Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Kiinnostusta vai ahdistusta? : Opettajaksi opiskelevien akateemiset tunteet, motivaatio ja opiskelun ongelmat suhteessa hyvinvointiin ja menestykseen aktivoivalla luentokurssilla

Previous studies indicate that positive learning experiences are related to academic achievement as well as to well-being. On the other hand, emotional and motivational problems in studying may pose a risk for both academic achievement and well-being. Thus, emotions and motivation have an increasing role in explaining university students learning and studying. The relations between emotions, motivation, study success and well-being have been less frequently studied. The aim of this study was to investigate what kind of academic emotions, motivational factors and problems in studying students experienced five days before an exam of an activating lecture course, and the relations among these factors as well as their relation to self-study time and study success. Furthermore, the effect of all these factors on well-being, flow experience and academic achievement was examined. The term academic emotion was defined as emotion experienced in academic settings and related to studying. In the present study the theoretical background to motivational factors was based on thinking strategies and attributions, flow experience and task value. Problems in studying were measured in terms of exhaustion, anxiety, stress, lack of interest, lack of self-regulation and procrastination. The data were collected in December 2009 in an activating educational psychology lecture course by using a questionnaire. The participants (n=107) were class and kindergarten teacher students from the University of Helsinki. Most of them were first year students. The course grades were also gathered. Correlations and stepwise regression analysis were carried out to find out the factors that were related to or explained study success. The clusters that presented students´ problems in studying as well as thinking strategies and attributions, were found through hierarchical cluster analysis. K-means cluster analysis was used to form the final groups. One-way analysis of variance, Kruskal-Wallis test and crosstabs were conducted to see whether the students in different clusters varied in terms of study success, academic emotions, task value, flow, and background variables. The results indicated that academic emotions measured five days before the exam explained about 30 % of the variance of the course grade; exhaustion and interest positively, and anxiety negatively. In addition, interest as well as the self-study time best explained study success on the course. The participants were classified into three clusters according to their problems in studying as well as their thinking strategies and attributions: 1) ill-being, 2) carefree, and 3) committed and optimistic students. Ill-being students reported most negative emotions, achieved the worst grades, experienced anxiety rather than flow and were also the youngest. Carefree students, on the other hand, expressed the least negative emotions and spent the least time on self-studying, and like committed students, experienced flow. In addition, committed students reported positive emotions the most often and achieved the best grades on the course. In the future, more in-depth understanding how and why especially young first year students experience their studying hard is needed, because early state of the studies is shown to predict later study success.

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.

Cultural differences and postmerger problems: Misconceptions and cognitive simplifications.

Researchers and practitioners have increasingly explained post-merger organizational problems with cultural differences, especially in the context of cross-border mergers and acquisitions. It is suggested here that cultural differences have great explanatory power in the context of post-merger change processes. There are, however, problems with a number of superficial cultural conceptions that are common in research in this area and in managerial rhetoric. This critical article provocatively delineates misconceptions widely held by researchers and practitioners in this field, which not only disregard cultural differentiation, fragmentation, inconsistencies and ambiguities, but further, illustrate a lack of understanding of cultural permeability and embeddedness in the environment, an overemphasis on abstract values and lack of attention to organizational practices, an overemphasis on initial structural differences and lack of attention to the new cultural layer, a lack of recognition of the political dimensions and a failure to recognize cultural differences as sources of value and learning. In this article, the theoretical problems associated with these misconceptions are examined and new conceptual perspectives suggested. The risks at stake for decision makers are also discussed.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.