Band asymptotics of eigenvalues for the Zoll manifold

It is well known that the spectrum of the Laplace-Beltrami operator for a Zoll metric on the sphere consists of clusters of eigenvalues. This Letter considers the asymptotic band structure of these clusters and gives a explicit formula for it on the basis of the theory of Hamiltonian dynamical systems and symbol calculations of pseudodifferential operators.     

Improvement in quantitative correction in SIMS using Saha-Eggert equation

Summary Improvement in Quantitative Correction in SIMS Using Saha-Eggert Equation A quantitative conversion of the secondary-ion current intensities into the elemental concentrations using the Saha-Eggert ionization equation was tried with a 78Ni-18Cr-1Ti-1Fe-1Cu-1Zr (each in at %) alloy. Improvements were made on the best-fit search of fitting parameters (T andN _e). It proved to be important for the success in the conversion (1) to use the secondary-ion intensities from the sample in oxygen gas of >1.5×10^–3 Pa, (2) to add the molecularion intensities to those of mother atomic ions even when the former are small and (3) to search for the fitting parameters considering the relative errors of concentrations not only for the internal standards but for as many elements as possible. With these procedures the largest error of elemental concentration could be reduced to 22% (Ar⁺ bombardment), 31% (O₂ ⁺ bombardment) and 19% (N₂ ⁺bombardment).A part of this paper was presented at the 4th International Conference on Secondary Ion Mass Spectrometry, Osaka, November 1983.     

A simple and portable colorimeter using a red-green-blue light-emitting diode and its application to the on-site determination of nitrite and iron in river-water.

A portable colorimeter using a red-green-blue light-emitting diode as a light source has been developed. An embedded controller sequentially turns emitters on and off, and acquires the signals detected by two photo diodes synchronized with their blinking. The controller calculates the absorbance and displays it on a liquid-crystal display. The whole system, including a 006P dry cell, is contained in a 100 x 70 x 50 mm aluminum case and its mass is 280 g. This colorimeter was successfully applied to the on-site determination of nitrite and iron in river-water.     

Spanning Trees Crossing Few Barriers

We consider the problem of finding low-cost spanning trees for sets of $n$ points in the plane, where the cost of a spanning tree is defined as the total number of intersections of tree edges with a given set of $m$ barriers. We obtain the following results: (i) if the barriers are possibly intersecting line segments, then there is always a spanning tree of cost $O(\min(m^2,m\sqrt{n}))$; (ii) if the barriers are disjoint line segments, then there is always a spanning tree of cost $O(m)$; (iii) ] if the barriers are disjoint convex objects, then there is always a spanning tree of cost $O(n+m)$. All our bounds are worst-case optimal, up to multiplicative constants.     

Mössbauer study on Fe0.068Ni0.932Cl2 with competing spin anisotropies

Mössbauer measurements on Fe_0.068Ni_0.932Cl₂ were done at temperatures between 55K and 4.2K. We have found that below T_N-50K an observed spectrum is composed of two kinds of spectra and that the composition ratio changes gradually with temperature. The average angle of Fe²⁺ spins, \(\overline {\theta _{Fe} } \) , with the c-axis is smaller than \(\overline {\theta _c } \) by ?15° at each temperature below T_N, where \(\overline {\theta _c } \) is the average angle of total spins with the c-axis in this system obtained from the neutron scattering measurements. This is reasonably understood if we take into account that Fe²⁺ spins have the strong uniaxial anisotropy along the c-axis. We discuss the coexistence of the two kinds of spectra by considering the exchange energy of Fe²⁺ spins and the local magnetic anisotropy.     

Effect of alkali metal ions on photochromic behavior of bisviologen-incorporated oligo-oxyethylene units

Two bisviologen derivatives, 1,11-bis(N-propyl-4,4'-bipyridinium)-3,6,9-trioxaundecane tetrakis-(hexafluorophosphate) (1) and 1,8-bis(N-propyl-4,4'-bipyridinium)-3,6-dioxaoctane tetrakis-(hexafluorophosphate) (2), each incorporating trioxaundecane and dioxaoctane groups between two viologen units, respectively, were prepared so that their photochromic behavior in the absence and the presence of alkali metal ions in a thin polymer film could be investigated. Photoirradiation of the films containing 1 and 2 caused color changes from pale yellow to blue, associated with the photoinduced reduction of the viologen units from the dication to the radical cation. The addition of alkali metal ions, especially, K+ and Na+, caused change in the spectra of the photoreduced viologen radical cation for 1 and 2, respectively, because of the increase in the fractional amplitude for the dimer component of the radical cation rather than the monomer one. This may be related to the guest-induced conformational change of 1 and 2, in which the alkali metal ion is surrounded by the oligo-oxyethylene unit of 1 and 2. The regulation in photochromic properties of viologen derivatives can be achieved by addition of alkali metal ions.     

Electrical conductivities of potassium ferrites doped with divalent metal oxide

The electronic and ionic conduction in three kinds of potassium ferrites with β-alumina structure was studied. Undoped ferrite, K₂O·6Fe₂O₃, prepared by sintering at 1400°C after prefiring a mixture of potassium carbonate and ferric oxide, was a mixed conductor with about 1% ionic conduction and predominantly electronic conduction. The nickel- or zinc-doped potassium ferrite showed decreasing conductivity in the range of a single phase as the content of dopant increased. Variations of the electronic conduction in the doped potassium ferrites were assigned to changes of ferrous ion concentration accompanied by structural changes in the spinel-like blocks. Potassium ion conductivities of the three sorts of samples were estimated from the total conductivities and the transport numbers obtained by dc-polarization technique and electrolysis method. The decreases of the ionic conductivities were explained by narrowing of the alkali-oxygen slot caused by doping.