A universal central limit theorem for the distance of two balls in random split trees

In der vorliegenden Arbeit wird ein Modell des zufälligen Splitbaumes untersucht. Dies ist ein verallgemeinertes Modell, das bei passender Wahl der zugehörigenParameter viele konkrete Suchbäume umfasst. Das Modell ist in der Arbeit von L. Devroye beschrieben: Nach einem zufallsbasierten Algorithmus werden den Knoten des Baumes Daten in Form von Kugeln hinzugefügt. Tiefe und Höhe sind dabei grundlegende Größen, die die Komplexität von Suchoperationen beschreiben, wenn das Suchbaummodell als Datenstruktur verwendet wird. Das Augenmerk der Arbeit richtet sich auf eine weitere entscheidende Größe: Den Abstand zweier rein zufällig gewählter Kugeln im Baum. Aufbauend auf Devroyes Erkenntnissen zum asymptotischen Verhalten der Tiefe der zuletzt eingefügten Kugel im Splitbaum, wird ein neues Resultat erzielt: Ein universeller Zentraler Grenzwertsatz für den Abstand der Kugeln. Als Anwendungsbeispiel werden zwei vom allgemeinen Modell abgedeckte Suchbäume betrachtet und der jeweilige Grenzwertsatz für die Abstände aus dem universellen Satz abgeleitet.In this work, the random split tree is being analyzed. This general structure depends on several parameters which can be chosen to create specific trees. The previous work of Devroye is used as a foundation. He described the split tree as a random based algorithm, in which data are being symbolized by balls and are allocated to the nodes of the tree. When this search tree model is used as a data structure, depth and height are traditionally considered to be fundamental measures to describe the complexity of search functions in the tree. The focus of this work is on another crucial measure, the distance of two randomly chosen balls in the tree. Based on Devroyes findings concerning the asymptotic behavior of the depth of the last inserted ball in the tree, a new result is achieved: A universal central limit theorem for the distance of two balls. As an example of use of the universal theorem, particular limit theorems for two specific random search trees are derived

Ansichten der Elite Rußlands über den Westen im Kontext der Systemtransformation

'Das Verhältnis der Elite Rußlands zum Westen ist ein Problem, das bereits einige Jahrhunderte lang aktuell ist und in den verschiedenen Phasen der Geschichte seine jeewilige Spezifik hatte, die von der außen- und innenpolitischen Situation abhing. Doch bei allen historischen Veränderungen ist eines konstant geblieben: Die Frage nach dem Verhältnis zum Westen war mit dem Kampf der verschiedenen politischen Parteien und Gruppen verbunden. Im 19. Jahrhundert waren dies die 'Westler' und die 'Slawophilen', 1998 sind es die 'Kommunisten' und 'Demokraten'. Konstant bleibt auch die 'Plattform' des Kampfes, d.h. der Problemkreis, um den sich der politische Kampf dreht. Der Bericht basiert auf verschiedenen Informationsquellen. Dies sind Ergebnisse der Meinungsumfrage von 200 Vertretern der Elite über die Entwicklungswege Rußlands im Kontext seines Verhältnisses zum Westen; die Ergebnisse einer Kontentanalyse politischer Programme von 40 Parteien; Antworten von 15 Vertretern der intellektuellen Elite auf eine spezielle Meinungsumfrage 'Rußland und der Westen'; Pressematerialien über die wirtschaftlichen und politischen Wechselbeziehungen zwischen Rußland und dem Westen.' (Textauszug)'The Russian elite's relationship with the West is a problem that has already been ongoing for several centuries and has taken on different specific characteristics in the various phases of history, depending on the domestic and international political situation at the time. But for all the changes it has undergone in the course of history, one thing has remained the same: the question as to the correct relationship with the West has always been linked with the struggle between the various political parties and groups of the day. In the 19th century these were the 'Westernizers' and the 'Slavophiles', in 1998 they are the 'Communists' and the 'Democrats'. Another thing that has remained constant is the 'platform' for that struggle, i.e. the gamut of problems around which the political battle circles. The report is based on various information sources. These comprise the results of an opinion poll conduced among 200 representatives of the elite on questions concerning the possible courses of Russia's developemnt in the context of its relationship with the West; the findings of an analysis of the content of the political manifestos of 40 parties; the replies by 15 members of the intellectual elite to a special opinion poll on 'Russia and the West'; press material on reciprocal economic and political relations between Russia and the West.' (extract

Features of the tourist enterprises image formation

The article defines the types of tourist enterprises depending on the duration of operation on the market and the features of activities to maintain and develop their image based on the empirical data obtained as a result of the tourist services market research in Yalta (Republic of Crimea). These are enterprises that are that for the first time begin to operate in the tourist market and form their image, enterprises that are active in the market, but do not form their image; enterprises that need to review or completely change their image building activities.For each type of enterprise, the stages of the image formation, including the necessary marketing tools, have been developed and substantiated: for the first type of the enterprises – determination of the image audience, development and approval of corporate identity, implementation of internal and external image building, image management; for the second type – image audit, analysis of the causes of the loyalty loss, development and implementation of image events; for the third type – image audit, choice of approach to the image program implementation. It is proved that the image of the tourist enterprise is characterized by a life cycle.It is proposed to consider four stages of the life cycle: formation; development; stability; blurring and loss. The characteristic features of the stages, management goals and the program of image building events have been determined

Electrical properties of UHMWPE/graphite nanoplates composites obtained by in-situ polymerization method

There are described nanocomposites based on ultra high molecular weight polyethylene and graphite nanoplates prepared by in-situ polymerization method. It is carried out a comprehensive study of electric properties of these composites, including direct current (dc) and alternating current (ac) properties. There is explored dependence of the conductivity and dielectric permeability on filler concentration, temperature, deformation and frequency of electric field. These relationships are compared with those for composites based on other carbon fillers including both nanoscale (carbon nanotubes, carbon black) and micron-sized (graphite, schungite) fillers. More specific electrical properties of investigated materials such as lower percolation threshold and higher dielectric permittivity compared to those for composites based on other carbon fillers are attributed to the plate-like shape of graphite nanoplates. These materials are distinguished also by their high electrical stability against temperature and deformation. Therefore, it makes graphite nanoplates the most preferable conductive filler for some practical applications. Some possible application areas for UHMWPE/graphite nanoplates nanocomposites will be also discussed