Model Theory of Holomorphic Functions

This thesis is concerned with a conjecture of Zilber: that the complex field expanded with the exponential function should be `quasi-minimal'; that is, all its definable subsets should be countable or have countable complement. Our purpose is to study the geometry of this structure and other expansions by holomorphic functions of the complex field without having first to settle any number-theoretic problems, by treating all countable sets on an equal footing. We present axioms, modelled on those for a Zariski geometry, defining a non-first-order class of ``quasi-Zariski'' structures endowed with a dimension theory and a topology in which all countable sets are of dimension zero. We derive a quantifier elimination theorem, implying that members of the class are quasi-minimal. We look for analytic structures in this class. To an expansion of the complex field by entire holomorphic functions $\mathcal{R}$ we associate a sheaf $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ of analytic germs which is closed under application of the implicit function theorem. We prove that $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ is also closed under partial differentiation and that it admits Weierstrass preparation. The sheaf defines a subclass of the analytic sets which we call $\mathcal{R}$-analytic. We develop analytic geometry for this class proving a Nullstellensatz and other classical properties. We isolate a condition on the asymptotes of the varieties of certain functions in $\mathcal{R}$. If this condition is satisfied then the $\mathcal{R}$-analytic sets induce a quasi-Zariski structure under countable union. In the motivating case of the complex exponential we prove a low-dimensional case of the condition, towards the original conjecture

Two-gap superconductivity in single crystal Lu2_2Fe3_3Si5_5 from penetration depth measurements

Single crystal of Lu$_2$Fe$_3$Si$_5$ was studied with the tunnel-diode resonator technique in Meissner and mixed states. Temperature dependence of the superfluid density provides strong evidence for the two-gap superconductivity with almost equal contributions from each gap of magnitudes $\Delta_1/k_BT_c=1.86$ and $\Delta_1/k_BT_c=0.54$. In the vortex state, pinning strength shows unusually strong temperature dependence and is non-monotonic with the magnetic field (peak effect). The irreversibility line is sharply defined and is quite distant from the $H_{c2}(T)$, which hints on to enhanced vortex fluctuations in this two-gap system. Altogether our findings provide strong electromagnetic - measurements support to the two-gap superconductivity in Lu$_2$Fe$_3$Si$_5$ previously suggested from specific heat measurements

Dietary supplementation of essential oils in dairy cows: evidence for stimulatory effects on nutrient absorption

Results of recent in vitro experiments suggest that essential oils (EO) may not only influence ruminal fermentation but also modulate the absorption of cations like Na+, Ca2+ and NH4+ across ruminal epithelia of cattle and sheep through direct interaction with epithelial transport proteins, such as those of the transient receptor potential family. The aim of the current study was to examine this hypothesis by testing the effect of a blend of essential oils (BEO) on cation status and feed efficiency in lactating dairy cows. In the experiment, 72 dairy cows in mid-to-end lactation were divided into two groups of 36 animals each and fed the same mixed ration with or without addition of BEO in a 2×2 cross-over design. Feed intake, milk yield and composition, plasma and urine samples were monitored. Feeding BEO elevated milk yield, milk fat and protein yield as well as feed efficiency, whereas urea levels in plasma and milk decreased. In addition, plasma calcium levels increased significantly upon BEO supplementation, supporting the hypothesis that enhanced cation absorption might contribute to the beneficial effects of these EO

Enhanced quasiparticle heat conduction of the multigap superconductor Lu2Fe3Si5

The thermal transport measurements have been made on the Fe-based superconductor Lu2Fe3Si5 (Tc ~ 6 K) down to a very low temperature Tc/120. The field and temperature dependences of the thermal conductivity confirm the multigap superconductivity with fully opened gaps on the whole Fermi surfaces. In comparison to MgB2 as a typical example of the multigap superconductor in a p-electron system, Lu2Fe3Si5 reveals a remarkably enhanced quasiparticle heat conduction in the mixed state. The results can be interpreted as a consequence of the electronic correlations derived from Fe 3d-electrons.Comment: 5 pages, 4 figure

Correlations between spectra with different symmetry: any chance to be observed?

