We study the Dirichlet problem in a bounded plane domain for the heat equation with small parameter multiplying the derivative in t. The behaviour of solution at characteristic points of the boundary is of special interest. The behaviour is well understood if a characteristic line is tangent to the boundary with contact degree at least 2. We allow the boundary to not only have contact of degree less than 2 with a characteristic line but also a cuspidal singularity at a characteristic point. We construct an asymptotic solution of the problem near the characteristic point to describe how the boundary layer degenerates.

del Pezzo surfaces are isomorphic to either P¹ x P¹ or P² blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P² blown up <i>a</i> times with <i>a</i> ranging from 0 to 6. We will show that when we count points of bounded height on one of these surfaces, the number of points on lines give us the primary growth order, but the secondary growth order calculates the number of points on the rest of the surface and hence is a better representation of the geometry of the surface.

BAKGRUND: Anorexia nervosa är latin och betyder ”nervös aptitlöshet” och det som präglar sjukdomen är självförvållad svält. Sjukdomen börjar vanligtvis med en bantning för att gå ned i vikt som spårar ur.  Anorexia nervosa förkommer hos cirka 1 % unga kvinnor, vilka också är de som drabbas i störst utsträckning. En rad allvarliga somatiska komplikationer kan ses till följd av sjukdomen som i svåra fall kan leda till döden.  Sjukdomen är individuell och det finns av den anledningen ingen självklar behandling. SYFTE: Syftet med studien är att beskriva kvinnors upplevelser av vändpunkter vid anorexia nervosa efter tillfrisknande. METOD: Fem självbiografier analyserades med hjälp av kvalitativ innehållsanalys. RESULTAT: Den kvalitativa innehållsanalysen resulterade i fyra kategorier som beskrev vändpunkter vid anorexia nervosa efter tillfrisknande: Sjukdomsinsikt, Motivation, Tillit samt Beslut. Tillfriskningsprocessen har visat sig vara individuell och olika kvinnor i studien har upplevt olika kombinationer av de nämnda vändpunkterna i tillfrisknandet. DISKUSSION: Sjukdomsinsikt har visat sig vara den viktigaste vändpunkten vid tillfrisknande i anorexia nervosa. Om en person inte vet om att hon eller han är sjuk, är det svårt att bli frisk. / BACKGROUND: Anorexia nervosa is latin for “nervous appetite lose” and what characterizes the disease is self-starvation. It usually starts with dieting to lose weight which loses control. Anorexia nervosa exists in about 1 % of all young women, and young women are also in the front of the disease. A number of serious somatic complications can follow the disease which in severe cases can cause death. The disease is individual and there is no obvious treatment. AIM: The aim of the study is to describe woman’s experiences of the turning-points in anorexia nervosa after recovery. METHOD: Five autobiographies were analyzed with qualitative content analysis. RESULTS: Qualitative analyses revealed four core categories who described the turning points of recovery in anorexia nervosa: Awareness of disease, Motivation, Trust and Decision. The recovery has proved to be individual and different women in the study have experienced different combinations of those turning-points for recovery. DISCUSSION: Awareness of disease provides to be the most essential turning-point for recovery in anorexia nervosa. If a person doesn’t know she or he is sick, there is no reason to get well.

del Pezzo surfaces are isomorphic to either P¹ x P¹ or P² blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P² blown up <i>a</i> times with <i>a</i> ranging from 0 to 6. We will show that when we count points of bounded height on one of these surfaces, the number of points on lines give us the primary growth order, but the secondary growth order calculates the number of points on the rest of the surface and hence is a better representation of the geometry of the surface.

<p>We study how the preimages of a mapping f : X &rarr Y between manifolds vary under perturbations. First, we consider the preimage of a single point and track the history of its connected component as this point varies in Y. This information is compactly represented in a structure that is the generalization of the Reeb graph we call the Reeb space. We study its local and global properties and provide an algorithm for its construction. Using homology, we then consider higher dimensional connectivity of the preimage. We develop a theory quantifying the stability of each homology class under perturbations of the mapping f . This number called robustness is given to each homology class in the preimage. The robustness of a class is the magnitude of the perturbation necessary to remove it from the preimage. The generality of this theory allows for many applications. We apply this theory to quantify the stability of contours, fixed points, periodic orbits, and more.</p> / Dissertation

This thesis presents an investigation into Paleoindian projectile-point morphology. A goal of this research is to determine if evidence of a normative cultural manufacturing protocol can be identified on Clovis projectile points which can then be used to address research questions concerning Clovis point variability, and ultimately, the spread of this tool-form across North America. This paper addresses obstacles to behavioral investigations of stone tool morphology such as the effects of resharpening and raw material type on tool shape. I argue that a culturally normative process of manufacture was maintained throughout the life-history of Clovis projectile points which translated into a specific shape maintained to the time of exhaustion and discard. As an analytical tool, this study utilizes the geometric morphometric method to retain the geometry of each artifact throughout analysis by focusing on spatial covariation among landmarks uniformly found on each tool. This thesis investigates variability in 123 fluted projectile points from 23 archaeological sites in North America which met criteria meant to control for security of context in the archaeological record. Principle components describing the shape-variability inherent in this data-set were generated using geometric morphometrics and multivariate statistical analyses were employed to identify major factors of variability. This research concluded that Clovis projectile-point shape was determined by normative cultural behavior maintained throughout the life of the artifact and not the result of raw material type or resharpening processes. Therefore, the projectile-point variability found to be geographically patterned provided evidence of Paleoindian movement and the spread of tool form. Multivariate analysis of variance determined that a regional trend in variability was present. The distribution of within-site variance suggested that artifacts from sites in the West were very homogeneous while artifacts from Eastern sites were more variable. The multivariate cluster and discriminant function analyses also demonstrated a closer affinity between artifacts in the Southwest and Northwest than either has with the Northeast. The similarities in projectile point morphology between the Southwest and Northwest regions suggest movement beginning with a Southwest point of origin from which Pleistocene peoples may have carried their fluted point technology north and east.

