Matematiska resonemang har kommit att betonas alltmer i såväl styrdokument som i internationella jämförelser mellan skolsystem. Parallellt med detta har ett allt större fokus lagts på processer i matematikundervisningen. Med utgångspunkt i de nio resonemangsprocesser som ges av Jeannotte och Kieran (2017) analyserades i denna li tteraturstudie vilka resonemangsprocesser som förekom i empiriska studier avelevers matematiska resonemangsförmåga, samt hur dessa förhöll sig till definitionerna av matematiska resonemang. Artiklar om resonemang publicerade i ledande matematikdidaktiska tidskrifter de senaste tio åren samlades in och analyserades med tematisk analys. I materialet identifierades fyra teman: det strikt logiska resonemanget, informella resonemang, imitativa och kreativa matematiska resonemang (i Lithners (2008) betydelse) samt resonemang från det generella till det specifika. Strikt logiska resonemang var starkt sammankopplade med processen formell bevisföring i både definitioner ochundersökningar. Informella resonemang karaktäriserades av processerna antagande, jämförande, klassificering, rättfärdigande och bevisföring, vilka har gemensamt att de inte är kopplade till en med nödvändighet sann matematisk utsaga. Imitativa resonemang kunde utifrån definitionen kopplas samman med processen antagande, vilket dock inte återspeglades i de exemplifierande uppgifterna. Kreativa matematiska resonemang var så brett definierade att ingen specifik process kundesägas karaktärisera dem, men var i de exemplifierande uppgifterna de enda somkrävde en generaliseringsprocess för att lösa. Slutligen föreslogs en resonemangsprocess som tar sin utgångspunkt i generella matematiska kunskaper för att generera en utsaga om ett specifikt matematiskt objekt. En dylik process förekommer inte i det teoretiska ramverket. Utifrån studiens resultat kan lärare identifiera vilka resonemangsprocesser som är karaktäristiska för olika resonemangssyner. Detta kan användas för att uppmuntra användande av de som är ändamålsenliga för särskilda kontexter och kompensera för de som saknas i en viss resonemangssyn. Därigenom kan elevernas matematiska resonemangsförmåga främjas.

This thesis presents the theoretical material needed to price European call options in the classical and rough version of the Heston model, as well as how to do this in practice from a computational perspective. The theoretical material includes an introduction to measure theory, which is then used to build the foundations of probability theory and stochastic calculus, together with more novel topics such as fractional calculus and a short exposition of the fractional Brownian motion. Moreover, parameter estimation for the respective models and computational methods to calculate options prices are also discussed. / Den här avhandlingen presenterar det nödvändiga materialet för att prissätta europeiska köpoptioner i den klassiska och grova (från engelskans "rough") versionen av Hestonmodellen, samt hur detta görs i praktiken från ett beräkningsperspektiv. Det teoretiska materialet inkluderar en introduktion till måtteori, som sedan används för att lägga grunderna för sannolikhetsteori samt stokastisk analys, tillsammans med ovanligare ämnen såsom fraktionell analys och en kort utläggning av fraktionell Brownsk rörelse. Utöver detta diskuteras även parameteruppskattning för båda modellerna samt metoder för att beräkna optionspriser i dem.

In order to create a sustainable portfolio, more sustainable assets may be chosen to be included and less sustainable assets may be chosen to be excluded from the portfolio. A potential risk that could arise as a result, is that the choice to include or exclude assets may affect the liquidity profile of the portfolio. For example if less liquid assets are included and more liquid assets are excluded. This thesis thus aims to investigate how the liquidity, but also other risks related to a stock portfolio, are related to the assets chosen to be included or excluded from the portfolio.  The main results obtained showed that the both the more and less sustainable assets on average had similar liquidity risk when considering the volume-based measure ILLIQ and the price-based measure MEC. The transaction cost-based measure the bid-ask spread, showed that the more sustainable assets had a significantly lower spread than the less sustainable, indicating that the market has a harder time agreeing on a fair price for these assets. The more sustainable assets also had a lower risk of potential losses compared to both the less sustainable and the market as a whole when considering the weekly returns, and also performed better over the considered time period. However, the less sustainable assets were shown to be slightly less volatile compared to the other assets. / För att skapa en hållbar aktieportfölj kan både mer hållbara värdepapper väljas in, och mindre hållbara väljas bort. En potentiell risk som kan uppstå på grund av dessa val, är portföljens likviditet kan påverkas om värdepapper med låg likviditet väljs in och värdepapper med hög likviditet väljs bort. Detta examensarbete syftar därför att undersöka hur likviditeten, men även andra risker som kan uppstå i en aktieportfölj, är relaterad till värdepapper som väljs in eller väljs bort ur en hållbar aktieportfölj.  Arbetets resultat visar att de både mer och mindre hållbara värdepappren hade liknande likviditetsrisk när de volym- och prisbaserade måtten ILLIQ respektive MEC undersöktes. Det transaktionskostnadsbaserade måttet bid-ask spread, visade att de mer hållbara värdepappren var mer likvida än de mindre hållbara värdepappren, då de hade lägre spridning. Detta kan tyda på att marknadsaktörer har svårare att komma överens om ett pris för de mindre hållbara än för de mer hållbara bolagen. De hållbara bolagen uppvisade även lägre risk för potentiella förluster jämfört med de mindre hållbara bolagen och marknaden som helhet, då den veckovisa avkastningen togs i beaktning. Dessutom uppvisade de hållbara bolagen även en större kumulativ avkastning över den analyserade perioden. De mindre hållbara bolagen visade sig däremot vara mindre volatila än övriga bolag.

