Esta pesquisa elaborou e descreveu situaÃÃes didÃticas sobre Integrais ImprÃprias ou Generalizadas, tendo como suporte a SequÃncia Fedathi que utilizamos como metodologia de ensino e a Engenharia DidÃtica como metodologia de pesquisa. Vale ressaltar que desta empregamos apenas duas fases (anÃlise preliminar e anÃlise a posteriori) de modo completo. AlÃm de usar o software GeoGebra como ferramenta para elaborar e descrever situaÃÃes didÃticas, tambÃm realizamos anÃlise de conteÃdo na perspectiva de Bardin (1977, 2009) dos livros de Guidorizzi (1998) e Stewart (2011) sobre Integrais ImprÃprias. Por ser um mestrado profissional produzimos como produto educacional, vÃdeoaulas e um blog para divulgaÃÃo de materiais sobre Integrais ImprÃprias. Essa pesquisa apontou que o ensino e aprendizagem das Integrais ImprÃprias pode ter como aliado Ãs novas tecnologias, fazendo uso da geometria dinÃmica sem perder o rigor matemÃtico, e que os alunos de instituiÃÃes superiores, principalmente os que tÃm o CÃlculo II como disciplina em alguns cursos como MatemÃtica e as Engenharias podem ganhar em metodologias e ferramentas de ensino e aprendizagem, com isso terÃamos uma melhoria no ensino da disciplina de CÃlculo II, em especial o conteÃdo de Integrais ImprÃprias. / This research developed and described didactic situations on Improper integrals or generalized, supported the Fedathi sequence that we use as teaching methodology and the Didactic Engineering as a research methodology. Note that this only employ two phases (preliminary analysis and a posteriori analysis) comprehensively. In addition to using GeoGebra software as a tool to develop and report didactic situations, we also content analysis from the perspective of Bardin (1977, 2009) of books Guidorizzi (1998) and Stewart (2011) on Improper integrals. Being a professional master produced as an educational product, video classes and a blog to disseminate materials on Improper integrals. This research pointed out that the teaching and learning of the Improper integral may have as an ally to new technologies, using the dynamic geometry without losing the mathematical rigor, and that students of higher institutions, especially those with the Calculus II as a discipline in some courses as Mathematics and Engineering can earn in methodologies and teaching and learning tools, with that we would have an improvement in the teaching of the discipline of Calculus II, in particular the content of the Improper integral.

This paper consists of a discussion of the properties and applications of certain improper integrals, namely the gamma function and the beta function. There are also specific examples of application of these functions in certain fields of applied science.

In the last decade, wireless applications have witnessed a tremendous growth. This can be envisioned in the surge of smart devices which became almost in everyone's possession, demand for high speed connection and the internet of things (IoT) along with its enabling technologies. Hence, the multiuser interference became the main limiting factor in wireless communications. Moreover, just like diamonds and emeralds, the electromagnetic spectrum is limited and precious. Therefore, the high data rate application may not be satisfied by our current technologies. In order to solve this spectrum scarcity problem, researchers have steered their focus to develop new techniques such as cognitive radio (CR) and in-band full-duplex (FD). However, these systems suffer from the interference problem that can dramatically impede their quality-of-service (QoS). Therefore, investigating communication techniques/systems that can relieve the interference adverse signature becomes imperative. Improper Gaussian signaling (IGS) has been recently shown to outperform the traditional proper Gaussian signaling (PGS) in several interference-limited systems. In this thesis, we use IGS in order to mitigate the interference issue in three different communication settings. IGS has the ability to control the interference signal dimension, and hence, it can be considered as one form of interference alignment. In the first part, we investigate an underlay CR system with in-band FD primary users (PUs) and one-way communication for the secondary user (SU). IGS is employed to alleviate the interference introduced by the SU on the PUs. First, we derive a closed form expression and an upper bound for the SU and PUs outage probabilities, respectively. Second, we optimize the SU signal parameters, represented in its power and the circularity coefficient, to achieve the design objectives of the SU while satisfying certain QoS constraints for the PU under instantaneous, average and partial channel state information (CSI). Finally, we provide some numerical results that demonstrate the advantages that can be reaped by using IGS to access the spectrum of the FD PUs. Specifically, with the existence of week PU direct channels and/or strong SU interference channels, PGS tends to use less transmit power while IGS uses more power along with increasing the signal impropriety. Part 2 studies the potential employment of IGS in FD cooperative settings with non-negligible residual self-interference (RSI). In this part, IGS is used in an attempt to alleviate the RSI adverse effect in full-duplex relaying (FDR). To this end, we derive a tight upper bound expression for the end-to-end outage probability in terms of the relay signal parameters. We further show that the derived upper bound is either monotonic or unimodal in the relay's circularity coefficient. This result allows for easily locating the global optimal point using known numerical methods. Based on the analysis, IGS allows FDR systems to operate even with high RSI. It is shown that, while the communication totally fails with PGS as the RSI increases, the IGS outage probability approaches a fixed value that depends on the channel statistics and target rate. The obtained results show that IGS can leverage higher relay power budgets than PGS to improve the performance, meanwhile it relieves its RSI impact via tuning the signal impropriety. In part 3, we investigate the potential benefits of adopting IGS in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no CSI is available at the source. In this regard, we assume that the two relays use IGS and the source uses PGS. Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.

