Maximal K3's and Hamiltonicity of 4‐connected claw‐free graphs

Let cl(G) denote Ryjá?ek's closure of a claw‐free graph G. In this article, we prove the following result. Let G be a 4‐connected claw‐free graph. Assume that G[N_G(T)] is cyclically 3‐connected if T is a maximal K₃ in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267–276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262–272]. © 2011 Wiley Periodicals, Inc. J Graph Theory     

The Cut Loci, Conjugate Loci and Poles in a Complete Riemannian Manifold

Let M be a complete Riemannian manifold. We first prove that there exist at least two geodesics connecting p and every point in M if the tangent cut locus of ${p \in M}$ is not empty and does not meet its tangent conjugate locus. It follows from this that if M admits a pole and ${p \in M}$ is not a pole, then the tangent conjugate and tangent cut loci of p have a point in common. Here we say that a point q in M is a pole if the exponential map from the tangent space T _q M at q onto M is a diffeomorphism. Using this result, we estimate the size of the set of all poles in M having a pole whose sectional curvature is pinched by those of two von Mangoldt surfaces of revolution, meaning that their Gaussian curvatures are monotone and nonincreasing with respect to the distances to their vertices.     

Helicity induction on a poly(phenylacetylene) bearing a phosphonate residue by chiral dendrons

A series of optically active dendrons with a primary amino group at the terminal were prepared from L - or D -glutamic acid, and their helicity induction abilities for a poly(phenylacetylene) bearing a phosphonate pendant were characterized with ultraviolet–visible and circular dichroism spectroscopy. The magnitude of the Cotton effects of the polymer induced by the dendrons significantly increased upon complexation with a higher generation dendron. The effect of the chirality of the glutamate residues (L and D ) on the helicity induction was also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4580–4586, 2004     

Every Graph Is an Integral Distance Graph in the Plane

We prove that every finite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.     

Statistics of Gaussian Speckles with Enhanced Fluctuations

Some first-order statistics of speckle fields obeying the complex Gaussian probability density are investigated with the special emphasis on a possibility for the speckle contrast to exceed unity. It is shown that such enhanced fluctuations of speckle fields are generated when the probability density of the complex amplitude is non-circular with the vanishing mean. This means that Gaussian speckles having the contrast of unity are not necessarily fully developed speckles. Some practical situations producing such enhanced fluctuations in speckle fields are discussed.     

Development and commercialization of ionic-type photosensitive polyimides

Toray's ionic-type photosensitive polyimide, “Photoneece”, is widely used as an interdielectric and as a protection layer for microelectronics, because of its properties, such as the removal of photoreactive groups at low temperature, excellent thermal, mechanical and electrical film properties and excellent adhesion to various substrates. Toray has developed a new type of “Photoneece”, UR-5100, which is a low-stress photosensitive polyimide. In addition to a low thermal expansion coefficient (25 ppm/°C), “Photoneece” UR-5100 also features high resolution with an aspect ratio of more than 2.0 in 40 μm imaged film, and excellent mechanical properties in the cured film such as high elongation (>20%) and tensile strength (>200 MPa), even after 60 hr heat treatment at 350°C. “Photoneece” UR-5100 can be applied in multichip modules (MCMs), hybrid circuits, ICs and LSIs. In this paper the characterization and processing of this “Photoneece” UR-5100 are described.     

Chemical stability and electroconductivity of 7,7,8,8-tetracyanoquinodimethane salts containing polycation polymers

The chemical and electrical stabilities of 7,7,8,8-tetracyanoquinodimethane (TCNQ) salts composed of neutral TCNQ (TCNQ^?), anion radicals of TCNQ(TCNQ^?·), and polycation polymers were studied by measuring their electronic spectra and resistivities (ρ). The results of spectral and chemical analyses confirmed that TCNQ^?· in TCNQ salts was decomposed to α,α-dicyano-p-toluoylcyanide (DTC^?) as the final product by the intermediate formation of TCNQ^? and p-phenylenediamalononitrile (H₂TCNQ) and that H₂O played an important part in the reaction. From these results it was concluded that TCNQ salts are decomposed by two reaction processes: The resistivity of TCNQ salts increases with the decomposition of TCNQ^?·. Studies on electroconductivity of TCNQ salts assume that the change in resistivity arises from the loss of unpaired electrons which become conduction carriers and also from the disintegration of the TCNQ^? and TCNQ^?· complex which forms the conduction path.     

Detection and amplification of chirality by helical polymers

A unique feature of synthetic helical polymers for the detection and amplification of chirality is briefly described in this article. In sharp contrast to host-guest and supramolecular systems that use small synthetic receptor molecules, chirality can be significantly amplified in a helical polymer, such as poly(phenylacetylene)s with functional pendants, which enable the detection of a tiny imbalance in biologically important chiral molecules through a noncovalent bonding interaction with high cooperativity. The rational design of polymeric receptors can be possible by using chromophoric helical polymers combined with functional groups as the pendants, which target particular chiral guest molecules for developing a highly efficient chirality-sensing system. The chirality sensing of other small molecular and supramolecular systems is also briefly described for comparison.     

Reaction of a diphosphene with various halogens

Bis(2,4,6-tri-$\text{tert}$-butylphenyl) diphosphene reacts with various halogens to give the corresponding phosphoric dihalides, haloarene, and arene depending upon the halogen and solvent used.     

Aerobic ruthenium-catalyzed oxidative cyanation of tertiary amines with sodium cyanide

RuCl3-catalyzed oxidative cyanation of tertiary amines with sodium cyanide under molecular oxygen (1 atm) at 60 degrees C gives the corresponding alpha-aminonitriles, which are versatile synthetic intermediates of various compounds such as amino acids and unsymmetrical 1,2-diamines, in excellent yields. This reaction is clean and should be an environmentally benign and useful process.