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The paper will focus on the early texts of Galileo Galilei (1613~1623) and Daniel Bernoulli (1738) as examples of pure combinatorical analysis and perspectively considerations within the mathematical discipline of probability theory. It is argued that Bernoulli's approach needed to be developed further in order to achieve a successful and satisfactory theory of risk. In modern economy the need for a proper definition of a notion of risk is seen and currently discussed within the frame of ISO standards. But as already mentioned this interest is mainly owed to the governmental demands of the Basel II and Solvency standards and therefore an external demand. On the other hand an intrinsic understanding of the meaning of risk, as could be provided by a conclusive theory, could lead to a better success in modelling various risks and help to achieve better prognosis.
This article generalizes Schwinger’s mechanism for particles production in the arbitrary finite field volume. McLerran-Venugopolan(MV) model and iterative solution of DGLAP equation in the double leading log approximation for small x gluon distribution function were used to derive the new formula for initial chromofield energy density. This initial chromofield energy is distributed among color neutral clusters or strings of different length. This strings are stretched by receding nucleus. From the proposed mechanism of string fragmentation or color field decay based on exact solution of Dirac equation in the different finite volume, the new formulae for esimated baryon kinetic energy loss and rapidity spectrum of produced partons were derived.
Der Zusammenhang fundamentaler Symmetriestrukturen mit dem Zugang moderner Naturwissenschaften zur abstrakten Beschreibung komplexer Systeme wird dargestellt. Beginnend mit der geometrischen Symmetrie der Schneeflocke und dem symmetrietheoretischen Ansatz in Platons Timaios wird der symmetrietheoretische Ansatz moderner Naturwissenschaften exemplifiziert und analysiert. Die mathematische Abstraktion wird als reduktionistische Methode verstanden.
To preserve the required beam quality in an e+/e- collider it is necessary to have a very precise beam position control at each accelerating cavity. An elegant method to avoid additional length and beam disturbance is the usage of signals from existing HOM-dampers. The magnitude of the displacement is derived from the amplitude of a dipole mode whereas the sign follows from the phase comparison of a dipole and a monopole HOM. To check the performance of the system, a measurement setup has been built with an antenna which can be moved with micrometer resolution to simulate the beam. Furthermore we have developed a signal processing to determine the absolute beam displacement. Measurements on the HOM-damper cell can be done in the frequency domain using a network analyser. Final measurements with the nonlinear time dependent signal processing circuit has to be done with very short electric pulses simulating electron bunches. Thus, we have designed a sub nanosecond pulse generator using a clipping line and the step recovery effect of a diode. The measurement can be done with a resolution of about 10 micrometers. Measurements and numerical calculations concerning the monitor design and the pulse generator are presented.
Vortrag gehalten am 12. Januar 2005 in Frankfurt am Main, am Physikalischen Verein, anläßlich der Verleihung des Philipp-Siedler-Wissenschaftspreises an Dipl.-Phys. Christine Meurer, als Anerkennung für ihre Diplomarbeit "Xi- und Xi+ Produktion in Pb+Pb Stößen bei 40 A GeV am CERN SPS" (urn:nbn:de:hebis:30-13740). Am CERN, dem Europäischen Kernforschungszentrum, werden Bleiatomkerne auf nahezu Lichtgeschwindigkeit beschleunigt und zur Kollision gebracht. Dabei wird die Materie in einer Art Feuerball extrem verdichtet und erhitzt. Unter diesen Bedingungen brechen die Bestandteile der Atomkerne, die Nukleonen, auf und der Blick auf die eigentlichen Bausteine der Materie, die Quarks, wird möglich. Nach der Kollision expandiert der Feuerball und viele neue Teilchen, darunter auch die sogenannten seltsamen Teilchen, entstehen. Ihre Besonderheiten werden im Vortrag diskutiert: Ergebnisse zur Produktion des seltsamen Xi- -Teilchens in Pb+Pb-Stößen bei einer Energie von 40 A GeV werden vorgestellt. Aus dem transversalen Massenspektrum bei mittlerer Rapidität erhält man einen inversen Steigungsparamenter von T Xi- = (210±11±21)MeV . Die Integration des Rapiditätsspektrums liefert eine totale Anzahl der s im gesamten Phasenraum von (2.41 ± 0.15 ± 0.24) Teilchen pro Kollision. Desweiteren wird die Anregungsfunktion des Xi- -Hyperons sowie seine Zentralitätsabhänigkeit bei 40 A GeV diskutiert.
We calculate the kaon HBT radius parameters for high energy heavy ion collisions, assuming a first order phase transition from a thermalized Quark-Gluon-Plasma to a gas of hadrons. At high transverse momenta K_T ~ 1 GeV/c direct emission from the phase boundary becomes important, the emission duration signal, i.e., the R_out/R_side ratio, and its sensitivity to T_c (and thus to the latent heat of the phase transition) are enlarged. Moreover, the QGP+hadronic rescattering transport model calculations do not yield unusual large radii (R_i<9fm). Finite momentum resolution effects have a strong impact on the extracted HBT parameters (R_i and lambda) as well as on the ratio R_out/R_side.
We calculate the antibaryon-to-baryon ratios, anti-p/p, anti-Lambda/Lambda, anti-Xi/Xi, and anti-Omega/Omega for Au+Au collisions at RHIC (sqrt{s}_{NN}=200 GeV). The effects of strong color fields associated with an enhanced strangeness and diquark production probability and with an effective decrease of formation times are investigated. Antibaryon-to-baryon ratios increase with the color field strength. The ratios also increase with the strangeness content |S|. The netbaryon number at midrapidity considerably increases with the color field strength while the netproton number remains roughly the same. This shows that the enhanced baryon transport involves a conversion into the hyperon sector (hyperonization) which can be observed in the (Lambda - anti-Lambda)/(p - anti-p) ratio.