On a generalization of distance sets

A subset X in the d-dimensional Euclidean space is called a k-distance set if there are exactly k distinct distances between two distinct points in X and a subset X is called a locally k-distance set if for any point x in X, there are at most k distinct distances between x and other points in X.Delsarte, Goethals, and Seidel gave the Fisher type upper bound for the cardinalities of k-distance sets on a sphere in 1977. In the same way, we are able to give the same bound for locally k-distance sets on a sphere. In the first part of this paper, we prove that if X is a locally k-distance set attaining the Fisher type upper bound, then determining a weight function w, (X,w) is a tight weighted spherical 2k-design. This result implies that locally k-distance sets attaining the Fisher type upper bound are k-distance sets. In the second part, we give a new absolute bound for the cardinalities of k-distance sets on a sphere. This upper bound is useful for k-distance sets for which the linear programming bound is not applicable. In the third part, we discuss about locally two-distance sets in Euclidean spaces. We give an upper bound for the cardinalities of locally two-distance sets in Euclidean spaces. Moreover, we prove that the existence of a spherical two-distance set in (d−1)-space which attains the Fisher type upper bound is equivalent to the existence of a locally two-distance set but not a two-distance set in d-space with more than d(d+1)/2 points. We also classify optimal (largest possible) locally two-distance sets for dimensions less than eight. In addition, we determine the maximum cardinalities of locally two-distance sets on a sphere for dimensions less than forty.     

Metric packing for K 3+K 3

In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K ₃+K ₃, which is dual to the multiflow feasibility problem for the commodity graph K ₃+K ₃. We prove a strengthening of Karzanov’s conjecture concerning quarterintegral packings by certain bipartite metrics.     

Glass-forming Photoconductive Organic Compounds II1: Glass-forming Properties of 1,3,5-Triaryl-2-pyrazolines

Glass-forming properties of 2-pyrazoline derivatives were examined and discussed in terms of the molecular structure. The results show that the molecular shape of 1,3,5-triaryl-2-pyrazolines is responsible for the glass-forming properties of these compounds. Glass transition points of several 1,3,5-triaryl-2-pyrazoline derivatives were measured.     

Hydrogen Intercalation in Potassium-C60

Abstract

Solid state ¹H NMR of (KH)₃C₆₀ was measured in the temperature range between ?80 and 60 °C. A doublet spectrum composed of main peak at ?7.0 ppm and shoulder peak at ～0 ppm was observed at room temperature. The negative chemical shift of the main peak indicates that hydrogen in (KH)₃C₆₀ exists as a hydride-like ion. The 60 °C spectrum became singlet at ?5.8 ppm due to motional narrowing.     

EXAFS and XANES Studies on 3d Transition Metal Intercalation Compounds M x TiS2

Abstract

EXAFS and XANES spectra of Ti K-edge have been measured for 3d transition metal intercalation compounds M _x TiS₂ (M = Mn, Fe, Co and Ni; x ≤ 0.33). We have found that the interatomic distance between Ti and the first nearest neighbor S atoms, R(Ti-S), increases with the guest concentration x. The variation in XANES spectra with x reveals the reduction of the valence state of Ti atoms upon intercalation of M. From these results as well as the M K-edge EXAFS data studied previously, we have proposed a simple model on the local structure of M _x TiS₂ to reproduce the observed values of R(Ti-S) by averaging local shift of S atoms caused by intercalation.     

Effects of pressure and temperature on the solubility of monosodium L-glutamate monohydrate in water

Abstract

The solubility of monosodium L-glutamate monohydrate (MSG.H₂O) in water was measured at pressures in the range of 0.10-300MPa and 298.15K. The density of MSG solution at high concentrations and heat of solution at saturated concentration were also measured at atmospheric pressure. The solubility, m_s, increased with increasing pressure and the pressure coefficient, Θ_p, [?(? In m_s,? p)_T] at 0.10 MPa was (2.0 ± 0.1) × 10-¹⁰Pa-1. It agrees well with (2.1 ±0.2)× 10-¹⁰ Pa-¹ thermodynamically estimated using the partial molar volume, the activity coefficient of the solute in solution, and the molar volume of the crystal. The excellent agreement at 0.10MPa gives us confidence in the solubility data at higher pressures. The heat of solution data and other pertinent values were used to calculate the temperature coefficient of solubility, Θ_T [? (? In m_s/?(1/T))_p], by a thermodynamic equality. The resulting Θ_T compares well with the data directly measured by Ogawa.     

Energy loss of 1000 keV electrons in thin silicon crystals as measured by high voltage electron microscopy

Abstract

Energy loss spectra of 1000 keV electrons transmitted by [111]-: riented thin silicon crystals were observed by an energy analyzer attached to the HVEM. The crystals were set to the systematic 220 Bragg reflection. Measurements were made for crystal thickness ranging from 1000 to 10,000 Å, which were determined by observations of pendellösung fringes.

Results were analyzed with Landau's transport equation, giving the : onclusion that the loss probability, which is the reciprocal of the mean free path, is 0.52 ± 0.02 × 10^?3 A^?1 for plasmon excitation and 1.50 ± 0.02 × 10^?3 A^?1 for L-electron excitation.     

Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed

We study a curvature-dependent motion of plane curves in a two-dimensional infinite cylinder with spatially undulating boundary. The law of motion is given by V=κ+A$V=\kappa +A$, where V is the normal velocity of the curve, κ is the curvature, and A is a positive constant. The boundary undulation is assumed to be almost periodic, or, more generally, recurrent in a certain sense. We first introduce the definition of recurrent traveling waves and establish a necessary and sufficient condition for the existence of such traveling waves. We then show that the traveling wave is asymptotically stable if it exists. Next we show that a regular traveling wave has a well-defined average speed if the boundary shape is strictly ergodic. Finally we study what we call “virtual pinning”, which means that the traveling wave propagates over the entire cylinder with zero average speed. Such a peculiar situation can occur only in non-periodic environments and never occurs if the boundary undulation is periodic.