This thesis makes a survey of converse theorems for Dirichlet series. A converse theo-rem gives sufficient conditions for a Dirichlet series to be the Dirichlet series attachedto a modular form. Such Dirichlet series have special properties, such as a functionalequation and an Euler product. Sometimes these properties characterize the modularform completely, i.e. they are sufficient to prove the proper transformation behaviourunder some discrete group. The problem dates back to Hecke and Weil, and has morerecently been treated by Conrey et.al. The articles surveyed are: "An extension of Hecke's converse theorem", by B. Conrey and D. Farmer "Converse theorems assuming a partial Euler product", by D. Farmer and K.Wilson "A converse theorem for ¡0(13)", by B. Conrey, D. Farmer, B. Odgers and N.Snaith The results and the proofs are described. The second article is found to contain anerror. Finally an alternative proof strategy is proposed.

Abstract The use of standard agreements can hardly be overestimated in the society of today. The amount of standard agreements should barely decrease. One of the standard agreement’s main purposes, to make the concluding of the contract more effective, strongly agrees with the companies will to accomplish fast concluding of agreements using as small resources as possible A dispute that can arise in these contexts is that dissimilar standard agreements collide. Between nations this is called Battle of Forms. It is a situation of practice which is difficult to solve through the basic rules of contract law. The aim of the essay is to bring clarity into how the legal problems concerning Battle of Forms is solved in Sweden respectively Germany. Also CISG, Unidroit and PECL’s solutions of the same problem is going to be mentioned. A critical examining of the different solutions that the system of rules has in disposal will also be done. In the context of the situation an examination will show if there is any resistance towards these. If that is the case some parts of the critic will be presented. To be able to answer my questions at issue a traditional method of legal-dogmatism has been used together with comparative strains. Sweden lacks a direct law-prescribed solution of Battle of Forms, nor is there a direct legal usage. Sweden has tried to apply the directions of 6 § AvtL on the problem, but this one suits the context badly. Besides the directions in AvtL some solution models are found which can build the foundation for a settlement. Consequently the problem remains unsolved in the Swedish legal system. Neither does Germany have a legal rule which is directly applicable. Some guidance is however given from the German law. According to the German law the settlement should be settled with The knock-out doctrine as its foundation. When harmonising is not possible one should fall back on The Last shot or optional law, it depends on the occurrence of abwehrklauseln (protection clauses). Neither has CISG directly pointed on how to solve the problem. CISG’s legal usage also advocates that The knock-out doctrine should build the foundation. What tool that should be used to fill the holes that the harmonising leaves behind is somewhat indistinct. It should be The last shot, optional law or an interpretation of article 7 about “good faith”. Unidroit and PECL state that agreed terms shall be applied. Consequently the person applying the law should practise the Knock-out doctrine. However the rules give no guidance about how the arising holes should be filled after the harmonising. Above all Swedish literature directs strong criticism towards the different solutions. The criticism is especially pointed at the lack of predictability and also at the risk of making arbitrary settlements. This of course depends on what kind of solution model that is discussed. In Germany there has been, and still is, a solution which the person applying the law can use. In Germany protection clauses has an important role of the settlement. Even in these cases criticism is directed towards the solution. However the criticism is not as hardly directed towards the lack of predictability. Instead the criticism is pointed at the unsuitability of applying the optional law in some commercial relationships. And also that the applicability of the last shot results in a “ping pong” similar situation of passing terms back and force. Also in the international world of law some criticism has been delivered that agrees with both the Swedish and the German criticism. / Sammanfattning Användningen av standardavtal kan knappast överskattas i dagens samhälle. Mängden standardavtal torde knappast avta. Ett av standardavtalets huvudsyftesyften, att effektivisera avtalsslutet, stämmer väl överens med företagens vilja att genomföra snabba avtalsslut med så liten resursåtgång som möjligt. En tvist som kan uppkomma i detta sammanhang är att olikartade standardavtal kolliderar. Detta kallas, internationellt sett, Battle of Forms. Det är en praktisk situation som med de grundläggande avtalsrättsliga reglerna är svårlöst. Syftet med uppsatsen är att bringa klarhet i hur den rättsliga problematiken kring Battle of Forms löses i Sverige respektive Tyskland. Även CISG, Unidroit och PECL’s lösningar på samma problem kommer att beröras. Det ska även göras en kritisk granskning av de olika lösningar som regelsystemen tillhandahåller. I sammanhanget ska det undersökas om det finns motstånd till dessa och om så är fallet ska delar av kritiken presenteras. För att kunna besvara mina frågeställningar, har det huvudsakligen, använts en traditionell rättsdogmatisk metod med komparativa inslag. Sverige saknar en direkt lagstadgad lösning på Battle of Forms, inte heller finns någon direkt rättpraxis. Sverige har försökt applicera bestämmelserna i 6 § AvtL på problemet, men denna passar illa i sammanhanget. Utöver bestämmelsen i AvtL återfinns det ett antal lösningsmodeller som kan läggas till grund för ett avgörande. Problemet är således fortfarande olöst i svensk rätt. Inte heller Tyskland har en rättsregel som är direkt tillämplig. Den tyska lagen ger dock viss vägledning. Avgörandet enligt tysk rätt ska ske med The knock-out doctrine som grund. När harmonisering inte är möjlig ska rättstillämparen falla tillbaka på The Last shot eller dispositiv rätt, det beror på förekomsten av abwehrklauseln (skyddsklausuler). Inte heller CISG har direkt reglerat hur problemet ska lösas. Även rättspraxis i CISG förespråkar att The knock-out doctrine ska ligga till grund. Vilket redskap som ska hjälpa till att fylla de luckor som harmoniseringen efterlämnar är något oklart. Det torde vara The last shot, dipositiv rätt eller en tolkning av artikel 7 om ”good faith”. Unidroit och PECL anger att överrensstämmande villkor ska tillämpas. Således ska rättstillämparen praktisera The knock-out doctrine. Reglerna ger dock ingen vägledning om hur luckorna som uppstår efter harmoniseringen ska fyllas. Det finns speciellt i den svenska litteraturen en stark kritik mot de olika lösningarna. Framförallt riktas kritiken mot bristande förutsebarhet och även mot risken för godtyckliga avgöranden. Det beror givetvis på vilken lösningsmodell som diskuteras. I Tyskland har det funnits och finns en lösning som rättstillämparen har att tillämpa. Skyddsklausuler har i Tyskland stor betydelse för avgörandet. Det finns även i dessa fall en kritik mot lösningen. Den riktar dock inte lika hård kritik mot bristande förutsebarhet. Kritiken riktas istället mot att tillämpningen av dispositiv rätt i vissa kommersiella förhållanden kan passa väldigt illa, samt att tillämpningen av The last shot leder till ett ”ping-pong” liknande översändande av villkor. Även i den internationella rättsvetenskapliga världen har viss kritik framkommit som stämmer överens med den svenska och tyska kritiken

