Birefringence in YAlO3∶Ce between 2–5 eV

This contribution presents birefringence spectra for orthorhombic YAlO₃Ce single crystal in the region 2–5 eV. The spectra were measured by means of a reflection method of null ellipsometry and were compared with spectra of YAlO₃:Nd determined from values measured in the region of lower energies (1·1–2·2 eV). We have found that there are differences between the spectra of YAlO₃Nd and YAlO₃:Ce which are most pronounced in thea-axis direction.The author is most grateful to Ing. . Viovský CSc. for helpful discussions during the course of this work and to Monokrystaly Turnov for preparation of the samples.     

Energy independent number of clusters and multiplicity distribution at Collider and beyond

Multiplicity distributions up to the Collider energies could be described by various two-parameter compounded distributions having in common Poisson distributed number of clusters. Among them the logarithmic distribution for hadronization via decaying clusters leads to energyindependent number of clusters above the ISR energies, replacing the previous KNO-scaling.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

A comparison of the stochastic theory of the crystal growth and the Stefan problem

The stochastic theory of the crystal growth is compared with the solution of the Stefan problem in the case of Sn solidification. It is shown that the stochastic theory gives the same results as the solution of the Stefan problem if kinetic processes at the solidification front are very rapid.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

Problems and results on additive properties of general sequences,V

A very special case of one of the theorems of the authors states as follows: Let 1a ₁a ₂... be an infinite sequence of integers for which all the sumsa _i +a _j , 1ij, are distinct. Then there are infinitely many integersk for which 2k can be represented in the forma _i +a _j but 2k+1 cannot be represented in this form. Several unsolved problems are stated.Dedicated to our friend Professor E. Hlawka on the occasion of his seventieth birthday     

How large can a hereditarily separable or hereditarily Lindelöf space be?

The main result of this paper is that ifV satisfies GCH andω ₁<λ<μ are arbitrary regular cardinals, then in some cardinal preserving forcing extensionW ofV we have λ^<λ=λ=2 ^N 0,μ=2 ^λ and there are a hereditarily separableX ?2 ^λ with |X|= \(2^{\aleph _0 } \) =μ and a hereditarily LindelöfY ?2 ^μ withw(Y)= \(2^{2^\aleph 0} \) =μ. So far similar results have only been obtained under the assumption of CH.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Coloring of universal graphs

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH (G) _r ¹ . Answering a question of A. Hajnal we show that countably universal graphU ₃ satisfiesU ₃ (U₃) _r ¹ for every finiter.