The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational points on certain algebraic varieties in function fields. The aim is to establish asymptotic relations that are relatively robust to changes in the characteristic of the base finite field. More notably, in the case when the characteristic is "small", the results are sharper than their integer analogues.

Video games are a part of modern culture. As video game spaces begin to enter a new generation’s spatial lexicon, it is important for architects, curators of spatial design, to understand this new medium of space. This thesis aims to introduce two concepts specific to video game design, the magic circle and flow, to architects as a means of understanding the design of video game spaces. First coined by the Dutch historian Johann Huizinga in Homo Ludens, and later adapted by video game designers Katie Salen and Eric Zimmerman, the magic circle refers to the boundary created by the rules of a game that separate reality from the fantasy of the game. Within the magic circle, the rules of play can transform and give new meaning to spatial organizations that could be considered problematic in real world architectural design. Flow is a psychological concept introduced by Hungarian psychology professor Mihály Csíkszentmihályi. When completing a task, flow occurs when both the skill level of the participant and the challenge level of the task are equally high. When a state of flow is achieved, the task becomes enjoyable and can be carried out indefinitely until the balance is broken. Effective video games spaces are specifically designed to contribute to flow experiences, while ineffective spaces can make a game too easy or too hard, creating a boredom or anxiety for the player. Through a series of explorations and video game case studies, specifically in the first-person and third person shooter genre, this thesis first observes the transformation of implied spatial meanings in the magic circle. It then introduces the unique spatial languages used to generate spaces that support the creation of flow alongside the gameplay and narrative of a video game. This thesis culminates with the design and execution of an original capture the flag map created with the Unreal Engine that tests the concepts of the magic circle and flow in video game spaces. As video games become increasingly ubiquitous, this thesis acts as means of entry for architects to understand the unique properties of an emerging form of spatial design.

This thesis focuses on the decision making in the most common business form: family businesses. A well-established theoretical model within the family business field is The three circle-model, which is based on three different dimensions: family, ownership and business. Most of the family businesses stay small but the ones expanding face the dilemma of balancing the best development of the dimensions. However, these three dimensions can contradict each other and as a result the founders are forced to choose which of the dimensions to prioritize when taking decisions.The purpose of this thesis is to create an understanding of how the family, the ownership and the business dimensions affect founders thoughts and reasoning behind decisions in the expansion phase in first generation family firms with few owners.We have reached the conclusions with a qualitative approach using case studies. We have gathered the empirical data by using Life story and Critical incident to define expansion decisions in two companies. Furthermore we used semi-structured interviews with the aim of creating an understanding of the founders thoughts and reasoning behind the taken decisions.Our conclusion shows that business opportunities and the objective to remain in control of the family business highly influence the decision making during the expansion phase. Another conclusion is that the family has been affected far more by the decisions than it has had an impact on the decisions. The thesis gives insight about an area within the family business field, which previously has been neglected by researchers.

I läroplanen för förskolan Lpfö-98 står det att barnen på förskolan skall ges möjligheter att vistas såväl inomhus som utomhus och att utomhusvistelsen skall ge barnen möjligheter till lek i planerad och naturmiljö. Syftet med studien är dels att upptäcka om och i så fall på vilket sätt samlingen, som en planerad aktivitetsform i förskolan, skiljer sig om den sker utomhus från om den genomförs inomhus och dels att undersöka vilket inflytande barn tilldelas på samlingar inomhus respektive utomhus.   Studien utgår från kvalitativ ansats och bygger på videoobservationer och återkopplande intervjuer (stimulated recall). I studien ingår två lärare verksamma i förskolan och barn i åldrarna 3-5 år.   Resultatet visar att det inte förekommer skillnad mellan samlingarna inomhus och utomhus när det gäller form, lärarens förhållningssätt och barnens inflytande. Skillnaden som resultatet visar handlar om lärarnas olika sätt att hålla i samlingen och inte om deras sätt att använda sig av möjligheter som utomhusmiljön erbjuder. Barns möjligheter till inflytande påverkas inte av att samlingen hålls vare sig inomhus eller utomhus. Vilket inflytande barnen ges och på vilket sätt de kan vara med och påverka innehållet i samlingen är beroende av lärarens förhållningssätt och synen på barns lärande. / In the curriculum for preschool "Lpfö-98" it states that the children attending preschool shall be given the opportunity to be both indoors as well as outdoors and that being outdoors shall give the children the opportunity to play in a planned and natural environment. The purpose of the study is to discover if, and how the circle time as a planned activity, differs if it is indoors or outdoors. The purpose is also to see how the form and contents of the circle times outdoors, encourage childrens' participation and influence.   Data collection methods are: video recording/observation using a digital video camera and feedback on videotaped observation – interviews with teachers in the form of talk about subjects based on the videotaped circle time context. In the study participated two teachers, who are working in preschool with 3-5 year old childrens'.   The result shows that the circle times indoors and outdoors have similarities when it comes to form, the teachers' attitude and the childrens' influence. It´s clear that the difference that the result shows, deals with teachers different ways to work with circle times and not their ways to use the many encourages that the outdoor environment offers. The childrens' chances to influence doesn't depend on if the circle time is indoors or outdoors. In which extent and in which way the children can influence the contents of the circle times is depending to teachers’ different attitudes and the sight on childrens' learning.

