The NaDyBr4 complex; its molecular structure and thermodynamic properties

The molecular geometry, vibrational frequencies, relative stabilities, and some thermodynamic properties of different isomers of the NaDyBr₄ complex were determined by computation. We investigated, to our knowledge for the first time for such a complex, the possible effect of the partially filled 4f orbitals on the molecular properties of an MLnX₄ complex by using a “small core” effective core potential of the Stuttgart group. The tridentate complex, with three Na–Br bridges, was found to be the ground-state structure with the bidentate one only about 4–6 kJ/mol higher in energy. The relative abundance of these isomers changes with temperature and at the high-temperature conditions of a metal halide lamp the bidentate isomer is the more abundant isomer.     

Summability of formal solutions to the n-dimensional inhomogeneous heat equation

The Cauchy problem for n-dimensional inhomogeneous complex heat equation is considered. The Borel summability of formal solutions is characterised in terms of analytic continuation with an appropriate growth condition of some function connected with the inhomogeneity and the Cauchy data.     

Studies on the Properties of ZnO Crystal Plane Grown by the Innovated Hydrothermal Method

ZnO single crystals were grown by the innovated hydrothermal method. The crystal surfaces were polished, and then studied by atom force microscope （AFM） and wet-chemical etching （WCE）. It was found that the Zn polar plane was smoother than O polar plane under the same polishing conditions. The etch pit density of Zn polar plane is 4.3×10^3 cm^-2, which is consistent with the previous report, while the density of etch pit of O polar plane is more than 103cm^-2. After annealing treatment, the density of etch pit of Zn plane reduces to 5.8×102 cm^2 and is superior to the current report. This investigation reveals that the high quality ZnO single crystals with fine Zn polar plane can be obtained by the innovated hydrothermal method.     

Vicinal and on-axis surfaces of 6H-SiC(0001) thin films observed by scanning tunneling microscopy

Surfaces of 6H-SiC(0001) homoepitaxial layers deposited on vicinal (3.5° off (0001) towards [11 0]) and on-axis 6H---SiC wafers by chemical vapour deposition have been investigated using ultra-high vacuum scanning tunneling microscopy. Undulating step configurations were observed on both the on-axis and the vicinal surfaces. The former surface possessed wider terraces than the latter. Step heights on both surfaces were 0.25 nm corresponding to single bilayers containing one Si and one C layer. After annealing at T>1100°C for 3–5 min in UHV, selected terraces contained honeycomb-like regions caused by the transformation to a graphitic surface as a result of Si sublimation. A model of the observed step configuration has been proposed based on the observation of the [ 110] or [1 10] orientations of the steps and energetic considerations. Additional deposition of very thin (2 nm) SiC films on the above samples by gas source molecular beam epitaxy was performed to observe the evolution of the surface structure. Step bunching and growth of 6H---SiC layers and formation of 3C---SiC islands were observed on the vicinal and the on-axis surfaces, respectively, and controlled by the diffusion lengths of the adatoms.     

Investigating the lateral motion of SiGe islands by selective chemical etching

SiGe islands grown by deposition of 10 monolayers of Ge on Si(0 0 1) at 740 °C were investigated by using a combination of selective wet chemical etching and atomic force microscopy. The used etchant, a solution consisting of ammonium hydroxide and hydrogen peroxide, shows a high selectivity of Ge over Si_xGe_1−x and is characterized by relatively slow etching rates for Si-rich alloys. By performing successive etching experiments on the same sample area, we are able to gain a deeper insight into the lateral displacement the islands undergo during post growth annealing.     

A complex semigroup approach to group algebras of infinite dimensional Lie groups

A host algebra of a topological group G is a C ^*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C ^*-algebra C ^*(S,α), and we describe a setting which permits us to conclude that this C ^*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative case is left for the future. To K.H. Hofmann on the occasion of his 75th birthday     

HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS

The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.     

Where do we stand on econophysics?

This issue contains papers selected from the contributions presented at the 5th International Conference on “Applications of Physics in Financial Analysis” (APFA5) held in Torino from June 29th to July 1st, 2006 (http://www.polito.it/apfa5). The issue collects recent applications of models and methods of statistical physics to economic problems. This interdisciplinary field of research, known as Econophysics, has seen intensive growth over the last decade. The challenge for econophysicists will be to go beyond the traditional views of economics and physics unifying the separate lines of development followed by the two disciplines over great part of the 20th century.“The conventional view serves to protect us from the painful job of thinking”, John Kenneth Galbraith (1908-2006).     

Geometrical and physical interpretation of evolution governed by general complex algebra

In this paper we explore a geometrical and physical matter of the evolution governed by the generator of General Complex Algebra, GC₂. The generator of this algebra obeys a quadratic polynomial equation. It is shown that the geometrical image of the GC₂-number is given by a straight line fixed by two given points on Euclidean plane. In this representation the straight line possesses the norm and the argument. The motion of the straight line conserving the norm of the line is described by evolution equation governed by the generator of the GC₂-algebra. This evolution is depicted on the Euclidean plane as rotational motion of the straight line around the semicircle to which this line is tangent. Physical interpretation is found within the framework of the relativistic dynamics where the quadratic polynomial is formed by mass-shell equation. In this way we come to a new representation for the momenta of the relativistic particle.