On aberration in gravitational lensing

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily interpreted in terms of aberration of light-rays. Both radial and transverse motions with relativistic velocities are considered. The lens equation is derived by first considering geodesic motion of photons in the rest-frame Schwarzschild spacetime of the lens, and, then, light-ray detection in the moving observer's frame. Due to the transverse motion images are displaced and distorted in the observer's celestial sphere, whereas the radial velocity along the line of sight causes an effective re-scaling of the lens mass. The Einstein ring is distorted to an ellipse whereas the caustics in the source plane are still point-like. Either for null transverse motion or up to linear order in velocities, the critical curve is still a circle with its radius corrected by a factor (1+z_d) with respect to the static case, z_d being the relativistic Doppler shift of the deflector. From the observational point of view, the orbital motion of the Earth can cause potentially observable corrections of the order of the microarcsec in lensing towards the super-massive black hole at the Galactic center. On a cosmological scale, tangential peculiar velocities of cluster of galaxies bring about a typical flexion in images of background galaxies in the weak lensing regime but future measurements seem to be too much challenging.Comment: 8 pages, 2 figures, in press on PR

Seasonal feeding patterns, growth dynamics and the impact of warming on the grazing effects of invasive freshwater bivalves

In the present study factors affecting the filtration activity and grazing effects of the freshwater bivalves Corbicula fluminea and Dreissena polymorpha were investigated. This was done with a combination of laboratory and field related experimental approaches. Both bivalves represent keystone species, who can have a large impact on planktonic community composition and the flux of matter in ecosystems. Additionally the whole seasonal population dynamics of C. fluminea were investigated to provide a basis for future predictions and modelling approaches. The first part of the present work concentrated on the impact of warming on the grazing rates of C. fluminea and D. polymorpha and their natural prey organisms such as heterotrophic flagellates. Therefore filtration experiments were performed in circulating flow channels to provide a natural current by using untreated water from a large river (River Rhine, NRW, Germany). It was shown that the increase of the prey´s growth rates was much stronger than that of the predator´s grazing rates when temperatures were increased from 19°C to over 25°C. When performing the same experiments using a benthic microbial predator community (biofilms dominated by suspension-feeding ciliates), an increase of the grazing rates relative to the growth rates with temperature could be observed. The data shows, that a predator-prey interaction between the macrofauna (Bivalves) and their unicellular prey community can change significantly under the impact of increasing temperature when consumpiton and growth rates develop differentially. This can lead to netto-decrase of the prey abundance. The data suggests that the predator-prey interaction which is balanced at moderate temperatures can become unbalanced with increasing temperature. In the second part of this work the role of Dreissena polymorpha in mediating effects of high summer temperatures on the dominant components of natural river plankton was investigated. It was shown that both heterotrophic flagellates and algae increase in abundance at temperatures above 20°C because of decreasing grazing activity of D. polymorpha at such temperatures. Bacteria, as the main prey of the heterotrophic flagellates, decreased in abundance with increasing temperature, suggesting a trophic cascade (mussel - flagellates - bacteria) that is altered by the temperature response of the mussel ingestion. The data thus demonstrates that microbial communities controlled by a macrofaunal component can experience substantial changes at high summer temperatures because of differential development of direct and indirect grazing effects with temperature. In the third part of the present work, seasonal and interannual variability of C. flumineas grazing activity was investigated. Strong seasonal variations, such as a 50-fold increase from February to July, were observed. These variations were only poorly linked to temperature, as they could be found at both the ambient field temperature and a constant temperature of 15°C. It was shown that highest grazing activity was found at periods of highest reproduction activity. Additionally it was shown that the grazing activity was very low from March to August 2009 compared to the same period in 2008 after the bivalves experienced a period of two weeks with low winter temperatures close to the lethal temperature of 2°C. Such low temperatures lead to reduced reproduction rates as shown in previous studies. It was demonstrated that other factors besides temperature probably associated to life-history can have a large impact on the grazing activity of bivalves. The last part of this study concentrated on the shell growth of C. fluminea. The shell growth of more than 50 individuals was observed over a period of more than one year. It was confirmed, that shell growth decreases with increasing shell size. The data was used to generate growth curves over a period of several years with the help of a von Bertalanffy growth model. Additionally the model was used to estimate the age at a given length, the maximum age (7.3 years) and the maximum shell length of C. fluminea in the River Rhine. Taken together, the present study demonstrated that temperature increase can alter a predator-prey interaction when grazing rates of the predators and growth rates of the prey develop asynchronously with increasing temperature. It was shown that warming can differentially influence organisms on different trophic levels by trophic cascading (mussels-flagellate-bacteria). Additionally, the long-term (whole season) studies showed that there are other factors besides temperature such as cold winter periods or reproduction activity that can surpass direct temperature effects. The last part of the study provided basic data about population dynamics of C. fluminea. Both the short-term grazing experiments and the long-term studies provide new patterns and mechanics, which are relevant to accurately predict the performance and the effects of invasive bivalves under changing environmental conditions

