On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Landskommunens beslutsfattande kvinnor : Om kvinnors representation i kommunalfullmäktige ochförekomst i fullmäktigeprotokoll i Kalmar länslandskommuner 1939-1951

Syftet med denna uppsats är att undersöka den kvinnliga representationen i Kalmar läns landskommuners kommunalfullmäktige från 1938 till kommunsammanslagningen 1951. Detta innefattar att söka en översikt över i vilken grad kvinnor är representerade i länets kommunalfullmäktigeförsamlingaroch att undersöka hur dessa kvinnliga ledamöter syns i protokollsmaterial i ett par kommuners fullmäktigeprotokoll. Södra Möckelby och Vickleby kommuner med relativt hög andel kvinnliga ledamöter har valts som exempel.Undersökningen av valstatistiken visar en ökning i både antal kvinnor och antal kommunalfullmäktige med kvinnlig representation under perioden. Länet ligger under riksgenomsnittet, men ökningen är ungefär densamma i relativa termer. Närläsningen av protokoll visar att kvinnor främst omnämns vid frånvaro, vid val till olika uppdrag eller vid uppföljning av dessa val. I den kommun som har en längre tradition av relativt hög kvinnlig representation märks kvinnor i fler sammanhang som förutsätter att man tar ett större utrymme på mötena. Dessa tillfällen sammanfaller med en speciell kvinnas aktiva period i fullmäktige och försvinner när den kvinnliga representationen minskar till en ensam kvinna.

La confrontation de la laideur avec la beauté dans lesromans Mercure et Attentat. Une étude sur lareprésentation de la dualité thématique laideur-beautéchez Amélie Nothomb. : "Where there is Quasimodo, there is also Esmeralda." The confrontationbetween ugliness and beauty in the novels Mercure and Attentat. Astudy on the representation of the duality beauty-ugliness in the worksof Amélie Nothomb.

This paper studies one of the recurrent topics of writing found in Amélie Nothomb’snovels: beauty and ugliness. The novels Mercure and Attentat are analyzed in detail,with respect to figures of speech used to describe the extreme physical appearance ofthe protagonists and the role of the duality beauty-ugliness in the advancement of theplot.

Representation and interpretation : textbooks, teachers, and historical culture

This article presents a study of how contemporary Swedish lower secondary school textbooks present the emergence of the Cold War and how 10 active lower secondary school history teachers interpreted a quotation that was ambiguous in relation to the general narrative in the studied Swedish textbooks, seeking to analyse textbooks both from the perspectives of content and reception. Applying a theoretical framework of uses of history, the study finds that the narratives presented in the studied textbooks are what could be called traditional in the sense that they do not acknowledge perspective and representation in history. While the interviewed teachers generally acknowledged that textbook narratives are representations of history and contingent on perspective, few teachers extended this to include how their own views affect their interpretations, suggesting an intermediary appreciation of the contextual contingency of historical narratives.

Representations of culture in EIL : Cultural representation in Swedish EFL textbooks

The English language has become an international language and is globally used as a lingua franca. Therefore, there has been a shift in English-language education toward teaching English as an interna-tional language (EIL). Teaching from the EIL paradigm means that English is seen as an international language used in communication by people from different linguistic and cultural backgrounds. As the approach to English-language education changes from the traditional native-speaker, target country context, so does the role of culture within English-language teaching. The aim of this thesis is to in-vestigate and analyse cultural representations in two Swedish EFL textbooks used in upper-secondary school to see how they correspond with the EIL paradigm. This is done by focusing on the geograph-ical origin of the cultural content as well as looking at what kinds of culture are represented in the textbooks. A content analysis of the textbooks is conducted, using Kachru’s Concentric Circles of English as the model for the analysis of the geographical origin. Horibe’s model of the three different kinds of culture in EIL is the model used for coding the second part of the analysis. The results of the analysis show that culture of target countries and "Culture as social custom" dominate the cultural content of the textbook. Thus, although there are some indications that the EIL paradigm has influ-enced the textbooks, the traditional approach to culture in language teaching still prevails in the ana-lysed textbooks. Because of the relatively small sample included in the thesis, further studies need to be conducted in order to make conclusions regarding the Swedish context as a whole.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

Integral representation with convex capacities that are squeeze of (additive) probability measures

In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternatives forrnulations of the Choquet integral (and I will extend these forrnulations to the Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.