Syftet med denna kvalitativa studie var att undersöka vilken inverkan boendesegregation har på ungdomars utbildningsmöjligheter. Studien innefattade 15 vetenskapliga artiklar och rapporter som analyserades med hjälp av systemteori och Bourdieus teori om kapitalformer. Resultaten visade att den sociala omgivningen är en viktig faktor för ungdomarnas studieresultat. Bostadsområdets vuxna är viktiga som rollmodeller. Normer och beteenden i närmaste omgivningen spelar en viktig roll i ungdomarnas socialisering. En avgörande del i hur ungdomarna presterar och väljer skola är hur mycket och vilka olika former av kapital de har med sig sedan tidigare. Med ett sämre kapital minskar möjligheterna att införskaffa de resurser som krävs för att välja bort skolan i närområdet och gå till en resursstarkare skola. Slutsatsen visar att ungdomars studieresultat påverkas av vilka system de ingår i och hur starkt kapital de har. Var och hur man bor inverkar även på ungdomars möjligheter till framtida studier och skolval. / The aim of this qualitative study was to examine the impact of residential segregation on young people´s educational opportunities. The study included 15 scientific articles and reports which were analyzed by using system theory and Bourdieu´s theory of capital forms. The results showed that the social environment is an imortant factor in explaining the academic performance of young people. The adults in the residential area are important as role models. Norms and behaviors in the immediate environment play a crucial role in the socialization of young people. A determining factor of young people´s academic performance and on their school choice is which forms of capital forms and resources they bring from their childhood. With less capital, it also follows that they can not acquire the resources that are necessary to choose a resourceful school instead of the school in the neighbourhood. The conclusion shows that young people´s school results are affected by the system they are part of and how strong capital resources they bring. Where and how you live, do have an impact on young people’s opportunities for further studies.

Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known. Hooley derived a conjectural formula for the average of class numbers of real quadratic fields. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, i.e., the average of an arbitrary real power of class numbers. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work. In the final chapter we consider the case of the -1 power from a numerical point of view and develop an efficient algorithm to compute the average for the -1 class number power without computing class numbers.

Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known. Hooley derived a conjectural formula for the average of class numbers of real quadratic fields. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, i.e., the average of an arbitrary real power of class numbers. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work. In the final chapter we consider the case of the -1 power from a numerical point of view and develop an efficient algorithm to compute the average for the -1 class number power without computing class numbers.