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular, because in semiclassics spectra of different symmetry are expressed in terms of the same set of periodic orbits. We reexamine this question and find absence of correlation in the universal regime. In the case of continuous symmetry the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time

TDC Chip and Readout Driver Developments for COMPASS and LHC-Experiments

A new TDC-chip is under development for the COMPASS experiment at CERN. The ASIC, which exploits the 0.6 micrometer CMOS sea-of-gate technology, will allow high resolution time measurements with digitization of 75 ps, and an unprecedented degree of flexibility accompanied by high rate capability and low power consumption. Preliminary specifications of this new TDC chip are presented. Furthermore a FPGA based readout-driver and buffer-module as an interface between the front-end of the COMPASS detector systems and an optical S-LINK is in development. The same module serves also as remote fan-out for the COMPASS trigger distribution and time synchronization system. This readout-driver monitors the trigger and data flow to and from front-ends. In addition, a specific data buffer structure and sophisticated data flow control is used to pursue local pre-event building. At start-up the module controls all necessary front-end initializations.Comment: 5 pages, 4 figure

Providing Remote Access to Robotic Telescopes by Adopting Grid Technology

We present an architecture for enabling remote access to robotic telescopes through the adoption of Grid technology. With this architecture, Internet connected robotic telescopes form a global network and are controlled by a global resource management system (scheduler), similar to individual compute resources in a Grid. By virtualizing the access to these telescope resources and by describing them and observation requests in a generic language (RTML). Astronomers are provided with an interface to a telescope network, from which they can get the appropriate resources for their observations. Moreover, new kinds of coordinated observations become feasible, such as multi-wavelength campaigns or immediate and continuous monitoring of transient astronomical events. This paper describes the architecture, the processing of observation requests and new research topics in a global network of robotic telescopes

Mode-locking of incommensurate phase by quantum zero point energy in the Frenkel-Kontorova model

In this paper, it is shown that a configuration modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero point energy is taken into account. It is also found that the specific heat for an incommensurate phase shows different parameter-dependence in sliding phase and pinning phase. These findings provide a possible way for experimentalists to verify the phase transition by breaking of analyticity.Comment: 6 pages in Europhys style, 3 eps figure

Radiative transfer effects on Doppler measurements as sources of surface effects in sunspot seismology

We show that the use of Doppler shifts of Zeeman sensitive spectral lines to observe wavesn in sunspots is subject to measurement specific phase shifts arising from, (i) altered height range of spectral line formation and the propagating character of p mode waves in penumbrae, and (ii) Zeeman broadening and splitting. We also show that these phase shifts depend on wave frequencies, strengths and line of sight inclination of magnetic field, and the polarization state used for Doppler measurements. We discuss how these phase shifts could contribute to local helioseismic measurements of 'surface effects' in sunspot seismology.Comment: 12 pages, 4 figures, Accepted for publication in the Astrophysical Journal Letter

Proton stopping in C+C, d+C, C+Ta and d+Ta collisions at 4.2A GeV/c

The shape of proton rapidity distributions is analysed in terms of their Gaussian components, and the average rapidity loss is determined in order to estimate the amount of stopping in C+C, d+C, C+Ta and d+Ta collisions at 4.2A GeV/c. Three Gaussians correspond to the nuclear transparency and describe well all peripheral and also C+C central collisions. Two-component shape is obtained in case of d+C and C+Ta central collisions. Finally one Gaussian, found in d+Ta central collisions, corresponds to the full stopping. The calculated values of the average rapidity loss support the qualitative relationship between the number of Gaussian components and the corresponding stopping power. It is also observed, in central collisions, that the average rapidity loss increases with the ratio of the number of target and the number of projectile participants.Comment: 9 pages REVTeX, 1 PS figure replaced, to be published in Phys.Rev.