Studien syftar till att ge kunskaper om samlingen i förskolan. Utgångspunkten för studien är lärares uppfattningar om samlingens funktion i förskolan och vilken innebörd den har för dem. Frågeställningarna formulerades som Vilken funktion fyller samlingen i förskolans vardag? samt Vilken innebörd har samlingen för lärare?För att kunna ta reda på lärares uppfattningar om samlingen användes en kvalitativ forskningsmetod med intervjuer som teknik. Från två förskolor valdes sex lärare med olika utbildningar, val av förskolor och lärare grundar sig på bekvämlighetsurval. Resultatet visar att samlingens funktion har två innebörder dels som ett fenomen, dels som en arbetsform. Samling som ett fenomen visar att lärarna beskriver samlingen som ”något” där innehållet är i fokus, till exempel att samlingen har en social funktion där gruppen stärks. Resultatet visar också att samlingen beskrivs som en arbetsform för lärarna där syftet är att vidga synen på samlingen och få kunskap om barnen som deltar. Efter genomförd samling kan lärarna reflektera över sig själva och sina insatser. / The study aims to give deeper knowledge about the circle time in preschool. The studys starting point is teachers understandings about the function of circle time in preschool and what meaning it has for them. The questions of issue in the study are: What function does the circle time have in preschool? and What meaning have the circle time for teachers?To find out more about teachers' understanding about the circle time, a qualitative method with the interview technique was used. Six teachers with various educations from two preschools was asked to participate, choice of preschools and teachers is based on convenience. The result of the study is that the circle time has two meanings, partly as a phenomenon, partly as a working method. Circle time as a phenomenon shows that the teachers describe the circle time as “something” with focus on the content, for example that the circle time has a social function where the group is strengthen. The result shows that the circle time is a working method that teachers use to widen their view on the circle time and to get knowledge about the children that participate. The circle time gives teachers opportunity to afterwards consider their role and the activity itself.

Recently, various approximate design problems for low-degree trigonometric regression models on a partial circle have been solved. In this paper we consider approximate and exact optimal design problems for first-order trigonometric regression models without intercept on a partial circle. We investigate the intricate geometry of the non-convex exact trigonometric moment set and provide characterizations of its boundary. Building on these results we obtain a complete solution of the exact D-optimal design problem. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of observations.

Complex number is a major mathematical discovery. It can be used in many scientific fields, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory. The aim of this paper investigates the problems of algebra, trigonometry and geometry, which can be solved cleverly by the properties of complex numbers.

