible for the as-implanted surface blistering.     

Effect of γ irradiation on the heat capacity of Rb2ZnBr4 in the vicinity of phase transitions

Heat capacity of Rb₂ZnBr₄ as a function of γ irradiation dose has been measured within the 85–300 K range by the adiabatic calorimeter technique. It is shown that, as the irradiation dose increases, the heat capacity peak in the vicinity of the incommensurate-commensurate first-order phase transition (PT) decreases, and the transition temperature T _c increases. The heat capacity peak in the region of the second-order PT at T ₃=112 K does not depend on γ irradiation, both in magnitude and in position, just as the heat capacity throughout the remainder of the temperature range studied. Fiz. Tverd. Tela (St. Petersburg) 40, 1106–1108 (June 1998)     

Representations of the cyclically symmetric q-deformed algebra U q(so3)

An algebra homomorphism from the nonstandard q-deformed (cyclically symmetric) algebra U _q(so₃) to the extension Û _q(sl₂) of the Hopf algebra U _q(sl₂) is constructed. Not all irreducible representations (IR) of U _q(sl₂) can be extended to representations of Û _q(sl₂). Composing the homomorphism with irreducible representations of Û _q(sl₂) we obtain representations of U _q(so₃). Not all of these representations of U _q(so₃) are irreducible. Reducible representations of U _q(so₃) are decomposed into irreducible components. In this way we obtain all IR of U _q(so₃) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra so₃ when q 1.