<p>U disertaciji se na bazi redefinisanih pojmova kako prostornog (inte-gralnog) izvoda tako i ostatka (rezidijuma) kompleksnih funkcija defini&scaron;e pojam totalne vrednosti nesvojstvenih integrala. Ova redefinisana vrednost integrala iskori&scaron;ćcena je za dokaz teoreme, koja je uop&scaron;tenje Dirihlejeve teoreme o razvoju realnih funkcija u Furijeov trigonometrijski red.</p> / <p>In this thesis we define the notion of the total value of improper integrals based on the redefined notions of the spatial (integral) derivative and the residue of complex functions. This redefined integrals is used to prove the theorem which is generalization of Dirichlet theorem on the expansion of real valued functions into Fourier trigonometric series.</p>

網際網路的規範向來具有爭議。監督團體與立法機關往往基於保護兒童及青少年免於受到不當資訊的影響，對於網際網路散佈的內容要求相當程度的管制。然而，此類規範經常導致主張言論自由亦應延伸至網際網路媒體的民權團體多所詬病。在回顧我國先前對於網際網路的規範以及相關案例之後，本研究綜合各界論點探討未來寬頻影音內容服務網站可行的規範之道。 截至目前為止，關於網際網路內容規範相關研究已成篇累牘。現行最適宜的解決之道紛紛指向採用安裝過濾軟體以及實施網站分級制度。民國九十三年四月二十六日行政院新聞局發布「電腦網路內容分級處理辦法」，希冀藉以解決目前規範網際網路缺乏法源以及分級制度採行標準的問題。但亂象叢生的網際網路，似乎無法在朝夕之間產生良善的轉變。例如，影音內容服務業者經營色情影音服務；利用寬頻影音網路視訊交友而進行色情交易的事件；利用影音聊天室散佈性交易訊息；抑或是學術網站的自律不嚴謹，引發種種批評與討論等。同時，該辦法目前僅針對「網站」進行分級，尚未落實至「網頁」分級的程度，對於寬頻影音內容的管理更是付之闕如。 針對網際網路不當資訊以及缺乏法令管制所呈現的困境，本研究目的包括： 一、探討國內寬頻影音內容服務網站各類不當資訊； 二、探討國內對於寬頻影音內容服務網站現行規範法規及其不足之處； 三、探討國際間對於寬頻影音內容服務不當資訊現行管制規範形式； 四、探討國內未來對於寬頻影音內容不當資訊具可行性之管制規範形式； 五、提供國內寬頻影音內容服務業者、公益媒體監督團體及政府行政機關未來規範不當資訊之建議。 為兼顧網際網路的自由與發展，本文綜合文獻分析及深度訪談資料，臚列以下建議：一、業者再改善身份認證系統及收費機制；二、政府妥善拿捏輔佐角色；三、規劃網際網路分級制度實施辦法相關配套法令；四、教育體制配合輔導健全的網路素養；五、落實網際網路舉報不法網站業者熱線。

Improper transposition of an EU Directive is a phenomenon that occurs in quite an appreciable amount and in the performance of duty of individual Member States this represents a relatively common, although undesirable situation. The submitted diploma thesis deals with this issue within the Czech Republic in the light of individual proceedings for the failure to fulfill an obligation resulting from EU Treaties, which were concucted against the Czech Republic. This thesis is divided into six chapters, based on the theoretical foundations that are subsequently applied in practical examples. The first chapter presents the theoretical center of gravity for embedding the concept of primary and secondary law with emphasis on the EU Directive, while the this EU legislation is analyzed both in general terms and in terms of its structure. The following second chapter then gives an explanation to the issue of proper and improper transposition of an EU Directive and individual consequences that are associated with improper transposition of an EU Directive. The practical part starts from the third chapter, which contains analytical summarization of the all proceedings against the Czech Republic, which were conducted because of improper transposition of an EU Directive and ended with a judgement, while the fourth chapter...

