On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Testing Isotropy and a related Random Walk problem

One comes across directions as the observations in a number of situations. The first inferential question that one should answer when dealing with such data is, “Are they isotropic or uniformly distributed?” The answer to this question goes back in history which we shall retrace a bit and provide an exact and approximate solution to this so-called “Pearson’s Random Walk” problem.

Service provider switching: a study on the switching process in retail banking

In a business environment that is characterized by intense competition, building customer loyalty has become a key area of focus for most financial institutions. The explosion of the services sector, changing customer demographics and deregulation and emergence of new technology in the financial services industry have had a critical impact on consumers’ financial services buying behaviour. The changes have forced banks to modify their service offerings to customers so as to ensure high levels of customer satisfaction and also high levels of customer retention. Banks have historically had difficulty distinguishing their products from one another because of their relative homogeneity; with increasing competition,the problem has only intensified with no coherent distinguishing theme. Rising wealth, product proliferation, regulatory changes and newer technologies are together making bank switching easier for customers. In order to remain competitive, it is important for banks to retain their customer base. The financial services sector is the foundation for any economy and plays the role of mobilization of resources and their allocation. The retail banking sector in India has emerged as one of the major drivers of the overall banking industry and has witnessed enormous growth. Switching behaviour has a negative impact on the banks’ market share and profitability as the costs of acquiring customers are much higher than the costs of retaining. When customers switch, the business loses the potential for additional profits from the customer the initial costs invested in the customer by the business get . The Objective of the thesis was to examine the relationship among triggers that customers experience, their perceptions of service quality, consumers’ commitment and behavioral intentions in the contemporary India retail banking context through the eyes of the customer. To understand customers’ perception of these aspects, data were collected from retail banking customers alone for the purpose of analysis, though the banks’ views were considered during the qualitative work carried out prior to the main study. No respondent who is an employee of a banking organization was considered for the final study to avoid the possibility of any bias that could affect the results adversely. The data for the study were collected from customers who have switched banks and from those who were non switchers. The study attempted to develop and validate a multidimensional construct of service quality for retail banking from the consumer’s perspective. A major conclusion from the empirical research was the confirmation of the multidimensional construct for perceived service quality in the banking context. Switching can be viewed as an optimization problem for customers; customers review the potential gains of switching to another service provider against the costs of leaving the service provider. As banks do not provide tangible products, their service quality is usually assessed through service provider’s relationship with customers. Thus, banks should pay attention towards their employees’ skills and knowledge; assessing customers’ needs and offering fast and efficient services.

Employment Realm in Technical Education in Kerala-A Study on the Problem of Unemployment among Engineers

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Research through DESIGN through research - a problem statement and a conceptual sketch

This paper re-addresses the issue of a lacking genuine design research paradigm. It tries to sketch an operational model of such a paradigm, based upon a generic design process model, which is derived from basic notions of evolution and learning in different domains of knowing (and turns out to be not very different from existing ones). It does not abandon the scientific paradigm but concludes that the latter has to be embedded into / subordinated under a design paradigm.

