Growth morphology of zinc tris(thiourea) sulphate crystals

The growth morphology of crystals of zinc tris(thiourea) sulphate (ZTS) is investigated experimentally, and computed using the Hartman-Perdok approach. Attachment energies of the observed habit faces are calculated for determining their relative morphological importance. A computer code is developed for carrying out these calculations. A special procedure is adopted for computing the cohesive energy of a slice of the structure parallel to any rational crystallographic plane. For estimating the cohesive energies, formal charges on the experimentally determined atomic positions in the molecules of ZTS are calculated by ab initio molecular-orbital computations, with wave functions obtained by the Hartree-Fock procedure. Fairly good agreement with the observed crystal morphology is obtained for a model of growth mechanism in which ZTS is assumed to exist in solution sa szinc tris(thiourea) ions and sulphate ions.     

Relative wavefunctions, vertex functions and coupling constants for the virtual decay of 4He

The d + d, t + p and h + n relative wavefunctions and their asymptotic normalizations are considered in the framework of the generator coordinate method (GCM) and compared with ATMS (amalgamation of two-body correlation into multiple scattering processes) method which used the realistic Reid soft core interaction. The asymptotic normalization of relative wavefunctions provide various coupling constants, the cluster probability amplitude (the so-called Z ^1/2-factor) and matter RMS radii. These wavefunctions are also used to obtain ⁴He − d − d, ⁴He − t − p and ⁴He − h − n vertex functions in the virtual decay of ⁴He. The extrapolation of vertex functions for negative values of q ² upto the corresponding poles provide the vertex constants which are comparable with other estimates. It is noticed that in GCM the coupling constants C ² for ⁴He − d − d vertex is less than 2 as has been obtained in the forward dispersion relation technique.     

Exotic Bialgebra S03: Representations, Baxterisation and Applications

The exotic bialgebra S03, defined by a solution of the Yang–Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra s03_F is studied. The Baxterisation of the dual algebra is given in two different parametrizations. The finite-dimensional representations of s03_F are considered. Diagonalizations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model. Communicated by Petr Kulish Dedicated to our friend Daniel Arnaudon Submitted: January 30, 2006 Accepted: April 3, 2006     

Multiplet classification of the indecomposable highest weight modules over the Neveu-Schwarz and Ramond superalgebras

All multiplets of reducible (and indecomposable) highest weight modules (HWM) over the Neveu-Schwarz and Ramond superalgebras are classified and parametrized. The reducible HWM are given a simple explicit parametrization. The homogeneity degrees of all singular vectors of the reducible HWM are explicitly given.Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria     

On the Unitarity of <Emphasis Type="Italic">D</Emphasis> = 9, 10, 11 Conformal Supersymmetry

We consider the unitarity of D = 9, 10, 11 conformal supersymmetry using the recently established classification of the UIRs of the superalgebras osp(12n, ).     

On the relevance of some constructions of highest weight modules over (super-) Kac-Moody algebras (in connection with a paper by Wakimoto)

We correct and improve results of Wakimoto on the (ir)reducibility of his construction ofA ₁ ⁽¹⁾ highest weight modules (HWM). For a very large class of (super-) Kac-Moody algebras we argue that such a HWM is most relevant when it is isomorphic to a proper factor-module of the corresponding reducible Verma module with the same highest weight. In the same situation we present a general procedure to check the reducibility of the HWM in consideration.     

Formation of metal membranes by direct duplication of etched ion-track templates

A method for direct electrochemical metal duplication of pores in ion-track polymer membranes is described. It allows fabrication of metallic membranes using any metal, which is readily deposited by electroplating from aqueous solutions. The metal is deposited on one side of the template membrane, facing the anode, which is made conductive by a thin metal cladding layer. During electroplating, the lateral tapping of the pores is prevented by applying a counter-solution from the opposite non-metallized side of the plastic membrane, which increases dramatically the deposition overvoltage in the vicinity of the pore orifices. Such metallic membranes can be generated with pore diameters in the nano- and micrometer range and with densities from single pores up to 10⁶–10⁷ pores/cm². They can replace plastic filters in cases when an application of polymer material is not desirable. They could be advantageous particularly in catalysis as well as in biological science and technology. Further, they may be useful as apertures and collimators for different kinds of radiation. Received: 14 February 2002 / Accepted: 21 May 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +49-6159/712-179, E-mail: r.neumann@gsi.de     

Copper nanowires electrodeposited in etched single-ion track templates

The replication of single-ion track templates opens up the possibility of accessing electrical properties of nanowires without using lithographic techniques. Polycarbonate foils of 30-m thickness were irradiated with single swift heavy ions (e.g. Au 11.4 or Xe 8.3 MeV/nucleon). By controlled one-sided etching of the damage trail caused by the ion, templates containing a single conical pore were prepared. The narrow pore openings had diameters down to 25 nm and opening angles up to 2°. By electrochemical deposition of copper, single conical wires were obtained. The electric current recorded during electrodeposition reflects the geometry of the pore. The wires were provided with electrical contacts. Current–voltage measurements confirmed that their resistance was ohmic. The wires could withstand a maximum current density above 10⁸ A/cm². PACS 61.46.+w; 81.07.-b     

q-conformally covariant q-Minkowski space-time and invariant equations

We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original.     

A Weyl group for the Virasoro andN=1 super-Virasoro algebras

We introduce a Weyl group for the highest weight modules over the Virasoro algebra and the Neveu-Schwarz and Ramond superalgebras. Using this group we rewrite the character formulae for the irreducible highest weight modules over these algebras in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semi-simple Lie algebras (and also of the Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras). This is the same group we introduced recently in order to rewrite in a similar manner the characters of the singular highest weight modules over the affine Kac-Moody algebraA ₁ ⁽¹⁾ .