This thesis consists of six chapters and deals with four topics related to De Rham Theory on semialgebraic sets. The first topic deals with L-infinity cohomology on semialgebraic sets. We introduce smooth L-infinity differential forms on a singular (semialgebraic) space X in Rn. Roughly speaking, a smooth L-infinity differential form is a collection of smooth forms on disjoint smooth subsets (stratification) of X with matching tangential components on the adjacent strata and of bounded size (in the metric induced from Rn). We identify the singular homology of X as the homology of the chain complex generated by semialgebraic singular simplices, i.e. continuous semialgebraic maps from the standard simplex into X. Singular cohomology of X is defined as the homology of the Hom dual to the chain complex of the singular chains. Finally, we prove a De Rham type theorem establishing a natural isomorphism between the singular cohomology and the cohomology of smooth L-infinity forms. The second topic is a construction of a Lipschitz deformation retraction on a neighborhood of a point in a semialgebraic set with estimates on its derivatives. Such a deformation retraction is the key to the results of the first and the third topics. The third topic is related to Poincare inequality on a semialgebraic set. We study Poincare type Lp inequality for differential forms on a compact semialgebraic subset of Rn for p >> 1. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives from the second topic and then we extend it to a global inequality by employing a technique developed in the appendix. As a consequence we obtain an isomorphism between Lp cohomology and singular cohomology of a normal compact semialgebraic set. The final topic is in the appendix. It deals with an explicit proof of Poincare type inequality for differential forms on compact manifolds. We prove the latter inequality by means of a constructive 'globalization' method of a local Poincare inequality on convex sets. The appendix serves as a model case for the results of the third topic in Chapter 5.

Offering business solutions instead of selling products has been identified by many firms as a strategy to fight against price pressure through commoditisation, to strengthen relationships with customers, and to increase ‘share of wallet’. Yet, three out of four companies selling business solutions fail to see a sustainable economic impact (Johansson et al., 2003). One approach to understanding how business solution suppliers could change this situation is to develop an understanding of the life cycle of business solutions, from idea generation to redeployment. This systematic review examines how the literature conceptualises the development, deployment and redeployment of business solutions. It systematically identifies and then analyses 31 scholarly articles contributing to our knowledge on this issue. The review discusses the literature within the framework of four aspects. Firstly, the review proposes the processes and phases of the development and deployment of business solutions. Secondly, it presents the components of the redeployment of business solutions. Thirdly, it provides information on the actors involved in the development, deployment, and redeployment of business solutions, and, fourthly, it discusses the interaction forms of these actors. The discussion shows that evidence in relation to the conceptualisation of the development, deployment, and redeployment of business solutions remains at a superficial, tentative and inconclusive level. The major limitations of the extant literature relate to the studies’ context-specificity, their lack of theoretical underpinning, and their deficiency of including actors of the supplier and/or customer network in the empirical investigation even though there is evidence that they play a role in the development, deployment, and redeployment of business solutions. Based on the limitations identified, the study suggests opportunities of further research.

This thesis consists of six chapters and deals with four topics related to De Rham Theory on semialgebraic sets. The first topic deals with L-infinity cohomology on semialgebraic sets. We introduce smooth L-infinity differential forms on a singular (semialgebraic) space X in Rn. Roughly speaking, a smooth L-infinity differential form is a collection of smooth forms on disjoint smooth subsets (stratification) of X with matching tangential components on the adjacent strata and of bounded size (in the metric induced from Rn). We identify the singular homology of X as the homology of the chain complex generated by semialgebraic singular simplices, i.e. continuous semialgebraic maps from the standard simplex into X. Singular cohomology of X is defined as the homology of the Hom dual to the chain complex of the singular chains. Finally, we prove a De Rham type theorem establishing a natural isomorphism between the singular cohomology and the cohomology of smooth L-infinity forms. The second topic is a construction of a Lipschitz deformation retraction on a neighborhood of a point in a semialgebraic set with estimates on its derivatives. Such a deformation retraction is the key to the results of the first and the third topics. The third topic is related to Poincare inequality on a semialgebraic set. We study Poincare type Lp inequality for differential forms on a compact semialgebraic subset of Rn for p >> 1. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives from the second topic and then we extend it to a global inequality by employing a technique developed in the appendix. As a consequence we obtain an isomorphism between Lp cohomology and singular cohomology of a normal compact semialgebraic set. The final topic is in the appendix. It deals with an explicit proof of Poincare type inequality for differential forms on compact manifolds. We prove the latter inequality by means of a constructive 'globalization' method of a local Poincare inequality on convex sets. The appendix serves as a model case for the results of the third topic in Chapter 5.