We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of the related set, \(\{W(A_0+zA_1) : z \in \partial \mathbb{D}\}\), in a specific case. We will use the theory of envelopes to explore what the boundary looks like and we will use geometric arguments to explore the number of flat portions on the boundary. We will then make a conjecture as to the number of flat portions on the boundary of the numerical range for any \(2 \times 2\) matrices \(A_0\) and \(A_1\). We finish by providing examples of flat portions on the boundary of the numerical range when \(A_0, A_1 \in M_n(\mathbb{C})\), for \(3 \leq n \leq 5\).

No description available.

Power to the People: Responsible Facilitation in Co-Creative Story-Making describes and applies a tool for recording and analyzing the co-productive creation process of digital storytelling (DST) workshops to be used by project facilitators for the purposes of reflection and for developing an ethics of responsibly in story-making practices. It provides a method for analyzing digital storytelling practices that focuses on the rhetorical, dialogic, co-productive, creative story-making space rather than the finished stories or the technologies. Looking through a new media lens, this dissertation aligns the DST genre and practice in relation to alternative media broadly, and tactical media specifically, to understand DST as a resource for storytellers. This dissertation situates DST as a co-creative media process created among participants, individual storytellers, facilitators, institutions, and the audience, and discusses the inter-relationships within the workshop setting as well as in those found in the dissemination of the final digital stories. The author discusses the relationships among the storytellers and the facilitators, the other workshop participants, and the viewing audience, examining this final relationship in terms of face-to-face and digital interactions. This dissertation provides a reflexive look at the responsibility of the facilitator in co-creative digital storytelling endeavors and makes use of diverse international case studies in addition to an analysis of the author's own facilitated project, "Exploring Our Information Diets," as examples. The author argues that co-creative storymaking facilitators should interpret their roles within the collaborative creation process to ensure that responsible facilitation practices based in "witnessing" guide the storytelling process, and create an environment that treats participants as subjects with the ability to respond to the world.

In Kecskemet, Hungary, three small colleges are discussing plans to form a new university and implement some of their courses using distance education technologies, if political and economic conditions are favorable. The purpose of this case study was to answer some basic questions about: (1) the accessibility to 74 different technologies which could be used in the planning and implementation of distance education programs, (2) the knowledge of the planners about these technologies, and (3) their experience using them. Planners were selected by respective college rectors as: ·Horticulture College (N=16), Mechanical Engineering and Automation College (N-16), Teacher Training College (N=7). The planners' selections were based on the assumption that they would likely be used in the development and implementation of future distance education programs. No other conditions were set for their selection in the hopes that the most natural conditions might be replicated, i.e., decisions for program planning and implementation ultimately rest with administrators' decisions. From the analysis of both individual and group data, it was determined that (1) the Horticulture and Mechanical Engineering and Automation Colleges were roughly equivalent in accessibility to and experience with the technologies surveyed, (2) the Mechanical Engineering and Automation College had more knowledge of the technologies than the other two colleges, (3) the Teacher Training and Horticulture Colleges had equal knowledge of these technologies, (4) the Teacher Training College had less accessibility to and experience with these technologies than the other two colleges, (5) as individuals, surveyed respondents possessed definite use and knowledge strengths and weaknesses, and (6) there was significant accessibility to many of these technologies outside of the three colleges that should be pursued. When final planning begins, it will be useful to look at table details rather than broader conclusions. In Tables 1-100 can be found: accessibility, knowledge and experience strengths and weaknesses (for both individuals and groups), internal and - external accessibilities, i.e., details which can be used to maximize networking and develop required staff and faculty training programs. Respondents' comments to open-ended questions, found in Tables 101-106, ask about: the potential use of distance education in their work assignments, colleges, geographic areas and all work assignments, their perceptions of the current degree of support for distance education, the political influence on distance education in Hungary, and the biggest barriers to implementing education in their schools. Also included are researcher reactions to some of these comments and ideas for overcoming some difficulties.

Speech is a process, yet studies in human communication generally examine speech as a product. Rather than studying the decisions employed in the construction and reception of messages, most research in speech focuses upon evaluating communication products. This study represents an effort to build communication theory within a different paradigmatic perspective, employing ethnographic interview method for the purpose of generating theory. The purpose of this study was to examine the composing processes of six successful student speakers as they prepared formal public speeches. The specific strategies and methods employed were found to vary among these students and to deviate significantly from instructors' prescriptions. The study also ascertained the degree to which past communication experiences and speech training influenced the students' attitudes, beliefs and values regarding speech communication. Applications to speech education at the post-secondary level were discussed, as was the impact of the factors of communication apprehension, gender and family background. Results were reported in extensive case-studies of each student subject.

No description available.

Voronoi diagrams are partitions of a metric space into Voronoi cells according to distance from points on some set w.r.t. some distance. In this thesis we examine Voronoi diagrams of manifolds and varieties w.r.t. the Wasserstein distance from probability theory. We give some upper and lower bounds on the dimension of Voronoi cells based on the geometry of the manifolds and Wasserstein distance balls. We provide an upper bound on the number of full-dimensional Voronoi cells of algebraic varieties and show examples of the bound being tight. / Voronoi diagram är partitioner av ett metriskt rum i Voronoiceller enligt avstånd från punkter på någon mängd med avseende på ett visst mått. I den här avhandlingen undersöker vi Voronoidiagram för mångfald och varieteter med avseende på Wasserstein avstånd från sannolikhetsteori Vi ger några över och nedre gränser för dimensionen på Voronoiceller baserat på geometrin hos mångfalden och avståndsklot med Wasserstein mått. Vi presenterar en övre gräns för antalet fulldimensionella Voronoiceller för algebraiska varieteter och visar exempel på när gränsen är strikt.