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.     

Photoluminescence properties of selectively grown InN microcrystals

We investigated the photoluminescence (PL) properties of regularly arranged N‐polar InN microcrystals with m ‐plane sidewall facets. We observed narrow PL emission at 0.678 eV with a linewidth of ～14 meV at 4 K and a clear band‐filling effect with increasing excitation power. We also observed a normal red shift of the PL peak energy as large as 51 meV (～150 nm) with increasing temperature from 4 to 300 K, similar to that observed for non‐degenerated semiconductors. The integrated PL intensity ratio I_300K/I_4K was measured to be 6.1%. These results indicate that InN microcrystals have a low residual carrier density and excellent optical properties without being adversely affected by surface electron accumulation, despite their relatively high surface area. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

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.     

Folding interactions in the scattering of soft heavy ions by light nuclei

Scattering of polarized ⁷Li by ¹²C and polarized ⁶Li by ¹⁶O at E_lab～20 MeV is studied by both cluster folding interactions and double folding ones, where projectile virtual excitation effects are included by the coupled-channel method. The results strongly depend on the choices of interactions and reaction mechanisms reflecting low Coulomb barrier effects.     

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.