The dominating number of a random cubic graph

We show that if G is a random 3-regular graph on n vertices, then its dominating number, D(G), almost surely satisfies .2636n ≤ D(G) ≤ .3126n. © 1995 John Wiley & Sons, Inc.     

Synthesis and structural characterization of a new heterobimetallic coordination complex of barium and cobalt for use as a precursor for chemical vapor deposition

Ba(dmae)2 (dmaeH=N,N-dimethylaminoethanol, C4H11NO) reacts with Co(acac)2 (acac=2,4-pentanedionate) to produce the trinuclear coordination complex [Ba2Co(acac)4(dmae)3(dmaeH)] in an 85% yield. Spectroscopic and single-crystal X-ray diffraction experiments indicate that the complex possesses a structure in which two barium atoms and a cobalt atom are bridged by acac and dmae groups. The barium centers are eight and nine coordinate with BaO7N and BaO7N2 coordination spheres while the cobalt is a more regular CoO5N octahedron. This 2:1 heterobimetallic molecular complex was investigated as precursor for the deposition of thin film by AACVD. The film was characterized by SEM and XRD. TGA shows that the complex starts thermal decomposition upon heating in nitrogen atmosphere at 105 degrees C to produce barium cobalt oxide material of a Ba2CoO3 composition with an orthorhombic structure. The synthetic approach detailed here represents a unique route to the formation of a heterobimetallic barium cobalt coordination complex.     

Differential expression of the skeletal muscle proteome in mdx mice at different ages

The mdx mouse is the most commonly used animal model for Duchenne muscular dystrophy (DMD), a disease caused by the absence of dystrophin. Although much has been done to elucidate the structure and function of dystrophin and the dystrophin-associated glycoprotein complex (DGC), little is known about the cascade of molecular events triggered by the absence of dystrophin that lead to muscle degeneration. To study the molecular basis of DMD, we decided to systematically study the skeletal muscle proteome in mdx mice at different ages. By using two-dimensional (2-D) gel electrophoresis, we defined changes in the protein expression pattern between mdx and control muscles. Approximately 46 differentially expressed proteins from the cytosolic fraction of mdx hindlimb muscles at three months of age were detected by 2-D gel analysis, of which 24 were identified by matrix assisted laser desorption/ionization- mass spectrometry. Most of the proteins fell into five groups of functionally related proteins. These functional categories are (i) metabolism and energy production, (ii) serine protease inhibitor family, (iii) growth and differentiation, (iv) calcium homeostasis, and (v) cytoskeletal reorganization and biogenesis. The potential roles of the differentially expressed proteins are discussed in the context of the mdx phenotype. Finally, we analyzed alterations of protein expression in mdx mice at one and six months of age to determine how protein expression changes with disease progression.     

Synthesis and structural characterization of tin(II) and zinc(II) derivatives of cyclic alpha-hydroxyketones, including the structures of Sn(maltol)(2), Sn(tropolone)(2), Zn(tropolone)(2), and Zn(hinokitiol)(2)

Zinc(II) and tin(II) derivatives of maltol (Hmalt), ethylmaltol (HEtmalt), tropolone (Htrop), hinokitiol (Hhino), and kojic acid (Hkoj) have been prepared and characterized, and the crystal structures of M(trop)(2) (M = Zn, Sn), Zn(hino)(2).EtOH, and Sn(malt)(2) have been determined. The Zn(trop)(2) is a polymeric structure in which tropolone has both a bridging and chelating role; zinc(hino)(2) crystallizes as an ethanol adduct of which the structure is a dimeric fragment of the Zn(trop)(2) polymer and in which each metal is "capped" by a molecule of alcohol. The tin complexes are notably air-stable despite adopting monomeric pseudo-trigonal-bipyramidal structures (SnO(4)E; E is a stereochemically active lone electron pair) in which the ligands only chelate a single metal center.     

Double photoionisation spectra of small molecules and a new empirical rule for double ionisation energies

Complete double photoelectron spectra are presented for 18 small molecules where the location of charges in the cations and dications is relatively clearly defined. The data demonstrate the importance of a coulombic repulsion contribution to the double ionisation energies. Examination of data for a wide range of molecules leads to a new empirical rule to calculate double ionisation energies from the molecules’ single ionisation energies and maximum dimensions. Where single and double ionisation energies are known the rule allows the deduction of plausible intercharge distances.     

Structural Characterization of the Condensation Polymer of Dipyridine Manganese II Dichloride with 1,3-Di-4-piperidy I propane

The synthesis of polymers derived from the condensation of dipyridine manganese II dichloride with 1,3-di-4-piperidylpro-pane is described. Structural analysis of the polyamines is detailed utilizing results based on infrared, thermal, elemental and solution analyses.     

Atmospheric pressure chemical vapour deposition of fluorine‐doped tin(IV) oxide from fluoroalkyltin precursors

Perfluoroalkytin compounds R_(4−n)Sn(R_f)_n (R = Me, Et, Bu, R_f = C₄F₉, n = 1; R = Bu, R_f = C₄F₉, n = 2, 3; R = Bu, R_f = C₆F₁₃, n = 1) have been synthesized, characterized by ¹H, ¹³C, ¹⁹F and ¹¹⁹Sn NMR, and evaluated as precursors for the atmospheric pressure chemical vapour deposition of fluorine‐doped SnO₂ thin films. All precursors were sufficiently volatile in the range 84–136 °C and glass substrate temperatures of ca 550 °C to yield high‐quality films with ca 0.79–2.02% fluorine incorporation, save for Bu₃SnC₆F₁₃, which incorporated <0.05% fluorine. Films were characterized by X‐ray diffraction, scanning electron microscopy, thickness, haze, emissivity, and sheet resistance. The fastest growth rates and highest quality films were obtained from Et₃SnC₄F₉. An electron diffraction study of Me₃SnC₄F₉ revealed four conformations, of which only the two of lowest abundance showed close F Sn contacts that could plausibly be associated with halogen transfer to tin, and in each case it was fluorine attached to either the γ‐ or δ‐carbon atoms of the R_f chain. Copyright © 2005 John Wiley & Sons, Ltd.     

A Ramsey‐type problem and the Turán numbers*

For each n and k, we examine bounds on the largest number m so that for any k‐coloring of the edges of K_n there exists a copy of K_m whose edges receive at most k?1 colors. We show that for , the largest value of m is asymptotically equal to the Turá number , while for any constant then the largest m is asymptotically larger than that Turá number. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 120–129, 2002     

A Bound on the Total Chromatic Number

. The proof is probabilistic. Received: November 26, 1996