Half‐transitive graphs of valency 4 with prescribed attachment numbers

A graph X is said to be ½‐transitive if its automorphism group Aut X acts vertex‐ and edge‐, but not arc‐transitively on X. Then Aut X induces an orientation of the edges of X. If X has valency 4, then this orientation gives rise to so‐called alternating cycles, that is even length cycles in X whose every other vertex is the head and every other vertex is the tail of its two incident edges in the above orientation. All alternating cycles have the same length 2r(X), where r(X) is the radius of X, and any two adjacent alternating cycles intersect in the same number of vertices, called the attachment number a(X) of X. All known examples of ½‐transitive graphs have attachment number 1, r or 2r, where r is the radius of the graph. In this article, we construct ½‐transitive graphs with all other possible attachment numbers. The case of attachment number 2 is dealt with in more detail. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 89–99, 2000     

Biodegradability of sol–gel silica microparticles for drug delivery

The biodegradability of porous sol–gel silica microparticles in physiological buffers has been investigated using a USP4 flow-through dissolution tester. In the open configuration, which most closely models in-vivo conditions, the particles dissolved rapidly at pH 7.4, with a rate dependent on the surface area and media flow rate. In the closed configuration, the fastest dissolving 4 mg silica sample was almost completely dissolved in 100 mL of buffer after 36 h. The initial dissolution rates appeared relatively linear but dropped off as dissolved SiO₂ concentrations approached 20–25 ppm. Addition of serum proteins acted to slow dissolution by 20–30%, suggesting a slower degradation in vivo. Silica microparticles administered for controlled release drug delivery would therefore be expected to be eliminated relatively rapidly from the body, depending on the sample size and local fluid flow conditions.     

Embeddings of covering projections of graphs

It is shown that any given k-fold covering projection of graphs p: G₁ → G₂ can be embedded in a k-fold covering projection of closed orientable surfaces π: S₁ → S₂ in the sense that there are embeddings of G₁ in S₁ and G₂ in S₂ such that p is the restriction of π. In the case of a regular covering projection p, which is the quotient map with respect to some group action on G₁, it is shown that there is a regular covering projection π of surfaces in which p can be embedded.     

Dimethylmetall-tropolonate des galliums,indiums und zinns

The reaction of GaMe₃ and InMe₃ (Me = CH₃) with equimolar amounts of α-tropolone forms dimethylgallium tropolonate and dimethylindium tropolonate, respectively, in high yields. Both compounds are monomeric in solution, almost planar 7-/5-ring bicyclic structures of C_2v symmetry can be discussed. According to the X-ray structure determination of Me₂GaTrop (Trop = C₇H₅O₂) this compound is dimeric in the solid state and crystallizes in the monoclinic space group P2₁/c with 4 formula units (2 dimers) per unit cell. Me₂SnTrop₂ is formed by the interaction of Me₂SnCl₂ with LiTrop in a $\text{1}\text{2}$ molar ratio. This ditropolonate is monomeric not only in solution but also in the solid state. The compound crystallizes in the triclinic space group P$\text{1}$ (Z = 4), and the molecules have a cis-structure of approximate C₂-symmetry. The vibrational and NMR spectra of all compounds were measured and are partly assigned.     

Nanodiamonds in sugar rings: an experimental and theoretical investigation of cyclodextrin-nanodiamond inclusion complexes

We report on the noncovalent interactions of nanodiamond carboxylic acids derived from adamantane, diamantane, and triamantane with β- and γ-cyclodextrins. The water solubility of the nanodiamonds was increased by attaching an aromatic dicarboxylic acid via peptide coupling. Isothermal titration calorimetry experiments were performed to determine the thermodynamic parameters (K(a), ΔH, ΔG and ΔS) for the host-guest inclusion. The stoichiometry of the complexes is invariably 1:1. It was found that K(a), ΔG and ΔH of inclusion increase for larger nanodiamonds. ΔS is generally positive, in particular for the largest nanodiamonds. β-Cyclodextrin binds all nanodiamonds, γ-cyclodextrin clearly prefers the most bulky nanodiamonds. The interaction of 9-triamantane carboxylic acid shows one of the strongest complexation constants towards γ-cyclodextrin ever reported, K(a) = 5.0 × 10(5) M(-1). In order to gain some insight into the possible structural basis of these inclusion complexes we performed density functional calculations at the B97-D3/def2-TZVPP level of theory.     

Electronic structures of WAlO(y) and WAlO(y) (-) (y = 2-4) determined by anion photoelectron spectroscopy and density functional theory calculations

The anion photoelectron spectra of WAlO(y) (-) (y = 2-4) are presented and assigned based on results of density functional theory calculations. The WAlO(2) (-) and WAlO(3) (-) spectra are both broad, with partially resolved vibrational structure. In contrast, the WAlO(4) (-) spectrum features well-resolved vibrational structure with contributions from three modes. There is reasonable agreement between experiment and theory for all oxides, and calculations are in particular validated by the near perfect agreement between the WAlO(4) (-) photoelectron spectrum and a Franck-Condon simulation based on computationally determined spectroscopic parameters. The structures determined from this study suggest strong preferential W-O bond formation, and ionic bonding between Al(+) and WO(y) (-2) for all anions. Neutral species are similarly ionic, with WAlO(2) and WAlO(3) having electronic structure that suggests Al(+) ionically bound to WO(y) (-) and WAlO(4) being described as Al(+2) ionically bound to WO(4) (-2). The doubly-occupied 3sp hybrid orbital localized on the Al center is energetically situated between the bonding O-local molecular orbitals and the anti- or non-bonding W-local molecular orbitals. The structures determined in this study are very similar to structures recently determined for the analogous MoAlO(y) (-)∕MoAlO(y) cluster series, with subtle differences found in the electronic structures [S. E. Waller, J. E. Mann, E. Hossain, M. Troyer, and C. C. Jarrold, J. Chem. Phys. 137, 024302 (2012)].