Thomas Barnes Cuming, Jr. and the location of Nebraska\u27s territorial capitol

On May 30, 1854, Franklin Pierce, President of the United States, signed into law the Kansas-Negraska Act. This act, long famous in American history, had as its purpose the territorial organization of the continental heart of the United States. Pioneering settlement had populated both coastal regions as well as the east central area lying along the great Mississippi River. Between these separated portions of the United States of America stretched the high plains, an area which had been considered unfit for white civilization for over twenty years, and which, as a result, had been given by the federal government to tribes of displaced Indians, to be held by them in perpetuity. By 1853, however, political and commercial necessities had made it clear to a number of powerful legislators in Washington that the area could not berelinquished to the Indian for all time; that it was needed in the federal framework in order to make possible transportation and communication connections between the two coastal sections. The American dream of the Pacific Railroad and, to a lesser degree, of a transcontinental telegraph, were the twin progenitors of teh Kansas-Nebraska Act

Der Fahrschein für den Anrufbus: Tarifgestaltung von bedarfsgesteuerten Bedienformen des öffentlichen Verkehrs im ländlichen Raum

Die flexible Bedienung im Flächenbetrieb besitzt großes Potential, die Mobilitätsbedürfnisse von Bewohnern dünnbesiedelter ländlicher Räume zu befriedigen. Im Fokus der Forschungsarbeit steht die Frage, welche Tarifsysteme in der betrieblichen Ausgestaltung von Anrufbussystemen derzeit Anwendung finden. Auf Basis einer umfangreichen Bestandsanalyse bestehender Anrufbussysteme wurde betrachtet, wie groß der Anteil der Anrufbussysteme ist, die einen Komfortzuschlag erheben. Die Auswertung ergab, dass zum Zeitpunkt der Betrachtung zwei Drittel der Anrufbussysteme in Deutschland einen Komfortzuschlag erheben. Chancen und Risiken der Einführung eines Komfortzuschlags und weitere Möglichkeiten der Steigerung des Kostendeckungsgrads werden diskutiert

Member Commitment and Switching Decisions in Dairy Cooperatives – A Factorial Survey

The membership base of dairy cooperatives has become increasingly unstable in the past decades. Understanding the factors influencing dairy farmers’ rescinding of such memberships is crucial for preventing supplier losses, which may threaten the cooperatives’ competitiveness. Since the dairy sector is characterised by substantial complexity and uncertainty, the broader context in which such decisions take place must be considered. To this end, a factorial survey experiment is developed. The experiment contains descriptions of realistic scenarios that have to be evaluated by the respondents in terms of the incentives to switch. The factors and processes described in the scenarios result from an extensive literature review and a qualitative pre-study with sector experts. Implemented by means of an online survey, the survey experiment was distributed by Northern German dairy cooperatives among their member suppliers. The obtained results provide evidence for the relevance of the prices paid by the cooperative, the current performance of the cooperative, as well as the importance of the farmer orientation of a dairy and the state of the relationship quality. Moreover, findings provide statistical evidence for the influence of other farmers’ switching decisions and neighbouring farmers delivering to a competitor