Le Théorème des Quatre Couleurs, conjecturé en 1852 et prouvé en 1976, est à l'origine de l'étude des partitions des sommets de graphes peu denses. Il affirme que toute carte plane peut être coloriée avec au plus quatre couleurs différentes, de telle manière que deux régions qui partagent une frontière aient des couleurs différentes. Énoncé en terme de théorie des graphes, cela veut dire que tout graphe planaire, c'est à dire tout graphe qui peut être représenté dans le plan sans que deux arêtes ne se croisent, peut voir son ensemble de sommets partitionné en quatre ensembles tels que chacun de ces ensembles ne contient pas les deux extrémités d'une même arête. Une telle partition est appelée une coloration propre en quatre couleurs. Dans cette thèse, on s'intéresse à l'étude de la structure des graphes peu denses, selon différentes notions de densité. D'une part, on étudie les graphes planaires sans petits cycles, et d'autre part les graphes dont tous les sous-graphes ont un degré moyen peu élevé. Pour ces classes de graphes, on recherche tout d'abord le plus petit nombre de sommets à retirer pour obtenir une forêt, c'est à dire un graphe sans cycles. Cela peut être vu comme une partition des sommets du graphe en un ensemble induisant une forêt et un ensemble de sommets contenant au plus une fraction donnée des sommets du graphe. La motivation première de cette étude est une conjecture d'Albertson et Berman (1976) comme quoi tout graphe planaire admettrait une telle partition où la forêt contient au moins la moitié des sommets du graphe. Dans un second temps, on s'intéresse aux partitions des sommets de ces graphes en deux ensembles, tels que les sous-graphes induits par ces deux ensembles ont des propriétés particulières. Par exemple, ces sous-graphes peuvent être des graphes sans arêtes, des forêts, des graphes de degré borné, ou des graphes dont les composantes connexes ont un nombre borné de sommets. Ces partitions des sommets sont des extensions de la notion de coloration propre de graphe.On montre, pour différentes classes de graphes peu denses, que tous les graphes de ces classes admettent de telles partitions. On s'intéresse également aux aspect algorithmiques de la construction de telles partitions. / The study of vertex partitions of planar graphs was initiated by the Four Colour Theorem, which was conjectured in 1852, and proven in 1976. According to that theorem, one can colour the regions of any planar map by using only four colours, in such a way that any two regions sharing a border have distinct colours. In terms of graph theory, it can be reformulated this way: the vertex set of every planar graph, i.e. every graph that can be represented in the plane such that edges do not cross, can be partitioned into four sets such that no edge has its two endpoints in the same set. Such a partition is called a proper colouring of the graph.In this thesis, we look into the structure of sparse graphs, according to several notions of sparsity. On the one hand, we consider planar graphs with no small cycles, and on the other hand, we consider the graphs where every subgraph has bounded average degree.For these classes of graphs, we first look for the smallest number of vertices that can be removed such that the remaining graph is a forest, that is a graph with no cycles. That can be seen as a partition of the vertices of the graph into a set inducing a forest and a set with a bounded fraction of the vertices of the graph. The main motivation for this study is a the Albertson and Berman Conjecture (1976), which states that every planar graph admits an induced forest containing at least one half of its vertices.We also look into vertex partition of sparse graphs into two sets both inducing a subgraph with some specific prescribed properties. Exemples of such properties can be that they have no edges, or no cycles, that they have bounded degree, or that they have bounded components. These vertex partitions generalise the notion of proper colouring. We show, for different classes of sparse graphs, that every graph in those classes have some specific vertex partition. We also look into algorithmic aspects of these partitions.

