Connectedness and Stability of Julia Sets of the Composition of Polynomials of the Form z2+cn

For a sequence (c_n) of complex numbers, the quadratic polynomialsf_cn(z) := z² + c_n and the sequence (F_n) of iterates F_n := f_cn...f_c1areconsidered. The Fatou set F_(cn) is by definition the set ofall z C^ such that (F_n) is normal in some neighbourhood ofz, while the complement of F_(cn) is called the Julia set J_(cn).The aim of this article is to study the connectedness and stabilityof the Julia set J_(cn) provided that the sequence (c_n) is bounded.     

Self-Orthogonal Compact Spreads and Unitals in Topological Translation Planes

A spread of is a set of l-dimensional subspaces L V partitioning V {0}. We construct examples of compact spreads that are identical with their sets of orthogonal spaces L . In the corresponding topological translation planes, every Euclidean sphere is a unital with the additional property that every point at infinity has flat feet.     

Einstein and Brans–Dicke Frames in Multidimensional Cosmology

Inhomogeneous multidimensional cosmological models with a higher-dimensional space-time manifold _{0 i=1} ⁿ M_i (n 1) are in stigated under dimensional reduction to a D ₀-dimensional effective non-minimally coupled -model which generalizes the familiar Brans–Dicke model. The general form of the Einstein frame representation of multidimensional solutions known in the Brans–Dicke frame is given with respect to cosmic synchronous time. As an example, the transformation is demonstrated explicitly for the generalized Kasner solutions where it is shown that solutions in the Einstein frame show no inflation of the external space although they can undergo deflation after the cosmic synchronous time inversion.     

High-performance AlGaAs-based VCSELs emitting in the 760 nm wavelength range

Vertical-cavity surface-emitting lasers (VCSELs) showing continuous-wave operation with emission wavelengths ranging between 717 and 790 nm have been fabricated. The samples are grown by solid source molecular beam epitaxy on GaAs substrates and are entirely based on the AlGaAs material system. A maximum single-mode output power of 2.0 mW is obtained at 754 nm wavelength by using the inverted surface relief technique.     

Sc Solid State NMR studies of the silicides ScTSi (T=Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt)

The silicides ScTSi (T=Fe, Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt) were synthesized by arc-melting and characterized by X-ray powder diffraction. The structures of ScCoSi, ScRuSi, ScPdSi, and ScIrSi were refined from single crystal diffractometer data. These silicides crystallize with the TiNiSi type, space group Pnma. No systematic influences of the ⁴⁵Sc isotropic magnetic shift and nuclear electric quadrupolar coupling parameters on various structural distortion parameters calculated from the crystal structure data can be detected. ⁴⁵Sc MAS-NMR data suggest systematic trends in the local electronic structure probed by the scandium atoms: both the electric field gradients and the isotropic magnetic shifts relative to a 0.2 M aqueous Sc(NO₃)₃ solution decrease with increasing valence electron concentration and within each T group the isotropic magnetic shift decreases monotonically with increasing atomic number. The ⁴⁵Sc nuclear electric quadrupolar coupling constants are generally well reproduced by quantum mechanical electric field gradient calculations using the WIEN2k code.     

New rare earth-rich aluminides and indides with cubic Gd4RhIn-type structure

Abstract  

The series of rare earth metal (RE)-rich intermetallics RE ₄ TAl and RE ₄ TIn (T = Ru, Rh, Ir) were synthesized by induction melting of the elements in sealed tantalum tubes. These compounds crystallize with the cubic Gd₄RhIn-type structure, space group F[`4]3mF\bar{4}3m. The structures of eight crystals (including the isotypic compounds Ce₄RuMg and Ce₄RuCd) have been refined from X-ray single-crystal diffractometer data. The structures are composed of condensed RE ₆ T trigonal prisms which form a rigid network with adamantane-like topology. Large cavities within these networks are filled with empty RE ₆ octahedra and Al₄, In₄, Mg₄, or Cd₄ tetrahedra, respectively. Some of the RE ₄ TAl and RE ₄ TIn show small homogeneity ranges that result from small degrees of Al/T and In/T mixing on the 16e sites. All cerium compounds show small anomalies in the plots of the cell volumes. This is confirmed by temperature-dependent magnetic susceptibility measurements. Ce₄RuMg, Ce₄RuCd, Ce₄RuAl, and Ce₄RuIn show intermediate cerium valence and no magnetic ordering down to 3 K. Ce₄RhAl shows essentially trivalent cerium.     

Multivalency as a Chemical Organization and Action Principle

Multivalent interactions can be applied universally for a targeted strengthening of an interaction between different interfaces or molecules. The binding partners form cooperative, multiple receptor–ligand interactions that are based on individually weak, noncovalent bonds and are thus generally reversible. Hence, multi‐ and polyvalent interactions play a decisive role in biological systems for recognition, adhesion, and signal processes. The scientific and practical realization of this principle will be demonstrated by the development of simple artificial and theoretical models, from natural systems to functional, application‐oriented systems. In a systematic review of scaffold architectures, the underlying effects and control options will be demonstrated, and suggestions will be given for designing effective multivalent binding systems, as well as for polyvalent therapeutics.