This paper provides a systematic study of order statistics drawn from discrete parent distributions. New procedures are followed for the derivation of the distribution of the r^th order statistic x_(r) and of the joint distribution of x_(r), x_(s) (s > r), that is, we first derive the cumulative probability distribution, from which the probability distribution comes directly. This approach is easier than the usual method, moreover the formulae for the c.d.f. derived in this way can be easily computed. To get the moments of X_(r), we use convenient formulae involving the tails of the c.d.f. of X_(r) rather than the p.d.f. of X_(r). The moments are then readily derived from general results for discrete distributions. We show the analogy between the results in the continuous and discrete cases. Applications to three discrete distributions are given. We consider some results on uncorrelated statistics which were established in the continuous case and show that the same results hold also for the discrete case. Many recurrence relations between moments of order statistics are derived in the discrete case yielding the same results as previously given by Govindarajulu (1963) and Sillitto (1951, 1964) in the continuous case. / M.S.

Aktualität des Themas: das vollwertige Kombifutter wird schon lange gebraucht, deshalb ist es sehr interessant, die Struktur solcher Ration und die nutzlichsten Zusätze in dieser Periode zu behandeln. Forschungsziel: Bewertung des Einflusses auf das Wachstumstempo der unterschiedlichen Rationstuktur und des Wertes für die Ferkel. Bei der Fütterung der Tiere mit dem vollwertigen Kombifutter wird ganz ihr genetisches Potential für die Produktionserzeugung benutzt. Die Tiere erhalten dann alle nötigen Nahrungsmittel in entsprechenden Proportionen und zu entsprechender Lebensperiode. Deshalb wird die Produktion der Kombifutter auf der ganzen Welt und in Litauen sehr erweitert. Im Verlauf der beiden Gruppen wurde der Gesundheitszustand der Tiere beoachtet. Die Untersuchungsergebnisse zeigen, dass die Versuchsgruppen der Schweine, die mit ganz balanzierter Ration bei der Anwendung von der Nahrungszusatz Liprot SG -9 gefüttert wurden, wuchsen schneller als die Schweine der Kontrollgruppe mit der Ration VM und Nahrungszusatz M51. Der durchschnittliche Zuwachs der Schweinversuchsgruppe pro 24 Stunden war 766 g oder 5 Prozente im Vergleich mit der Kontrollgruppe (716 g). Nicht nur das höhere Gewicht bekamen die Scvhweine der Versuchsgruppe, sondern auch der Futtergebrauch wurde zu 1 kg Zuwachs geringer. Nach der Berechnung des Futterpreises wurde bemerkt, dass die Selbstkosten des Kombifutters deutlicher geringer sind und der Preis des gebrauchten Futters zu einer Zuwachseinheit... [to full text]

Recently acquired WFC3 UV (F275W and F336W) imaging mosaics under the Legacy Extragalactic UV Survey (LEGUS), combined with archival ACS data of M51, are used to study the young star cluster (YSC) population of this interacting system. Our newly extracted source catalogue contains 2834 cluster candidates, morphologically classified to be compact and uniform in colour, for which ages, masses and extinction are derived. In this first work we study the main properties of the YSC population of the whole galaxy, considering a mass-limited sample. Both luminosity and mass functions follow a power-law shape with slope -2, but at high luminosities and masses a dearth of sources is observed. The analysis of the mass function suggests that it is best fitted by a Schechter function with slope -2 and a truncation mass at 1.00 +/- 0.12 x 10(5) M-circle dot . Through Monte Carlo simulations, we confirm this result and link the shape of the luminosity function to the presence of a truncation in the mass function. A mass limited age function analysis, between 10 and 200 Myr, suggests that the cluster population is undergoing only moderate disruption. We observe little variation in the shape of the mass function at masses above 1 x 10(4) M-circle dot over this age range. The fraction of star formation happening in the form of bound clusters in M51 is similar to 20 per cent in the age range 10-100 Myr and little variation is observed over the whole range from 1 to 200 Myr.

I present a spectroscopic study of the molecular gas in the Whirlpool Galaxy (M51) and the Antennae Galaxies (NGC 4038/39) using data from the Herschel Space Observatory (Herschel) and the Atacama Large Millime- ter/submillimeter Array (ALMA). Using data from the Herschel Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS), I perform an excitation analysis to determine the physical characteris- tics (temperature, density, column density) of the cold and warm molecular gas across both systems. I do not find significant variation in the cold molecular gas across an individual system or between the systems. The warm molecular gas temperature is greater in NGC 4038/39 than in M51, while the density in both M51 and the nucleus of NGC 4038 is greater than the rest of the Anten- nae system. Both galaxies exhibit a similar fraction of warm to cold molecular gas. I compare Herschel SPIRE-FTS data to models of photon dominated regions (PDRs) to determine the strength of the background far ultraviolet field (G0) within both systems and find little variation across each system. I find that PDRs alone can explain the observed Herschel SPIRE-FTS data in both systems. Using ALMA observations of dense molecular gas tracers in NGC 4038/39, I investigate the physical processes affecting the dense molecular gas. Ratios of various molecular gas tracers suggest that the contributions of mechanical heating relative to PDR heating are similar across the entire system. The dense gas fraction in the nucleus of NGC 4038 and the nucleus of NGC 4039 is higher than in the overlap region, which I attribute to an increase in the stellar potential within the two nuclei. Furthermore, I find evidence for an increased cosmic ray rate in the overlap region of NGC 4038/39 relative to the two nuclei, which I attribute to an increased supernova rate in the overlap region. Most of the molecular gas in M51 and NGC 4038/39 is in the form of PDRs, while the increased temperature of the warm molecular gas in NGC iii 4038/39 compared to M51 is likely due to an increase in the mechanical heating from both supernova and stellar winds and the ongoing merger. Furthermore, a comparison of these results to previous studies of the interacting galaxy M82 and the late-stage merger Arp 220 suggests that mergers and interactions have a greater effect on the warm molecular gas compared to the cold molecular gas. The results from this thesis help to further our understanding of the effects of merging and interacting galaxies on molecular gas, while helping understand differences between interacting galaxies and merging galaxies. / Thesis / Doctor of Philosophy (PhD)

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