Edge-reconstruction of planar graphs with minimum valency 5

The object of this paper is to show tht every planar graph of minimum valency 5 is reconstructible from its family of edge-deleted subgraphs.     

Averaging over N-dimensional balls and Cauchy problem for equations of mathematical physics

In this paper, we deal with averaging over balls in E_N and derive an equality describing a relation between scale and space dependence of the average function. We also show connections with equations of mathematical physics.     

Comparison of monomode and multimode microwave equipment in Suzuki-Miyaura reactions—en route to high throughput parallel synthesis under microwave conditions

The microwave heated Suzuki-Miyaura cross-coupling reaction of boronic acids, boronic esters and organotrifluoroborates served as a model reaction in a singlemode equipment. The reaction conditions were optimized with respect to temperature and reaction time and were transferred to multimode equipment which is well suited for multiparallel synthesis in a larger scale. The source of the Pd species chosen included immobilized Pd complexes and Pd particles. In fact the increased time to reach the required reaction time in multimode chambers suitable for 48 parallel reactions has to be taken into account. The nature of the boronic acid has no impact on the efficiency of the catalytic process. However, heterogenized Pd species perform less well in multimode chambers with larger vial volumes, which we ascribe to diffusion phenomena.     

Pyridine ligand rotation in self-assembled trigonal prisms. Evidence for intracage solvent vapor bubbles

The rate of interconversion of the two inequivalent edges of the pyridine rings in the trigonal prism 3c, self-assembled from 3 equiv of the star connector, tetrakis[4-(4-pyridylethynyl)phenyl]cyclobutadienecyclopentadienylcobalt, and 6 equiv of a platinum linker, cis-(Me3P)2Pt(2+) 2 TfO(-), was determined by DNMR in nitromethane. It exhibits a highly unusual bilinear Eyring plot. In the low temperature regime, the activation enthalpy DeltaH(double dagger) is approximately 12 kcal/mol and an activation entropy DeltaS(double dagger) ranges from approximately -15 to approximately 0 cal/mol x K as a function of the nature and concentration of the anions present. The reaction is attributed to hindered rotation of the pyridine rings about the Pt-N bond, facilitated by a tight pairing with a counterion. Above a counterion-dependent limiting temperature, DeltaH(double dagger) and DeltaS(double dagger) change abruptly to approximately 35 kcal/mol and approximately 60 cal/mol x K, respectively. The changes largely compensate, such that the reactions have comparable rates in the two regimes, both amenable to DNMR measurement, but their mechanisms clearly differ. Several kinetic models for the involvement of ion pairing equilibria fit the observed data nearly equally well, and they all contain a reaction step with high DeltaH(double dagger) and DeltaS(double dagger) values in the high-temperature regime. Its mechanism is proposed to involve a counterion-assisted reversible dissociation of one or two adjacent Pt-N bonds, followed by nearly free rotation of the terminal pyridine ring or rings and subsequent bond reclosure, which is similar to the last presumed step in the initial prism assembly. An interpretation of the very high DeltaS(double dagger) value is suggested by molecular dynamics calculations: at equilibrium, there is a bubble of gaseous nitromethane solvent inside the prism, and it collapses when the prism opens as the transition state is reached. A simple calculation of the entropy of cavitation provides quantitative support for this tentative proposal. The presence of such voids might be generally important for the formation and properties of self-assembled cages.     

Cytocompatibility of surface ground PE doped with calcium salt of 6-carboxycellulose

We studied the physical–chemical properties of polyethylene (PE) films doped with calcium salt of 6-carboxycellulose (Ca-oxy) in concentrations 0–20 wt.% and their interactions with cells. The interaction between the PE/Ca-oxy composite film and 3T3 cells has not been described so far. Modification by surface grinding to enhance material cytocompatibility was studied. The surface wettability of doped films was tested by contact angle measurements and the surface morphology by SEM microscopy and profilometry. Adhesion and proliferation of tissue cells (3T3 mouse fibroblasts) were studied in vitro on pristine and ground doped PE films. The ground samples have a higher contact angle values and the number of proliferated cells is greater on the ground samples than on pristine ones. The presence of Ca-oxy in PE film increases the adhesion of 3T3 cells on the doped substrate and on ground samples adhere more cells than on pristine ones.

The construction of good extensible rank-1 lattices

It has been shown by Hickernell and Niederreiter that there exist generating vectors for integration lattices which yield small integration errors for for all integers . This paper provides algorithms for the construction of generating vectors which are finitely extensible for for all integers . The proofs which show that our algorithms yield good extensible rank-1 lattices are based on a sieve principle. Particularly fast algorithms are obtained by using the fast component-by-component construction of Nuyens and Cools. Analogous results are presented for generating vectors with small weighted star discrepancy.

     

The gas-phase structure of 1-selena-closo-dodecaborane(11), 1-SeB11H11, determined by the concerted use of electron diffraction and computational methods

The molecular structure of 1-selena-closo-dodecaborane(11), 1-SeB11H11, has been determined by the concerted use of quantum chemical calculations and gas-phase electron diffraction. The structure has C(5v) symmetry and is distorted from a regular icosahedron mainly through the expansion of the pentagon of boron atoms adjacent to selenium, with r(a3,1)(B-B) = 192.2(2) pm. The Se-B bond length is extremely well determined [r(a3,1) (Se-B) = 212.9(2) pm] and this is reflected by a pronounced peak in the radial-distribution curve. The accuracy of the experimental structure, as well as that calculated at the MP2/962(d) level, has been gauged by comparison of the 11B chemical shifts (calculated at two different gauge-including atomic orbitals (GIAO) levels) with experimental NMR values. The inclusion of electron correlation in the magnetic property calculations (GIAO-MP2) gave superior results to those carried out using GIAO-Hartree-Fock.     

Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.