Pebbling numbers of some graphs

Chung defined a pebbling move on a graphG as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number of a connected graphG, f(G), is the leastn such that any distribution ofn pebbles onG allows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves. Graham conjectured that for any connected graphsG andH, f(G xH) ≤ f(G)f(H). In the present paper the pebbling numbers of the product of two fan graphs and the product of two wheel graphs are computed. As a corollary, Graham’s conjecture holds whenG andH are fan graphs or wheel graphs.     

Transformations of allylamine and N-allylacetamide on triosmium cluster complexes with hemilabile ligands

The cluster complexes (μ-H)Os₃(μ-OCR)(СО)₁₀ (R = Me (1); R = Ph (2)) catalyze the allylic rearrangement of N-allylacetamide at room temperature. Microwave irradiation greatly (by more than several thousand-fold) accelerates the reaction between the solution of 2 and allylacetamide. The interaction of cluster 2 with allylamine both at room and elevated temperatures results in cleavage of the C–N bond and coordination of the allylic fragment to one of the osmium atoms with the formation of Os₃(CO)₉(μ,η²-OC-Ph)(η³-C₃H₅) (4) cluster.     

Regioselective construction of polysubstituted phenols from Baylis-Hillman adducts via formal [4+2] annulation strategy

Polysubstituted phenol derivatives were synthesized regioselectively starting from the Baylis-Hillman adducts via the formal [4+2] annulation protocol as the key step.     

Hot electrical conductivity in lower hybrid current drive plasmas in the HT-7 tokamak

The interaction between the hot electrical conductivity and the residual electric field have been investigated in lower hybrid current drive (LHCD) experiments with non-zero loop voltage in the HT-7 tokamak. It has been found that the hot electrical conductivity contribute significantly to the current drive in partial non-inductively sustained plasmas. The hot electrical conductivities under different lower hybrid power levels and different parallel refractive indexes have been obtained. It is comparable to the Spitzer conductivity in high power LHCD experiments.     

Complete second order linear differential operator equations in Hilbert space and applications in hydrodynamics

We study the Cauchy problem for a complete second order linear differential operator equation in a Hilbert space of the form

Problems of this kind arise, e.g., in hydrodynamics where the coefficients , , and are unbounded selfadjoint operators. It is assumed that is the dominating operator in the Cauchy problem above, i.e.,

We also suppose that and are bounded from below, but the operator coefficients are not assumed to commute. The main results concern the existence of strong solutions to the stated Cauchy problem and applications of these results to the Cauchy problem associated with small motions of some hydrodynamical systems.

     

An efficient Galerkin averaging-incremental harmonic balance method for nonlinear dynamic analysis of rigid multibody systems governed by differential–algebraic equations

Nonlinear Dynamics - An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed for steady-state nonlinear dynamic analysis of index-3 differential algebraic...