Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Mössbauer, X-ray diffraction and magnetization studies of Fe–Mn–Al–Nb alloys prepared by high energy ball milling

Fe₆₀Mn₁₀Al₂₀Nb₁₀, (Fe₆₀Mn₁₀Al₃₀)₉₅Nb₅ and (Fe₆₀Mn₁₀Al₃₀)₉₀Nb₁₀ ball milled powdered alloys were investigated using X-ray diffraction, Mössbauer spectrometry, thermomagnetic (TGM) and magnetization measurements. We studied the influence of Nb content and of different milling times on the structural and magnetic properties. Two main features can be concluded: (1) the FeAlMn induces a BCC phase whatever the Nb content is, and (2) as both increasing Nb content and milling time give rise to an highly disordered state in conjunction with a decrease of the ferromagnetic behavior.