Studio portrait of unidentified Levy brother (most likely Arthur or Hermann) in military uniform; Nogent-Sur-Seine, France.

Photographer's imprint lower left corner

Writer Clara Michelson (second from left) seated at an outdoor table with three unidentified women and one unidentified man; Saint-Brevin-les-Pins, France Portraits Groups

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Outdoor portrait of Ellen Bernkopf nee Catzenstein with her husband Hans Bernkopf; Paris, France. Portraits Couples

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Sensory Systems in Sawfishes. 1. The Ampullae of Lorenzini

The distribution and density of the ampullary electroreceptors in the skin of elasmobranchs are influenced by the phylogeny and ecology of a species. Sensory maps were created for 4 species of pristid sawfish. Their ampullary pores were separated into pore fields based on their innervation and cluster formation. Ventrally, ampullary pores are located in 6 areas (5 in Pristis microdon), covering the rostrum and head to the gills. Dorsally, pores are located in 4 areas (3 in P. microdon), which cover the rostrum, head and may extend slightly onto the pectoral fins. In all species, the highest number of pores is found on the dorsal and ventral sides of the rostrum. The high densities of pores along the rostrum combined with the low densities around the mouth could indicate that sawfish use their rostrum to stun their prey before ingesting it, but this hypothesis remains to be tested. The directions of ampullary canals on the ventral side of the rostrum are species specific. P. microdon possesses the highest number of ampullary pores, which indicates that amongst the study species this species is an electroreception specialist. As such, juvenile P. microdon inhabit low-visibility freshwater habitats.

Brother of Lola Gruenthal in Nice, France Portraits Men

Brother of Lola Gruenthal

Portrait of Ya'akov Meir [Jacob Meyer], Head of the Rabbinical Court and President of the Consistorium of the Community of Strasbourg; France.

Caption: J. Meyer, Grand-Rabbin et President du Consistoire Israelite du Department du Bas-Rhin a Strasbourg; also translated in Hebrew

Hans Albert Einstein; Sete, France Portraits; Men

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Hanukkah lamp from France Coin

Obverse: 25 Lirot coin. Reverse: Hanukkah lamp from France

Hanukkah lamp from France Coin

Obverse: 25 Lirot coin. Reverse: Hanukkah lamp from France, 14th century

Cover page of a binder for maps of Crimea and Ukraine

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Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.