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<p>Static analysis on source code or binary code retrieves information about a software program. In object-oriented languages, static points-to analysis retrieves information about objects and how they refer to each other. The result of the points-to analysis is traditionally used to perform optimizations in compilers, such as static resolution of polymorphic calls, and dead-code elimination. More advanced optimizations have been suggested specifically for Java, such as synchronization removal and stack-allocation of objects. Recently, software engineering tools using points-to analysis have appeared aiming to help the developer to understand and to debug software. Altogether, there is a great variety of tools that use or could use points-to analysis, both from academia and from industry.</p><p>We aim to construct a framework that supports the development of new and the improvement of existing clients to points-to analysis result. We present two client analyses and investigate the similarities and differences they have. The client analyses are the escape analysis and the side-effects analysis. The similarities refer to data structures and basic algorithms that both depend on. The differences are found in the way the two analyses use the data structures and the basic algorithms. In order to reuse these in a framework, a specification language is needed to reflect the differences. The client analyses are implemented, with shared data-structures and basic algorithms, but do not use a separate specification language.</p><p>The framework is evaluated against three goal criteria, development speed, analysis precision, and analysis speed. The development speed is ranked as most important, and the two latter are considered equally important. Thereafter we present related work and discuss it with respect to the goal criteria.</p><p>The evaluation of the framework is done in two separate experiments. The first experiment evaluates development speed and shows that the framework enables higher development speed compared to not using the framework. The second experiment evaluates the precision and the speed of the analyses and it shows that the different precisions in the points-to analysis are reflected in the precisions of the client analyses. It also shows that there is a trade-off between analysis precision and analysis speed to consider when choosing analysis precision.</p><p>Finally, we discuss four alternative ways to continue the research towards a doctoral thesis.</p>

<p>Points-to analysis is a static program analysis which computes possible reference relations between different parts of a program. It serves as input to many high-level analyses. Points-to analyses differ, among others, in flow- and context-sensitivity, program representation, and object abstraction. Most program representations used for points-to analysis are sparse representations which abstract from, e.g., primitive data types and intra-procedural control-flow. Thus, a certain degree of information is sacrificed for compact program representation, which results in scalable performance. In this thesis, we present a framework which allows building different versions of Points-to SSA (P2SSA), a sparse, Memory SSA based program representation. Distinct instantiations of P2SSA contain different levels of abstraction from a program's full representation. We present another framework which allows running Points-to analyses on these program representations. We use these two frameworks to instantiate different versions of P2SSA and compare them in terms of analysis precision and execution time.</p>

It may be argued that ours is far away from a sustainable society. For all the technological wonders that we have been able to produce, some basic problems such as lack of universal access to the means to satisfy one's basic needs, human rights violations, systematic degradation of the environment, among others are still present. Not for a lack of effort, but scientific progress, political effort and economic growth appear to have real limitations in their capability to help us solve some of these problems that have endured through time. Donella Meadows, an expert in systems analysis, has developed a comprehensive list of points to intervene in a system in order to effect change. Using that framework as a basis, the present study aims to try to identify potential reasons for why most of the efforts conducted so far to solve some of the previously mentioned fundamental problems appear not to be so effective. Many of the fundamental assumptions of the mainstream economic school that heavily influence policy making and individual behavior to a large extent, have been identified as potentially important leverage points being pushed in the wrong direction! Economic powers and vested interests allow for the erosion of the self-controlling elements of the global political-economic system such as democratic institutions, what Meadows classifies as weakening of negative feedback loops. The mainstream economic models promoting "success to the successful" loops such as accumulation of resources in the hands of a few, all the while concentrating power can be pointed out as an example of a positive loop getting dangerously out of control. Uncontrolled positive loops inevitably lead to system collapse. Concentration of power is specially dangerous as it can bestow upon an elite the power to set the rules of the system, one of the most effective leverage points according to Meadows. Additionally, by curtailing biological, ideological and cultural diversity we are compromising one of the fundamental conditions for our systems to endure threatening changes, the ability to self-organize, or evolve. The most powerful leverage point is the paradigm out of which the whole system is constructed. The current mainstream economic thinking is fundamentally based on a single paradigmatic assumption of scarcity by mean of the supposed impossibility of satisfying human material wants, as 'new wants are always emerging'. In this mindset, it seems to make sense for the economic system to promote limitless growth and accumulation under the assumption of unlimited material wants. In the possibility to transcend such a paradigm lies an important potential for leverage in the efforts to solve the fundamental problems that still hold our society from attaining sustainability.