És difícil dibuixar una frontera, dins la Teoria de Sistemas Dinàmics, entre lleis de conservació i simetries doncs, sovint, les seves característiques es confonen. Un clar exemple d'aquest fenómen el constitueixen els sistemes Hamiltonians i els sistemes reversibles.Breument, un sistema dinàmic es diu temps-reversible (o, per nosaltres, simplement reversible) si és invariant sota l'acció d'un difeomorfisme involutiu a l'espai i una inversió en el sentit del temps. és en aquest marc on cal situar aquesta memòria. Concretament, ens centrem en dos punts molt particulars: la Teoria de Formes Normals i el fenómen del trencament de separatrius, tots dos introduïts per Poincaré a la seva tesi (1890).Respecte al primer d'aquests punts, en aquesta tesi s'introdueix el concepte de Pseudo Forma Normal (breument PNF), inspirat en idees d'en Moser, i que permet transformar, sota certes hipotesis, un sistema analític en un d'equivalent d'aspecte el més simple possible. Aquesta PNF és una generalització de la coneguda Forma Normal de Birkhoff amb la qual coincideix si el sistema considerat és Hamiltonià o reversible. Com a conseqüència, s'obté, en determinats casos, l'equivalència local entre aquests dos tipus de sistemes. Aquesta PNF pot esdevenir una eina útil per estudiar la dinàmica d'un sistema analític a l'entorn d'un equilibri (un punt, una òrbita periòdica o un tor).El segon punt, l'escissió de separatrius, fa referència a l'intersecció transversal de varietats invariants procedent del trencament d'una certa connexió homoclínica a l'afegir al sistema una petita pertorbació. Un dels motius d'interés sobre aquest fenòmen és que és un dels principals causants de comportament estocàstic en sistemes Hamiltonians.Un problema relacionat amb aquest trencament de separatrius és el de mesurar-lo, sigui a partir del càlcul de l'angle amb el que es troben aquestes varietats per primer cop, per l'àrea que tanquen entre elles, etc. El mètode habitualment utilitzat per a estimar-lo és l'anomenat mètode de Poincaré-Melnikov. Malhauradament, si la pertorbació és ràpidament oscil-latòria els termes que proporciona aquest mètode són exponencialment petits en el paràmetre pertorbador, fet que dificulta el seu càlcul. En aquesta tesi s'ha demostrat, tal i com passa en el cas Hamiltonià, que en el cas d'un sistema reversible, respecte a una involució lineal, 2-dimensional i pertorbat de manera ràpidament periòdica i reversible, el mètode de Poincaré-Melnikov és correcte i dóna en primer ordre l'anomenada funció de Melnikov. / It is difficult, in the Theory of Dynamical Systems, to draw a boundary line between conservation laws and symmetries because often their effects on the dynamics are very similar. This is the case of the Hamiltonian and the Reversible systems.Briefly, a dynamical system is called time-reversible (or, simply, reversible) if it is invariant under the action of an involutive spatial diffeomorphism and a reversion in time's arrow. This is the frame where this work must be placed. Precisely, we focus our attention in two particular points: the Theory of Normal Forms and the phenomenon of the splitting of separatrices, both introduced by Poincare in his thesis (1890).Regarding the first one of this topics, we introduce the concept of Pseudo-normal Form (PNF in short). It comes from ideas of Moser and allows to transform, under suitable conditions, an analytic system around an equilibrium in another equivalent one having a quite simple form. This PNF is a generalization of the celebrated Birkhoff Normal Form and both coincide if the system is Hamiltonian or reversible. Consequently, the local equivalence between both types of systems is derived in some cases. This PNF can become a useful tool to study the dynamics of an analytic system in a neighborhood of an equilibrium (a fixed point, a periodic orbit or a torus).The second topic, the splitting of separatrices, is related to the transversal intersection of invariant manifolds derived from the splitting of a given homoclinic connection when some small perturbation is considered. One of the reasons that makes this phenomenon interesting is that it seems to be one of the main causes of the stochastic behavior in Hamiltonian systems.One problem related to this splitting of separatrices becomes to measure it, studying, for instance, some angle the form when they meet for the first time, the area of the first lobe, etc. The standard method to estimate this size is the celebrated Poincaré-Melnikov method. Unfortunately, if the perturbation oscillates rapidly the terms provided by this method are exponentially small in the perturbation parameter, and this fact makes this computation more involved. In this work we prove, like it happens in the Hamiltonian case, that in the case of a 2-dimensional analytic reversible system (reversible with respect to a linear spatial involution) perturbed by a rapidly periodic reversible perturbation, the Poincaré-Melnikov method works and it provides, at first order, the well known Melnikov Function.

This study concerns the effects of public school redistricting on communities in Atlanta. It is based upon interviews with people in two neighborhoods which are part of the Atlanta Public Schools (APS) system directly affected by redistricting. All schools slated to close are located in low-income, minority areas and serve similar populations. Of the ten schools selected for closing, three were saved during the final APS board meeting in April 2012, and will remain open. I spoke with people who reside in a neighborhood where a local school is slated to close, as well as those in an area where a school was saved from closing. I asked informants why they felt their schools were identified for closure and how they responded to the threat of closing. I learned that both communities organized to save their schools but with different results based on available forms of social and cultural capital.