This thesis studies the large scale dimension theory of metric spaces. Background on dimension theory is provided, including topological and asymptotic dimension, and notions of nonpositive curvature in metric spaces are reviewed. The hyperbolic dimension of Buyalo and Schroeder is surveyed. Miscellaneous new results on hyperbolic dimension are proved, including a union theorem, an estimate for central group extensions, and the vanishing of hyperbolic dimension for countable abelian groups. A new quasi-isometry invariant called weak hyperbolic dimension (abbreviated $\wdim$) is introduced and developed. Weak hyperbolic dimension is computed for a variety of metric spaces, including the fundamental computation $\wdim \Hyp^n = n-1$. An estimate is proved for (not necessarily central) group extensions. Weak dimension is used to obtain the quasi-isometric nonembedding result $\Hyp^4 \not \rightarrow \Sol \times \Sol$ and possible directions for further nonembedding applications are explored. / Thesis / Doctor of Philosophy (PhD) / Shapes and spaces are studied from the "large scale" or "far away" point of view. Various notions of dimension for such spaces are studied.

Ce mémoire a deux objectifs principaux. Premièrement de développer et interpréter les groupes de cohomologie de Hochschild de basse dimension et deuxièmement de borner la dimension cohomologique des k-algèbres par dessous; montrant que presque aucune k-algèbre commutative est quasi-libre. / The aim of this master’s thesis is two-fold. Firstly to develop and interpret the low dimensional Hochschild cohomology of a k-algebra and secondly to establish a lower bound for the Hochschild cohomological dimension of a k-algebra; showing that nearly no commutative k-algebra is quasi-free.

Die Arbeit basiert auf zwei Veröffentlichungen zur graduierten kommutativen Algebra: Thema des ersten Artikels ist die Übertragung eines klassischen Ergebnisses zur Höhe von Primidealen in Polynomringen auf allgemeine multigraduierte Ringe; einige Anwendungen für die multigraduierte Dimensionstheorie werden vorgestellt. Der zweite Artikel behandelt Hilbertreihen von Moduln über einem standard-graduierten Polynomring über einem Körper. Ausgehend von einem grundlegenden Ergebnis über gewisse formale Laurentreihen werden unter anderem die möglichen Hilbertreihen und h-Vektoren solcher Moduln charakterisiert.

Titel: Kulturens modererande effekter på sambandet mellan CSR och CFP Nivå: Examensarbete på grundnivå (kandidatexamen) i ämnet företagsekonomi. Författare: Ferdous Foroughi och Shabab Hasan Handledare: Jan Svanberg Datum: 2019 - juni Syfte: Företagens sociala ansvar (CSR) har utvecklats till ett viktigt ämne både för företag och dess intressenter. Varierande resultat gällande effekten av CSR-insatser på företagsprestanda har tidigare rapporterats. Tidigare studier undersöker och fokuserar på en liten del av CSR med många olösta teoretiska och empiriska frågor till följd av detta. Det har även visats att kultur påverkar beslutsfattandet i synnerhet i relation till CSR. Syftet är därmed att undersöka om nationell kultur har modererande effekter på sambandet mellan CSR och finansiell prestation (CFP) hos börsnoterade bolag i världen.   Metod: Studiens vetenskapsteoretiska utgångspunkt är positivism med hypotetiskt-deduktiv ansats. En kvantitativ forskningsstrategi används för 3230 börsnoterade företag med data från en femårsperiod 2013 - 2017. Datan baseras på sekundärdata inhämtad från Thomson Reuters Eikon, Världsbanken och Hofstedes kulturindex, vilken analyserats med univariata och bivariata statistiska tester samt multipla regressionsanalyser i statistikprogrammet IBM SPSS Statistics. Resultat & slutsats: Det finns ett positivt samband mellan CSR och CFP. Nationella kulturer har modererande effekter på det sambandet. Genom att använda Hofstedes kulturdimensioner har det visats att maktdistans (PD), osäkerhetsundvikande (UAI), maskulinitet (MAS) och långtidsorientering (LTO) har negativ modererande effekter, medan individualism (IDV) och tillfredsställelse (IND) har positiv modererande effekter på sambandet mellan CSP och CFP. Examensarbetets bidrag: Studien bidrar med ny kunskap för att fylla forskningsgapet gällande nationella kulturers modererande effekter på sambandet mellan CSR och finansiell prestation. Studien bidrar på ett värdefullt sätt till både tidigare teori och empiri samt lyfter fram nationella kulturers påverkande roll för företagens finansiella prestation. Förslag till vidare forskning: Det behövs flera liknande studier med andra variabler som kontrollerar och analyserar sambandet. Vidare föreslår vi också att genomföra en liknande studie som även inkluderar icke-börsnoterade bolag, för att omfatta flera länder och dessutom en längre tidsperiod än fem år för att se om nationella kulturer påverkar sambandet på ett annat sätt. Nyckelord:Corporate social responsibility, corporate social performance, corporate financial performance, nationell kultur, Hofstedes kulturdimensionsteori. / Title: Culture’s moderating effects on the relationship between CSR and CFP Level: Student thesis for Bachelor’s Degree in Business Administration Authors: Ferdous Foroughi och Shabab Hasan Supervisor: Jan Svanberg Date: 2019 - june Aim: Corporate Social Responsibility (CSR) has been developed to become an important subject for both corporates and their stakeholders. Varying results have been reported regarding the effect of CSR initiatives. Prior studies investigate and focus on a small part of CSR with following unresolved theoretical and empirical questions. It has also been shown that culture affects decision making, particularly in relation to CSR. The aim of this study is hence to investigate whether national culture has moderating effects on the relationship between CSR and corporate financial performance (CFP) among listed corporations in the world. Method: A positive research methodology has been applied with a hypothetical-deductive approach. A quantitative research strategy is used for 3230 listed corporations with data from a five-year time period 2013 - 2017. Data is based on secondary data from Thomson Reuters Eikon, World Bank and Hofstedes cultural index, which were analyzed with univariate, bivariate and multivariate analyses in the statistical software IBM SPSS Statistics. Result & Conclusion: There is a positive correlation between CSR and CFP. National cultures have moderating effects on that correlation. Using Hofstede's cultural dimensions, it has been shown that power distance (PD), uncertainty avoidance index (UAI), masculinity (MAS) and long-term orientation (LTO) have negative moderating effects, while individualism (IDV) and indulgence (IND) have positive moderating effects on the relationship between CSP and CFP. Contribution of the thesis: The study contributes with new knowledge to fill the research gap regarding national cultures’ moderating effects on the relationship between CSR and financial performance. The study contributes in an insightful way to both prior theory and empirical data and emphasizes the role of national cultures on the corporates’ financial performance. Suggestion for future research: Several similar studies are needed with other variables that control and analyze the relationship. Furthermore, we also propose to carry out a similar study that also includes non-listed companies, to include several countries and, moreover, a longer time period than five years to see if national cultures affect the relationship in another way. Keywords:Corporate social responsibility, corporate social performance, corporate financial performance, national culture, Hofstede’s cultural dimension theory.