Asymptotics of maximum likelihood estimation for stable law with continuous parameterization

Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although these asymptotics have been provided with Zolotarev's $(B)$ parameterization, there are several gaps between. Especially in the latter, the density, so that scores and their derivatives are discontinuous at $\alpha=1$ for $\beta\neq 0$ and usual asymptotics are impossible. This is considerable inconvenience for applications. By showing that these quantities are smooth in the continuous form, we fill gaps between and provide a convenient theory. We numerically approximate the Fisher information matrix around the Cauchy law $(\alpha,\beta)=(1,0)$. The results exhibit continuity at $\alpha=1,\,\beta\neq 0$ and this secures the accuracy of our calculations.Comment: 16 pages, 2 tables, original articl

Exploring the Spatiotemporal Dynamics of Cooperative Members' Switching Decisions

This article analyses the spatiotemporal dynamics of the actual switching behaviour of farmers’ in a dairy cooperative’s membership base. Space-time permutation scan statistic is used to identify clusters of switching decisions in space and time, while objective and publicly available indicators are related to the occurrence of these clusters. The analysis reveals two classes of clustered switching decisions: Clusters in which many farmers switch on a particular day and clusters covering longer periods of time with farmers switching in a herd-like pattern. Additionally, the relationship between farm sizes as well as price incentives and clustered switching decisions is observed. [EconLit citations: Q13; C23; L25]

Generalized Intransitive Dice: Mimicking an Arbitrary Tournament

A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to D_j$, if $Prob(D_i > D_j) > \frac{1}{2}$. Examples are known of intransitive $6$-sided dice, i.e. $D_1 \to D_2 \to D_3$ but $D_3 \to D_1$. A tournament of size $n$ is a choice of direction $i \to j$ for each edge of the complete graph on $n$ vertices. We show that if $R$ is tournament on the set $\{ 1, \dots, n \}$, then for sufficiently large $N$ there exist sets of independent $N$-sided dice $\{ D_1, \dots, D_n \}$ such that $D_i \to D_j$ if and only if $i \to j$ in $R$

Nicht nur Sibelius!: eine neue "Geschichte der Musik Finnlands"

Fabian Dahlström / Mikko Heiniö / Erkki Salmenhaara, Suomen musiikin historia [Die Geschichte der Musik Finnlands], 4 Bde, Porvoo (Verlag Werner Söderström) 1995/96. Das Erscheinen einer nationalen Musikgeschichte zu einem Zeitpunkt, wo uns übernationale Zusammenhänge und Gemeinsamkeiten mehr interessieren als eine von Landesgrenzen bestimmte Eigengeschichte, läßt verwundern. Auf ein Werk dieser Art hat man jedoch in Finnland lange gewartet. Seit der Herausgabe der vorigen Musikgeschichte Toivo Haapanens "Die Tonkunst Finnlands", sind über fünfzig Jahre vergangen und obgleich dieser einbändige Abriß vielen Generationen von Musikstudenten treu gedient hat, ist er heute veraltet und in vieler Weise überholt. Eine derart gründliche Musikgeschichte des Landes, wie sie das hier vorzustellende Werk darstellt, hat es bisher nicht gegeben

Strong deflection limit of black hole gravitational lensing with arbitrary source distances

The gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds $\pi$, gravitational lensing can be analytically approximated by the so-called strong deflection limit. In this paper we remove the conventional assumption of sources very far from the black hole, considering the distance of the source as an additional parameter in the lensing problem to be treated exactly. We find expressions for critical curves, caustics and all lensing observables valid for any position of the source up to the horizon. After analyzing the spherically symmetric case we focus on the Kerr black hole, for which we present an analytical 3-dimensional description of the higher order caustic tubes.Comment: 20 pages, 8 figures, appendix added. In press on Physical Review