Length of Longest Cycles in a Graph Whose Relative Length is at Least Two

Let G be a graph. We denote p(G) and c(G) the order of a longest path and the order of a longest cycle of G, respectively. Let κ(G) be the connectivity of G, and let σ ₃(G) be the minimum degree sum of an independent set of three vertices in G. In this paper, we prove that if G is a 2-connected graph with p(G) ? c(G) ≥ 2, then either (i) c(G) ≥ σ ₃(G) ? 3 or (ii) κ(G)?=?2 and p(G) ≥ σ ₃(G) ? 1. This result implies several known results as corollaries and gives a new lower bound of the circumference.     

Quenching electron runaway in positive high-voltage-impulse discharges in air by laser filaments

Strong hard (ε>100 keV) x rays being observed from impulse atmospheric discharges with maximal voltages from U=0.5 to 0.9 MV just before the breakdown were completely stopped with the use of femtosecond-laser-filament plasma. Runaway electrons generating such x rays and being estimated to achieve their maximal energy, ε~U, near the positive electrode disappear if a laser filament plasma is ignited perpendicularly to the runaway near the positive electrode. A preheating mechanism for formation of the electron runaway in air is proposed.     

Measurement of two‐dimensional distribution of surface supersaturation over a sodium chlorate crystal surface using multidirectional interferometry

The two‐dimensional (2D) distributions of surface supersaturation of sodium chlorate crystals with and without solutal convection have been measured by means of a multidirectional interferometry (MDI) technique coupled with the principles of three‐dimensional (3D) computer tomography. When solutal convection was present over a top face, the supersaturation at the center of the face was depleted by a factor of >0.9 with reference to the value at the edges of the crystal. When the convection was suppressed using an upside‐down geometry, the depletion of supersaturation at the center of the face was much smaller, <0.4. Therefore, the supersaturation difference between the edges and the face center, which is responsible for the morphological stability due to volume diffusion for the solute, becomes less important compared to the effect of convection due to hydrodynamic reasons. This result should give us a key to solve why the crystal quality is sometimes better in convection‐free microgravity conditions because of improved stability of a crystal face caused by more homogeneous distribution of supersaturation over the crystal surface.     

Variationally determined electronic states for the theoretical analysis of intramolecular interaction. II. Qualitative nature of the P?O bond in phosphine oxides

We have developed a space‐restricted wave function (SRW) method for the analysis of various types of intramolecular interactions. In this study, we demonstrate the applicability of our SRW method to the analysis of the nature of the P? O bond in phosphine oxide (R₃PO), one of the hypervalent molecules. An interesting character of this bond has been extensively studied by focusing on the negative hyperconjugation of the O lone pair (n_O) with the R₃P group. We reinvestigated the nature of the bond in terms of a change in total energy to produce evidence for the validity of our method. The electronic states without the interaction involving three n_O orbitals (R₃P⁺?O^?) produced by the method were used as reference states in the assessment of the effects of this n_O–R₃P interaction. The result confirms that this interaction plays an essential role in the nature of the bond and occurs between the n_O orbitals and the P? R antibonding orbitals, in agreement with previous studies. A molecular orbital (MO)‐pair analysis technique shows that the n_O–R₃P interaction is decomposed into the negative hyperconjugation and the Pauli repulsion. Considering a reference state where the P? O bond is completely broken (R₃P²⁺···O^2?) at an interacting distance, P? O bond formation is attributed to one σ bond plus two 0.5 π bonds. This is equivalent to three banana bonds highly polarized to the O atom. Consequently, the SRW method suggested improved explanations of the nature of the P? O bond. © 2012 Wiley Periodicals, Inc.     

Reactivities of Dialkyl Dithiol Mesaconates in Radical Copolymerization with Styrene

Nine novel types of dialkyldithiol mesaconates (DRTM, M₁) were synthesized and copolymerized with styrene (Ma) in tetrahydro-furan at 60 °C in order to clarify the polymerization behavior of DRTM and the substituent effects on the copolymerization. From the results obtained, the monomer reactivity ratio r₁, r₂ and Q₁, e₁ values were determined. It was found that the relative reactivities l/r₂ of DRTM toward an attack by polystyryl radical were correlated only by the polar substituent constant σ? of the alkyl group in DRTM, but not by the steric substituent constant E, in Taft's equation: log (l/r₂) = σ?σ? + ΔE_s. It was also observed that the Q₁ and e₁ values for DRTM were correlated by Taft's σ? constant. The number-average molecular weights of the DRTM-ST copolymer were found to be between 5.0 × 10³ and 1.2 × 10⁴.     

Development of Layered Multiscale Porous Thin Films by Tuning Deposition Time and Molecular Weight of Polyelectrolytes

This work focuses on the design of porous polymeric films with nano‐ and micro‐sized pores existing in distinct zones. The porous thin films are fabricated by the post‐treatment of layer‐by‐layer assembled poly(allylamine hydrochloride) (PAH)/poly(acrylic acid) (PAA) multilayers. In order to improve the processing efficiency, the deposition time is shortened to ≈10 s. It is found that fine porous structures can be created even by significantly reducing the processing time. The effect of using polyelectrolytes with widely different molecular weights is also studied. The pore size is increased by using high molecular weight PAH, while high molecular weight PAA minimizes the pore size to nanometer scale. Having gained a precise control over the pore size, layered multiscale porous thin films are further built up with either a microsized porous zone on top of a nanosized porous zone or vice versa.

     

Catalytic Dehydrogenation of Ammonia Borane Mediated by a Pt(0)/Borane Frustrated Lewis Pair: Theoretical Design

A new efficient metal-based frustrated Lewis pair constructed by (P^tBu₃)₂Pt and B(C₆F₅)₃ was designed through density functional theory calculations for the catalytic dehydrogenation of ammonia borane (AB). The reaction was composed by the successive dehydrogenation of AB and H₂ liberation, which occurs through the cooperative functions of the Pt(0) center and the B(C₆F₅)₃ moiety. Two equivalents of H₂ were predicted to be liberated from each AB molecule. The generation of the second H2 is the rate-determining step, with a Gibbs energy barrier and reaction energy of 27.4 and 12.8 kcal/mol, respectively.