Some properties of specially multiplicative functions

In this paper we study some of the properties of specially multiplicative functions, which are multiplicative functions satisfying the identity (1.2). We define the norm of a specially multiplicative function (see (2.5)) and study its properties. We give several Dirichlet series identities involving specially multiplicative functions and close with a generalization of the Busche-Ramanujan identity.     

A structural and theoretical investigation of equatorial cis and trans uranyl phosphinimine and uranyl phosphine oxide complexes UO2Cl2(Cy3PNH)2 and UO2Cl2(Cy3PO)2

Phosphinimine ligands (Cy3PNH) readily react with UO2Cl2(THF)3 (THF=tetrahydrofuran) to give UO2Cl2(Cy3PNH)2, which contains strong U-N interactions and exists as cis and trans isomers in the solid and solution state. Solution NMR experiments and computational analysis both support the trans form as the major isomer in solution, although the cis isomer becomes more stabilized with an increase in the dielectric constant of the solvent. Mayer bond orders, energy decomposition analysis, and examination of the molecular orbitals and total electron densities support a more covalent bonding interaction in the U-NHPCy3 bond compared with the analogous bond of the related U-OPCy3 compounds.     

Self assembly and optical properties of dendrimer nanocomposite multilayers

Ultrathin multilayers are important for electrical and optical devices, as well as for immunoassays, artificial organs, and for controlling surface properties. The construction of ultrathin multilayer films by electrostatic layer-by-layer deposition proved to be a popular and successful method to create films with a range of electrical, optical, and biological properties. Dendrimer nanocomposites (DNCs) form highly uniform hybrid (inorganic-organic) nanoparticles with controlled composition and architecture. In this work, the fabrication, characterization, and optical properties of ultrathin dendrimer/poly(styrene sulfonate) (PSS) and silver-DNC/PSS nanocomposite multilayers using layer-by-layer (LbL) electrostatic assembly techniques are described. UV-vis spectra of the multilayers were found to be a combination of electronic transitions of the surface plasmon peaks, and the regular frequency modulations attributable to the multilayered film structure. The modulations appeared as the consequence of the highly regular and non-intermixed multilayer growth as a function of the resulting structure. A simple model to explain the experimental data is presented. Use of DNCs in multilayers results in abrupt, flat, and uniform interfaces.     

Shear stress analysis in axially symmetric flow using the Padé approximation technique

This paper evaluates the shear stress on the surface of a circular cylinder in axially symmetric flow within the boundary layer. An extended solution is obtained by established techniques, e.g. asymptotic series or Pohlhausen method. A Padé approximation technique is applied to the extended solution obtained. The region of validity of the solution is extended and the results are then compared and examined against known approximate Pohlhausen and series solutions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cut Vertices and Degree One Vertices of Zero-Divisor Graphs

This article continues to examine cut vertices in the zero-divisor graphs of commutative rings with 1. The main result is that, with only seven known exceptions, the zero-divisor graph of a commutative ring has a cut vertex if and only if the graph has a degree one vertex. This naturally leads to an examination of the degree one vertices of zero-divisor graphs.     

Probing the local coordination environment and nuclearity of uranyl(VI) complexes in non-aqueous media by emission spectroscopy

We describe the synthesis, solid state and solution properties of two families of uranyl(VI) complexes that are ligated by neutral monodentate and anionic bidentate P=O, P=NH and As=O ligands bearing pendent phenyl chromophores. The uranyl(VI) ions in these complexes possess long-lived photoluminescent LMCT (3)Π(u) excited states, which can be exploited as a sensitive probe of electronic structure, bonding and aggregation behaviour in non-aqueous media. For a family of well defined complexes of given symmetry in trans-[UO(2)Cl(2)(L(2))] (L = Ph(3)PO (1), Ph(3)AsO (2) and Ph(3)PNH (3)), the emission spectral profiles in CH(2)Cl(2) are indicative of the strength of the donor atoms bound in the equatorial plane and the uranyl bond strength; the uranyl LMCT emission maxima are shifted to lower energy as the donor strength of L increases. The luminescence lifetimes in fluid solution mirror these observations (0.87-3.46 μs) and are particularly sensitive to vibrational and bimolecular deactivation. In a family of structurally well defined complexes of the related anion, tetraphenylimidodiphosphinate (TPIP), monometallic complexes, [UO(2)(TPIP)(thf)] (4), [UO(2)(TPIP)(Cy(3)PO)] 5), a bimetallic complex [UO(2)(TPIP)(2)](2) (6) and a previously known trimetallic complex, [UO(2)(TPIP)(2)](3) (7) can be isolated by variation of the synthetic procedure. Complex 7 differs from 6 as the central uranyl ion in 7 is orthogonally connected to the two peripheral ones via uranyl → uranium dative bonds. Each of these oligomers exhibits a characteristic optical fingerprint, where the emission maxima, the spectral shape and temporal decay profiles are unique for each structural form. Notably, excited state intermetallic quenching in the trimetallic complex 7 considerably reduces the luminescence lifetime with respect to the monometallic counterpart 5 (from 2.00 μs to 1.04 μs). This study demonstrates that time resolved and multi-parametric luminescence can be of value in ascertaining solution and structural forms of discrete uranyl(VI) complexes in non-aqueous solution.     

Reversible modulation of photoluminescence from conjugated polymer nanotubes by incorporation of photochromic spirooxazine molecules

A novel photo-switching system based on fluorescent polymer nanotubes incorporating spirooxazine molecules has been designed. Reversible photoluminescence modulation of up to 60% has been shown in individual nanotubes subjected to repeated photo-conversion cycles.