A very special nonexistence theorem for abelian difference sets

It is wellknown that the technique of character sums together with the tools of algebraic number theory is the adequate method for the study of difference sets in abelian groups, compare for instance Ott [5] or Turyn [6]. In this paper we use this method to prove a new non-existence theorem for certain difference sets in abelian groups of order rp^a rp^a , where r 1 2 r \neq 2 and p are distinct primes.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Evidence for complex magnetic order in U2Zn17: A μ+ SR studySR study

μ⁺ SR-measurements in transversally applied magnetic fields of 2000 G and 4000 G on heavy-electron single crystal U₂Zn₁₇ are presented. They reveal that at least two types of interstitial sites are occupied by the positive muons. One of these sites (1/3, 2/3, 5/6) could be identified via induced local dipolar fields which aboveT _N=9.7 K can exactly be derived from the magnetic susceptibility. The corresponding component of the μ⁺-signal exhibits a steplike decrease by about 40% atT _N which is caused by the onset of a very broad distribution of static internal magnetic fields (ΔB≈1000 G) with zero average. Such a field distribution is in distinct contrast to dipolar-field calculations performed for the simple antiferromagnetic structure deduced from neutron diffraction. The remaining 60% of the muons contributing to this component belowT _N are subject to a narrow static field distribution (ΔB≈1 G). The induced dipolar fields at the site (1/3, 2/3, 5/6) are temperature-independent belowT _N. A weak dipolar coupling to the U-moments renders similar observations for muons occupying the second type of interstitial impossible.     

Antiferromagnetism of type II in nonstoichiometric YbP

A polycrystalline smaple of nonstoichiometric ytterbium phosphide, YbP_0.84, was investigated by neutron scattering, Mössbauer spectroscopy and bulk magnetic measurements. Neutron diffraction experiments prove the existence of antiferromagnetic type II ordering belowT _N =0.64 K, in contrast to the observed antiferromagnetic type III ordering in the stoichiometric Kondo-like compounds YbN and YbAs. The temperature dependence of the average ordered magnetic moment per Yb³⁺ ion with saturation value _Yb = 1.03(7) _B is similar to that of YbN. Mössbauer experiments prove the magnetic phase transition to be first order with different regions in the sample having slightly different transition temperatures. By means of inelastic neutron scattering the crystal-field level scheme was established to be ₆ – ₈(19meV) – ₇(43meV).     

Untersuchungen an Alkylmetallalkoxiden der Elemente Aluminium,Gallium und Indium. III. Eigenschaften und Schwingungsspektren von Dialkylgallium- und Indiumalkoxiden

Studies on Alkyl Metal Alkoxides of Aluminium, Gallium, and Indium. III. Properties and Vibrational Spectra of Dialkylgallium- and Indium Alkoxides The preparation and the properties of dialkyl metal alkoxides R₂MOR′ (with R = CH₃, CD₃, C₂H₅; R′ = CH₃, CD₃ and M = Ga, In) are described. The vibrational data (IR and Raman) of the trimeric methyl derivatives point to puckered six-membered M₃O₃-ring systems.