The sharpnose pufferfish Canthigaster valentini is widespread over the Indo-Pacific tropical coral-reef region. The social system contains territorial male, non-territorial male, and territorial female. Territorial male always occupy a fixed territory and own several territorial females forming a harem in its territory. Previous researches were concerned about field observations or laboratory tests for agonistic respondences towards self-mirror stimuli. Research on dyad interaction is rarely seen in literature. The first objective of this study focuses on the agonistic interactions between two individuals from different combinations of the abovementioned (i.e., male-male and female-female) social categories under a more spacious laboratory condition. Characteristics for intra-individual behavioral sequences were described and compared. Besides, attentions were also paid to the possible factors (e.g., sex, social status) controlling the major aggressive display (i.e., Circling). The second objective is to conduct research on the water spitting behavior of this species that I had discovered. Factors including body size, presence of food and depth of water were tested to see if any of them is the releasing factor for this behavior. The amount of information transmitted in an intra-individual behavior sequence for a male winner was highest, whereas that for a female winner was lowest. Except for Circling, FRD, FLD, and HD were the other major aggressive behaviors. The average number of aggressive behavior in an intra-individual behavior sequence and display time for male were higher than that for female. More attacks were launched in female pairs than in male pairs. For female pairs, attacks were performed by both contestants , whereas only the winners attacked its opponent in male pairs. Male tended to launch the first attack after the longest Circling but that situation did not hold for female. Circling , a agonistic behavior nor quantitatively described in other studies, can be classified into S-type and C-type. The probability of occurrences for these two types of circling were not significant different. Cycle number was higher in the early phase of an aggressive interaction in male pairs. And male spent more time in circling during an aggressive interaction. Under the experimental setting of this study, body length did not affect the outcomes of a aggressive contest. For male pairs, ratio of body high/body length played a role in determining the outcomes. Presence of food , water depth, and movement of objects above the holding aquarium were all releasing factors for the water spitting behavior and presence of food might be the most important one.

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be determined e¡Óciently by standard constrained concave programming algorithms.

<p>I läroplanen för förskolan <em>Lpfö-98</em> står det att barnen på förskolan skall ges möjligheter att vistas såväl inomhus som utomhus och att utomhusvistelsen skall ge barnen möjligheter till lek i planerad och naturmiljö. Syftet med studien är dels att upptäcka om och i så fall på vilket sätt samlingen, som en planerad aktivitetsform i förskolan, skiljer sig om den sker utomhus från om den genomförs inomhus och dels att undersöka vilket inflytande barn tilldelas på samlingar inomhus respektive utomhus.</p><p> </p><p>Studien utgår från kvalitativ ansats och bygger på videoobservationer och återkopplande intervjuer (stimulated recall). I studien ingår två lärare verksamma i förskolan och barn i åldrarna 3-5 år.</p><p> </p><p>Resultatet visar att det inte förekommer skillnad mellan samlingarna inomhus och utomhus när det gäller form, lärarens förhållningssätt och barnens inflytande. Skillnaden som resultatet visar handlar om lärarnas olika sätt att hålla i samlingen och inte om deras sätt att använda sig av möjligheter som utomhusmiljön erbjuder. Barns möjligheter till inflytande påverkas inte av att samlingen hålls vare sig inomhus eller utomhus. Vilket inflytande barnen ges och på vilket sätt de kan vara med och påverka innehållet i samlingen är beroende av lärarens förhållningssätt och synen på barns lärande.</p> / <p>In the curriculum for preschool "Lpfö-98" it states that the children attending preschool shall be given the opportunity to be both indoors as well as outdoors and that being outdoors shall give the children the opportunity to play in a planned and natural environment. The purpose of the study is to discover if, and how the circle time as a planned activity, differs if it is indoors or outdoors. The purpose is also to see how the form and contents of the circle times outdoors, encourage childrens' participation and influence.</p><p> </p><p>Data collection methods are: video recording/observation using a digital video camera and feedback on videotaped observation – interviews with teachers in the form of talk about subjects based on the videotaped circle time context. In the study participated two teachers, who are working in preschool with 3-5 year old childrens'.</p><p> </p><p>The result shows that the circle times indoors and outdoors have similarities when it comes to form, the teachers' attitude and the childrens' influence. It´s clear that the difference that the result shows, deals with teachers different ways to work with circle times and not their ways to use the many encourages that the outdoor environment offers. The childrens' chances to influence doesn't depend on if the circle time is indoors or outdoors. In which extent and in which way the children can influence the contents of the circle times is depending to teachers’ different attitudes and the sight on childrens' learning.</p>