Three-dimensional aromaticity in deltahedral boranes and carboranes

Methods derived from topology and graph theory indicate that the deltahedral boranes B _n H _n ^2– and the corresponding carboranes C₂B_n–2H _n (6 n 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to -bonding and -bonding, respectively, in planar polygonal two-dimensional hydrocarbons CinnH _n ^(n–6)+ (n=5/7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes and carboranes are the deltahedral (D _n ) topology based on the skeleton of the underlying deltahedron and the complete (K _n ) topology based on the corresponding complete graph. Analyses of the Hoffmann-Lipscomb LCAO extended Hückel computations, the Armstrong—Perkins—Stewart self-consistent molecular orbital computations, and SCF MOab initio GAUSSIAN-82 computations on B₆H₆ ^2– indicate that the approximation of the atomic orbitals by the sum of the molecular orbitals, as is typical in modernab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D _n ) topology than by complete (K _n ) topology.This work was presented at the Workshop The Modern Problems of Heteroorganic Chemistry sponsored by the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (May 8–13, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1353–1360, August, 1993.     

Optical Nanocomposite Planar Waveguides Doped with Rare-Earth and Noble Metal Elements

The present paper is focused on multilayer Er³⁺-doped silica-titania planar waveguides, co-doped with silver, which were prepared by spin-coating on silica glass, or buffered single crystal silicon substrates. The single layer thickness (0.4 m) and refractive index (1.60–1.63) were measured by spectroscopic ellipsometry at 715 nm. The thickness of the waveguides (measured by mechanical profilometry) was 1 m and their optical propagation losses were measured at different laser wavelengths (488 nm, 514 nm and 633 nm), exhibiting an approximately Rayleigh-like behavior. The thermal precipitation of silver nanocrystallites was achieved, both in air and under a controlled atmosphere (dry nitrogen) and these were characterized by visible absorption spectroscopy, which clearly showed the development of a plasmon absorption band near 415 nm, by X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM). The Er³⁺ metastable level lifetimes for the emission at ca. 1.54 m were found to be ca. 4–6 ms, for Er³⁺ concentrations varying between 0.2–2.0 mol% (or (0.4–4.4) × 10²⁰ ions/cm³), but no significant variation was observed with the Ag concentration added (up to 2.5 mol%).     

Sequential centrifugal layer chromatography (SCLC): A new technique for the isolation of natural compounds. Part 2: Comparative study on centrifugal layer chromatography (CLC) and SCLC for the separation of furocoumarin isomers

The new sequential centrifugal layer chromatography extends the possibilities for preparative separation of furocoumarin isomers. In the present work, isobergapten, pimpinellin, bergapten, isopimpinellin, and sphondin were isolated from a prepurified extract of Heracleum sphondylium roots using two different techniques, namely, centrifugal layer chromatography (CLC) and sequential centrifugal layer chromatography (SCLC). The former technique was carried out with four plates, whereas the latter method required only one plate, using the same mobile phase in each case. A further advantage of the SCLC method was that all completely separated compounds could be quickly and efficiently eluted in small volumes of mehtanol.     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

Hamiltonian graphs of given order and minimum algebraic connectivity

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs on n vertices.     

THE MAXIMAL SUBNEAR-RINGS OF THE NEAR-RING OF ZERO-PRESERVING FUNCTIONS ON A FINITE GROUP

In this article for a finite group G, we characterize the maximal subnear-rings of the full near-ring of all zero-preserving functions on G.     

Parameters Tied to Treewidth

Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This article surveys several graph parameters tied to treewidth, including separation number, tangle number, well‐linked number, and Cartesian tree product number. We review many results in the literature showing these parameters are tied to treewidth. In a number of cases we also improve known bounds, provide simpler proofs, and show that the inequalities presented are tight.