Band 5, Heft 3

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.

In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by $$G_\alpha = \frac{{2\Gamma \left( {\frac{\alpha }{2}} \right)}}{{\pi ^{\alpha /2 - 1} (\alpha - 2)}}G$$ , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.

The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thusthey were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.

In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.

With the aid of the macroscopic dielectric continuum and Loudon’s uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/Al0.15Ga0.85N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.

A model of Dark Matter is proposed where the Dark Matter is a classical color field. The color fields are invisible as they may interact with colored elementary particles like the ’t Hooft-Polyakov monopole only. Comparison with the Universal Rotation Curve is carried out.

In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the sine-cosine method. As a result, compactons, periodic, and singular periodic wave solutions are found.

We consider the mean spin direction (MSD) of superpositions of two spin coherent states (SCS) | ± μ〉, and superpositions of | μ〉 and | μ*〉 with a relative phase. We find that the azimuthal angle exhibits a π transition for both states when we vary the relative phase. The spin squeezing of the states, and the bosonic counterpart of the mean spin direction are also discussed.

The paper concerns the application of the fibre bundle approach to the description of the magnetic structures and their symmetry groups. Hence the explicit formulas describing both the variety of magnetic structures and their symmetry groups have been derived. The assumption was made that the bundle sections correspond to magnetizations of the separate crystal planes multiplied by a certain Gaussian factor defined in ℝ3, the last factor making the problem continuous and more physical.

One of the most important and promising materials from metal oxides is ZnO with specific properties for near UV emission and absorption optical devices. The properties of ZnO thin films strongly depend on the deposition method. Among them, pulsed laser deposition (PLD) plays an important role for preparing various kinds of ZnO films, e.g. doped, undoped, monocrystalline, and polycrystalline. Different approaches — ablation of sintered ZnO pellets or pure metallic Zn as target material are described. This contribution is comparing properties of ZnO thin films deposited from pure Zn target in oxygen atmosphere and those deposited from sintered ZnO target. There is a close connection between final thin film properties and PLD conditions. The surface properties of differently grown ZnO thin films are measured by secondary ion mass spectrometry (SIMS), atomic force microscopy (AFM) and scanning electron microscopy (SEM). Furthermore, different approaches — ablation of sintered ZnO pellet or pure metallic Zn as target materials are described. The main results characterize typical properties of ZnO films versus technological parameters are presented.

Superconducting Tl-based films were prepared on a LaAlO3 single crystal substrate. Spray pyrolysis of Ba, Ca and Cu nitrate solutions was used for deposition of the precursor films. They were subsequently ex-situ thallinated in flowing oxygen (open system). While the superconducting Tl-2212 phase formed at an annealing temperature of 880°C, thallination at 900°C led to the formation of a Tl-2223 /Tl-2212 mixture. The amount of Tl-2223 increased with prolonged thallination, whereas the Tl-2212 phase progressively disappeared. Films prepared in such a manner were c-oriented and contained only low amounts of non-superconducting impurities. The resulting samples were characterized by XRD and SEM and their T C values were determined by resistive four-point measurements. They showed critical temperatures in the range of T ON = 125–135 K, T C0 = 91–93 K. Differences between the composition and properties of the obtained films and those thallinated in closed systems under 50 kPa of oxygen are discussed in this paper. Results show that the Tl-2212 → Tl-2223 transformation proceeds at a slower rate under flowing oxygen than in a closed system.

Stability of organic materials properties is essential for further applications and was intensely investigated in last few decades. The aim of this study is to detect the structural changes of dipalmitoyl-phosphatidylcholine (DPPC) monolayer as a model system of organic material under influence of alcohols solutions. As subphases of monolayers (Langmuir films), pure water, ethanol and methanol solutions were used. For detection of changes in charge states of the molecules as well as relation with structural and conformational changes, a contactless method employing Maxwell’s displacement currents (MDC) was used. In DPPC monolayer on the subphase of methanol-water, a gradual absorption of methanol molecules into the layer can appear. In DPPC monolayer on the subphase of ethanol-water adsorption of ethanol molecules on the layer can be observed. Influence of alcohols results in a significant change of mechanical and electrical properties as well as in the stability of thin films.

The field of predictive rendering concerns itself with those methods of image synthesis which yield results that do not only look real, but are also radiometrically correct renditions of nature, i.e., which are accurate predictions of what a real scene would look like under given lighting conditions. A real coating consists of pigments, effect pigments, clear lacquer and glaze. A novel and unique combination of real parameters that are commonly measured in the industry and a theoretical reflectance model consisting of measurable parameters is required. Here, the authors design perception parameters and put them into well known surface reflection functions such as He and Torrance. The original contributions are the study of the sub-surface scattering of real paint and the prediction of its appearance in rendered images by the proposed model of light reflection beneath the paint surface.

In this paper we present the results of research into a relation(s) between the bias voltage of an oxide/a-Si:H/c-Si sample during formation of very-thin and thin oxides and the resulting distribution of oxide/semiconductor interface states in the a-Si:H band gap. Two oxygen plasma sources were used for the first time in our laboratories for formation of oxide layers on a-Si:H: i) inductively coupled plasma in connection with its application at plasma anodic oxidation; ii) rf plasma as the source of positive oxygen ions for the plasma immersion ion implantation process. The oxide growth on a-Si:H during plasma anodization is also simply described theoretically. Properties of plasmatic structures are compared to ones treated by chemical oxidation that uses 68 wt% nitric acid aqueous solutions. We have confirmed that three parameters of the oxide growth process — kinetic energy of interacting particles, UV-VIS-NIR light emitted by plasma sources, and bias of the samples — determine the distribution of defect states at both the oxide/a-Si:H interface and the volume of the a-Si:H layer, respectively. Additionally, a bias of the sample applied during the oxide growth process has a similar impact on the distribution of defect states as it can be observed during the bias-annealing of similar MOS structure outside of the plasma reactor.

Thin films of mercury based superconductors were prepared on the R-plane sapphire with a CeO2 buffer layer using a two step process involving the deposition of the Hg-free precursor and ex situ mercuration in the sealed quartz tube. For the thin film preparation, a method with no contact between the mercury source and the precursor film was used for mercuration. We studied the influence of the basic parameters of the mercuration (annealing time, temperature and partial pressure of the mercury) regarding the composition and superconducting properties of prepared Hg-based films to determine appropriate conditions for this mercuration method. We found out that an increased partial pressure of mercury inhibited the creation of the parasitic Re-based phase and supported the crystallization of the superconducting phase. The advantage of this mercuration method is higher reproducibility as well as its capability to prepare high quality thin large areas films.