Bulk GaN crystals grown by HVPE

We succeeded in preparing very thick c-plane bulk gallium nitride (GaN) crystals grown by hydride vapor phase epitaxy. Growth of the bulk GaN crystals was performed on templates with 3 μm GaN layer grown by metal organic chemical vapor deposition on (0 0 0 1) sapphire substrates. Colorless freestanding bulk GaN crystals were obtained through self-separation processes. The crystal's diameter and thickness were about 52 and 5.8 mm, respectively. No surface pits were observed within an area of 46 mm diameter of the bulk GaN crystal. The dislocation density decreased with growth direction (from N-face side to Ga-face side) and ranged from 5.1×10⁶ cm⁻² near the N-face surface to 1.2×10⁶ cm⁻² near the Ga-face. A major impurity was Si, and other impurities (O, C, Cl, H, Fe, Ni and Cr) were near or below the detection limits by SIMS measurements.     

On stability and robust stability of positive linear Volterra equations in Banach lattices

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.     

Dielectric relaxation and glass transition temperature of copolymers

Dielectric relaxation measurements were made on methyl methacrylate—styrene and methyl methacrylate–p-chlorostyrene copolymers at temperatures higher than the glass transition temperature T_g. It was found that the temperature dependence of the relaxation time can be described satisfactorily by an expression derived recently for chain motion in amorphous polymers. The temperature T_g obtained from the expression agrees well with that determined by differential thermal analysis.     

Active polycondensation of diethyl 2,3,4,5-tetrahydroxyadipate with diamines

Polycondensation of diethyl 2,3,4,5-tetrahydroxyadipate with various diamines was carried out in solutions under mild conditions. The polycondensation reaction occurred rapidly even at room temperature in polar solvents such as alcohols, and in aqueous solution a cyclic product was obtained instead of linear polymers although the reaction with diamines was completed within several minutes. Polymers obtained from diethyl 2,3,4,5-tetrahydroxyadipate were a linear polyamide having pendant hydroxyl groups, which decomposed on heating at around 200°C. A solid-phase polycondensation of the precursor polyamide yielded a high molecular weight polyamide.     

On structures of bisubmodular polyhedra

A bisubmodular polyhedron is defined in terms of a so-called bisubmodular function on a family of ordered pairs of disjoint subsets of a finite set. We examine the structures of bisubmodular polyhedra in terms of signed poset and exchangeability graph. We give a characterization of extreme points together with an O(n ²) algorithm for discerning whether a given point is an extreme point, wheren is the cardinality of the underlying set, and we assume a function evaluation oracle for the bisubmodular function. The algorithm also determines the signed posetructure associated with the given point if it is an extreme point. We reveal the adjacency relation of extreme points by means of the Hasse diagrams of the associated signed posets. Moreover, we investigate the connectivity and the decomposition of a bisubmodular system into its connected components.     

Spectral Based Estimation of Optical Path Difference of Interference Colors

A spectral intensity distribution of interference colors which is a function of optical path difference (OPD) is represented as a pattern vector on a subspace. A new algorithm to design a color scale on the subspace to estimate OPD values is proposed. In experiments, interference colors generated by a differential interference microscope (DIM) were examined. A subspace spanned by four orthogonal bases was constructed to make a color scale to determine OPD values in the range between 0 nm and 1000 nm. Estimated OPD values almost coincided with these expected. In an experiment on two-dimensional interference colors obtained by a spherical surface of a ballbearing observed by DIM, the resultant OPD distribution coincided well with that expected within a standard deviation of 12.8 nm.     

Any algebraic variety in positive characteristic admits a projective model with an inseparable Gauss map

We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic p. In particular, it is shown that any variety in p>0 has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if p=2.     

A faster capacity scaling algorithm for minimum cost submodular flow

We describe an O(n ⁴ hmin{logU,n ²logn}) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the Edmonds–Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter δ. Capacities are relaxed by attaching a complete directed graph with uniform arc capacity δ in each scaling phase. We then modify a feasible submodular flow by relaxing the submodular constraints, so that complementary slackness is satisfied. This creates discrepancies between the boundary of the flow and the base polyhedron of a relaxed submodular function. To reduce these discrepancies, we use a variant of the successive shortest path algorithm that augments flow along minimum cost paths of residual capacity at least δ. The shortest augmenting path subroutine we use is a variant of Dijkstra’s algorithm modified to handle exchange capacity arcs efficiently. The result is a weakly polynomial time algorithm whose running time is better than any existing submodular flow algorithm when U is small and C is big. We also show how to use maximum mean cuts to make the algorithm strongly polynomial. The resulting algorithm is the first capacity scaling algorithm to match the current best strongly polynomial bound for submodular flow. Received: August 6, 1999 / Accepted: July 2001?Published online October 2, 2001