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.     

Micromechanisms and Mechanics of Damage and Fracture in Thin Film/Substrate Systems

The purpose of this paper is to review the mechanisms and available theoretical methods for modeling the strength and failure of thin film/substrate systems     

Quantitative assessment of solid oxide electrochemical doping

Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al₂O₃ (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al₂O₃ and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi₂Sr₂CaCu₂O_y (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm⁻²). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm⁻²). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount.     

Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities alg-rk(W) ≤ flat-rk(G) ≤ rk(|W|₀). Here, alg-rk(W) is the maximal Z-rank of abelian subgroups of W, and rk(|W|₀) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|₀. We can prove these inequalities under weaker assumptions. We also show that for any integer n ≥ 1 there is a simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G) = n and which is not linear.     

Automated derivatization for on-line solid-phase extraction-gas chromatography; phenolic compounds

An automated system for derivaatization was coupled on-line with solid-phase extraction-gas-chromatography (SPE-GC). The system was optimized for the determination of phenol and chlorinated phenols in aqueous samples. The test analytes were acetylated with acetic anhydride; proper buffering of the sample was a critical factor. Next, the phenol acetates were enriched on a SPE cartridge and transferred to a GC; two appraoaches were studied. In the first approach, the derivatives were enriched on disposable C18 cartridges (ASPEC type) and desorbed with methylacetate. Aan aliquot of the final eluate was injected on-line the GC by means of a loop-type interface. In the second approach, trace enrichment was performed on 10 × 2 mm i.d. LC-type precolumn packed with polystyrenedivinylbenzene copolymer (PLRP-S) this precolumn was dried with a mitrogen purge and the phenol acetates were desorbed with ethyl acetate which was injectedon-line into the retention gap of the GC under partially concurrent solvent evaporation (PCSE) conditions. The Derivatization-SPE-GC system which was based on the loop-type interface has the advantage of simplicity and easy operation, the main drawback is the impossibility to determine phenol acetates which elute prior to trichlorophenol acetates. With the derivatization-SPE-GC approach using PCSE-based desorption, even the most volatile analyte of the test series, phenol acetate, can be determined successfully. The entire procedure, including the derivatization step, was fully automated and integrated in one set-up. The precision data for the integrated on-line derivatization-SP-FID system were fully satisfactory, with RSD values of 1–12 % at the 1 μg/1 level. When a sample volume of 2.2 ml was analyzed, The detection limits for the chlorinated phenol acetates were in the 0.1–0.3 μg/1 range.     

Non-negative Wigner functions in prime dimensions

According to a classical result due to Hudson, the Wigner function of a pure, continuous-variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [1]. For the case of systems of odd prime dimension, a different, greatly simplified method of proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods. PACS  03.65.Fd; 03.65.Sq; 03.67.-a