On the spontaneous magnetization in the Ising model

The equality between the spontaneous magnetization and the long range order is established for the Ising model with nearest neighbour interactions for low and high temperatures. The proof is presented for the two-dimensional lattice but works also in higher dimensions. The result verifies that the valuem*=(1–(Sh)^–4)^1/8 of the spontaneous magnetization below the critical point calculated by Onsager and Yang is the true value, which has been a long standing open question.     

An yttrium Mξ source for ESCA

A new source for producing YMξ radiation in an ESCA spectrometer is described. The system makes use of continuous evaporation of yttrium on a rotating anode. It is demonstrated that this scheme allows YMξ-excited electron spectra to be recorded without gradual loss of resolution and intensity due to anode oxidation. Electron spectra of Ar, Hg and N₂ excited by YMξ radiation are studied. Relative photoelectric cross-sections of the 5d_{$\text{5}\text{2}$}, 5d_{$\text{5}\text{2}$} and 6s orbitals in Hg and the four valence orbitals in N₂ are measured. The valence electron shake-up spectrum of N₂ is discussed.     

Conditions for sulfite stabilization and determination by ion chromatography

The efficiencies of three groups of potential sulfite-stabilizing compounds were found to be in the order: carbonyls > alcohols = saccharides. A mole ratio of 1:1 between formaldehyde and sulfite was sufficient for stabilizing a sulfite solution for at least 72 h. The lower stabilizing efficiencies of the alcohols and saccharides examined could be compensated by using large excesses of these compounds. For example, if a 100-fold excess of glycerol over sulfite was used, the recovery of sulfite was 96% after 72 h compared with only 40% without addition of stabilizer. During separations by ion chromatography, almost no oxidation of the sample occurs provided the sample solution is directly injected into a deaerated eluent. For formaldehyde, the peak heights were found to depend on the molar ratio of the stabilizer to sulfite as well as on the concentration of sulfite. This effect was not found for the other stabilizers tested.     

The tensor polarization of 5Li (32−) in the reaction α + d → α + p + n

At the Hamburger Isochronous Cyclotron the formation of the particle unstable ground state of ${}^5\text{Li(}\text{3}\text{2}{}^{\mathrm{?}}$ has been investigated in the reaction α + d → α + p + n at E_α = 28.3 MeV. The neutrons were detected in two liquid scintillation counters, while a large Si (Li) detector was used to observe the α-particles. In a first analysis, the tensor polarization parameters of the five-nucleon system ⁵Li are determined from the experimental data. The results are in quite good agreement with theoretical predictions of Hackenbroich et al.     

Investigations of reactions involved in electrothermal atomic absorption procedures: Part 9. An atomization system with controlled atmosphere and temperature for the determination of volatile elements in complex matrices

A controlled temperature controlled atmosphere atomization system is described. The sample is placed on a tungsten wire provided with temperature-controlled heating. After thermal pretreatment of the sample the wire is inserted into a hot quartz tube and rapid vaporization is accomplished by separate electrothermal heating. The pyrolysis products formed are mixed with a gas buffer and are passed through two equilibrium zones. The residence time of the analyte in the system is of the order of seconds so that the probability of attaining a state close to equilibrium is high for high temperatures. A third zone is placed perpendicularly to the others and constitutes the atomic absorption measuring cell. The usefulness of the system is illustrated for the determination of lead, bismuth, cadmium and zinc. The system provides unique possibilities in controlling interference effects in complex matrices. Examples are given for lead in concentrated chloride and sulphate solutions. Good agreement between the experimental results and high-temperature equilibrium calculations was obtained for a large variation in the composition of the gas phase.     

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.