Sprachentwicklung und Fachlernen im Mechanikunterricht

Die empirische Studie untersucht das Wechselspiel zwischen der fachbezogenen Sprachentwicklung und dem Fachlernen von Schülerinnen und Schülern bei der Einführung in den Kraftbegriff. Sie betrachtet also sowohl sprachliche wie auch kognitive Aspekte des Lernens in der Mechanik. Dafür wurde ein Unterrichtskonzept entwickelt, das den Gebrauch des Fachwortes Kraft in der Wissenschaft und in der alltäglichen Sprache besonders thematisiert. Dieses Unterrichtskonzept basiert auf Empfehlungen und Ergebnissen der Kognitionspsychologie, Linguistik, Philosophie, Sprachlehrforschung und der Didaktiken der Physik und der Fremdsprachen. Im Rahmen des Unterrichts wurden die Schülerinnen und Schüler mit zwei Aufgabentypen konfrontiert: Beim ersten Aufgabentyp waren die Lerner aufgefordert, den Kraftbegriff so zu verwenden, wie es einer fachsprachlich angemessenen Form entspräche, etwa um die Bewegung eines Zuges zu beschreiben. Aufgaben des zweiten Typs sahen vor, dass die Schülerinnen und Schüler kurze Texte danach klassifizierten, ob sie der Alltagssprache oder der Fachsprache angehörten. Diese als Metadiskurs bezeichnete Form der Auseinandersetzung mit sprachlichen Aspekten verhalf den Schülerinnen und Schülern zu einer Gelegenheit, ihr eigenes Verständnis des Kraftbegriffs zu thematisieren. Weiter lieferte der Metadiskurs wichtige Hinweise darauf, ob die Schülerinnen und Schüler sich bei ihren Beurteilungen eher auf formal-sprachliche oder inhaltliche Aspekte der Sprache bezogen. Für die Datenerhebung wurden alle Unterrichtsstunden videografiert und transkribiert. Zusammen mit schriftlichen Arbeitsergebnissen und Tests stand ein umfangreicher Datensatz zur Verfügung, für dessen Auswertung ein inhaltsanalytisches Verfahren Anwendung fand. Die Ergebnisse zeigen, dass das Lernen im Fach Physik bestimmte Ähnlichkeiten mit dem Lernen einer Fremdsprache zeigt: Wenn die Schülerinnen und Schüler den Kraftbegriff fachsprachlich verwenden sollen, sehen sie sich oft einer Alternativentscheidung gegenüber. Entweder sie versuchen, einer fachsprachlichen Form zu gehorchen und verlieren dabei den Inhalt aus den Augen, oder sie konzentrieren sich auf den Inhalt, drücken sich dabei aber in ihrer Alltagssprache aus und folgen Alltagskonzepten, die weit entfernt von den fachlich intendierten liegen. Ähnliche Beobachtungen kann man im Sprachunterricht machen, wenn Schüler eine neue grammatische Regel einüben: Sie konzentrieren sich entweder auf die neu zu erlernende Regel, oder aber auf den Inhalt des Gesagten, wobei sie die grammatische Regel, die an sich Gegenstand der Übung ist, verletzen. Meistens fällt diese Entscheidung derart, dass die Konzentration auf den Inhalt des Gesagten gerichtet ist, nicht oder wenig auf seine Form. Im Unterschied zum Sprachunterricht ist der Physikunterricht allerdings nicht nur darauf gerichtet, fachsprachlich angemessene Formen einzuüben, sondern insbesondere darauf, den Blick für neue und ungewohnte Konzepte zu öffnen. Damit müssen die Schülerinnen und Schüler hier häufig sprachliche und kognitive Hürden zur selben Zeit bewältigen. Die detaillierte Analyse des Metadiskurses zeigt, dass das Problem des Nebeneinanders zweier unterschiedlicher Anforderung entschäft werden kann: Während die Schüler im Metadiskurs unterschiedliche Aspekte der Sprache diskutieren, sind sie eher in der Lage, sowohl formale wie inhaltsbezogene Merkmale der Sprache wahrzunehmen. Der Text referiert weitere Parallelen zwischen dem Physikunterricht und dem Fremdsprachenlernen, sodass die Auffassung gerechtfertigt ist, dass die Fremdsprachendidaktik als Ideenlieferantin dafür dienen kann, neue Verbesserungsmöglichkeiten für den Physikunterricht aufzufinden.

The problem of noncharacteristic quasimolecular X-rays in heavy ion collision

Quasi-molecular X-rays observed in heavy ion collisions are interpreted within a relativistic calculation of correlation diagrams using the Dirac-Slater model. A semiquantitative description of noncharacteristic M X rays is given for the system Au-I.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

The problem of the graphic artist

'The problem of the graphic artist' is a small example of applying elementary mathematics (divisibility of natural numbers) to a real problem which we ourselves have actually experienced. It deals with the possibilities for partitioning a sheet of paper into strips. In this contribution we report on a teaching unit in grade 6 as well as on informal tests with students in school and university. Finally we analyse this example methodologically, summarise our observations with pupils and students, and draw some didactical conclusions.