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.     

The structures of German mathematics textbooks

From a socio-cultural perspective it is argued that the modality of artefacts has, structuring effects on the activities in which the artefact is involved. The mathematics textbook is an artefact that has a major influence on the activity of learning mathematics. Against this setting, the structures of the units in German mathematics textbooks for different grades and ability levels have been analysed. Firstly, the different structural elements have been examined with regard to: characteristics in terms of content; linguistic characteristics; visual characteristics; their pedagogical functions within the learning process; and situative conditions. Secondly, the orders of the structural elements within the units of the different textbooks have been compared. The findings reveal that the structure of the units is very similar in different mathematics textbooks. The units are not only composed of analogous structural elements, but these elements are also arranged in almost the same sequence. In order to develop a deeper understanding of these findings the structure of the units has been compared to the influential learning theories of J. F. Herbart and H. Roth. On this basis it is argued that the structure of the units seems to reflect the phases of idealised learning processes in general. The issue is raised if this is an appropriate structure in order to provide opportunities to learn mathematics.     

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.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

Cylindrical spike model for the formation of diamondlike thin films by ion deposition

T /n_S of n_T rearrangements and n_S atoms in the spike volume as the crucial parameter characterizing the ability of a given ion–target combination to achieve complete rearrangement of the spike volume. n_T/n_S>1 is the optimum condition for diamondlike film growth. For aC films the ion energy dependence of n_T/n_S agrees well with the measured sp³ bond fraction. For Ar⁺-ion-assisted deposition of aC we find n_T/n_S>1 above 50 eV with no pronounced ion energy dependence. Furthermore, our model predicts optimum conditions for the formation of cubic boron nitride between 50 eV and 3 keV. Accepted: 14 October 1997