Η κατασκευή του Peano το 1890 μιας συνεχούς απεικόνισης από ένα τμήμα επί ενός τετραγώνου έδωσε αφορμή για το πρόβλημα εάν ένα τμήμα και ένα τετράγωνο είναι ομοιόμορφα, και γενικότερα εάν ο $n$-κύβος $I^{n}$ είναι ομοιόμορφος με τον $m$-κύβο $I^{m}$ για $n\neq m$. Το πρόβλημα αυτό λύθηκε από τον Brouwer το 1911 και η μελέτη αυτού του προβλήματος οδήγησε στον ορισμό των διαστάσεων ${\rm ind}$, ${\rm Ind}$ και ${\rm dim}$ και γενικότερα στη γένεση και ανάπτυξη της Θεωρίας Διαστάσεων. Στη διατριβή αυτή ορίζονται διαστάσεις-συναρτήσεις του τύπου ${\rm ind}$, ${\rm Ind}$ και ${\rm dim}$ και αποδεικνύονται βασικές ιδιότητες της Θεωρίας Διαστάσεων (θεωρήματα υποχώρου, αθροίσματος και γινομένου) για τις συναρτήσεις αυτές. Με τη βοήθεια των συναρτήσεων αυτών ορίζονται νέες κλάσεις τοπολογικών χώρων και μελετάται για τις κλάσεις αυτές το πρόβλημα της καθολικότητας, δηλαδή της ύπαρξης ή μη καθολικών χώρων για τις κλάσεις αυτές. Ένας τοπολογικός χώρος $T$ καλείται καθολικός για μια κλάση ${\rm I\!P}$ τοπολογικών χώρων, όταν ο $T$ ανήκει στην κλάση ${\rm I\!P}$ και κάθε τοπολογικός χώρος που ανήκει στην κλάση ${\rm I\!P}$ περιέχεται τοπολογικά στο χώρο $T$. Για την ύπαρξη καθολικών στοιχείων στις κλάσεις αυτές χρησιμοποιείται η μέθοδος κατασκευής Περιεκτικών Χώρων του βιβλίου: S.D. Iliadis, Universal spaces and mappings, North-Holland Mathematics Studies, 198. Elsevier Science B.V., Amsterdam, 2005. xvi+559 pp. / Peano' s construction in 1890 of a continuous map of a segment onto a square gave rise to the problem of whether a segment and a square are homeomorphic and generally whether the cubes $I^{n}$ and $I^{m}$ are homeomorhic for $n\neq m$. This problem was solved by Brouwer in 1911 and the investigation of this problem leads to the definitions of ${\rm ind}$, ${\rm Ind}$, and ${\rm dim}$ and generally to the beginning of Dimension Theory. In this thesis we define new dimension-like functions of the type ${\rm ind}$, ${\rm Ind}$ and ${\rm dim}$ and we give basic properties of Dimension Theory (subspace theorems, sum theorems, product theorems) for these dimension-like functions. Using the introduced dimension-like functions, new classes of spaces are defined and the investigation of the universality problem for these classes is given, that is whether there exists universal space in these classes. A space $T$ is said to be universal in a class ${\rm I\!P}$ of spaces if $T\in{\rm I\!P}$ and for every $X\in{\rm I\!P}$ there exists an embedding of $X$ into $T$. For the existence of universal elements in these classes is used the construction of Containing Spaces given in book: S.D. Iliadis, Universal spaces and mappings, North-Holland Mathematics Studies, 198. Elsevier Science B.V., Amsterdam, 2005. xvi+559 pp.