Este texto trata do Método dos Elementos de Contorno Dual empregando a solução fundamental anisotrópica. As integrais impróprias que surgem nesta formulação são regularizadas pela técnica da subtração de singularidade. Aplica-se a transformação de coordenadas auto-adaptativa de Telles para a avaliação das integrais quase-singulares. Apresenta-se o programa computacional desenvolvido utilizando os paradigmas da programação orientada a objetos e processamento em paralelo. Foram analisados diversos problemas e os resultados obtidos comparados àqueles da solução analítica. Os resultados alcançados mostraram-se satisfatórios validando a formulação proposta. / This text deals with the Dual Boundary Element Formulation Method using the fundamental solution for anisotropic body. The improper integrals that arise in this formulation are regularized using the singularity subtraction technique. The self-adaptive coordinate transformation developed by Telles is used to evaluate the near-singular integrals. The computer program developed using the paradigms of object-oriented programming and parallel processing is presented. Several problems were analyzed and its results compared with those proposed by analytical solution. The results achieved were satisfactory therefore validating the proposed formulation.

Companies use different forms of representation to promote business negotiations. The regulations for the right to deduction for the cost of representation are stated in Chapter 16 section 2 of the Swedish Income Tax Act (IL). According to the law there must be an im-mediate connection between the expenditure and the business practice and the claimed de-duction must be reasonable. The Swedish tax authority publishes general recommendations regarding representation which are used as guidelines for the tax payer to follow. The gen-eral provision about tax deduction can be found in Chapter 16 section 1 of the Swedish In-come Tax Act (IL), stating that expenses to acquire or retain income shall be deductible. Expenses that have an immediate connection with incomes count as tax deductible ex-penses in the business practice. The provision about deductible representation is in this manner more restrictive than the general principle in Chapter 16 section 1 of the Swedish Income Tax Act (IL). Taxation law is complicated and it may demand interpretation of the regulations. When gaps are present in regulations, certain interpretation methods and pro-cedures can be applied in order to increase the foreseeability for the tax payer. The Swedish tax authority’s general recommendation contributes to an increased foreseeability and con-formity since their instructions play a significant role regarding deduction for representa-tion. Personal living costs are not deductible according to Chapter 9 section 2 of the Swedish Income Tax Act (IL). The provision about representation in Chapter 16 section 2 of the Swedish Income Tax Act (IL) is not applicable on personal living costs since a strict de-mand for an immediate connection between the expenditure and business practices is re-quired. What is considered as an immediate connection between the expenditure and busi-ness practices is a matter of judgement on the basis of the circumstances in each individual case. The circumstances that need to be considered are differences between companies, type of movement, the form of representation and at how many occasions representation has occurred. Representation can adopt the form of bribes or other improper rewards as it lies in the na-ture of representation to function as an economic lubricant. According to Chapter 9 sec-tion 10 of the Swedish Income Tax Act (IL), expenses for bribes or other improper re-wards are not deductible. The meaning of improper is not further defined in the taxation regulations. Case law emanating from the criminal regulations in Chapter 17 section 7 and Chapter 20 section 2 of the Swedish Penal Code (BrB) may instead be used to clarify this conception. A judgement of all the circumstances in each individual case must be made to determine what is considered as improper. / Företag använder sig av olika former av representation för att främja affärsförhandlingar. Reglerna för rätt till avdrag för representation finns i 16 kap. 2 § IL. Enligt lagrummet skall det finnas ett omedelbart samband mellan utgiften och näringsverksamheten samt att det yrkade avdraget skall vara skäligt. SKV ger ut allmänna råd rörande representation vilka skall vara vägledande. Den allmänna bestämmelsen om avdragsrätt i 16 kap. 1 § IL anger att utgifter för att förvärva eller bibehålla inkomster skall vara avdragsgilla. Utgifter som har ett samband med inkomster räknas som omkostnad i näringsverksamhet. Bestämmelsen om representationsavdrag är sålunda restriktivare än den allmänna principen om avdrags-rätt. Skattelag är komplicerad och det kan krävas tolkning av lagreglerna. För en ökad för-utsebarhet för den skattskyldige används vissa tolkningsmetoder och tolkningsförfaranden vid komplettering av luckor i lag. SKV:s allmänna råd bidrar till ökad förutsebarhet och en-hetlighet då deras anvisningar har en betydande roll vad gäller representationsavdrag. Personliga levnadskostnader är inte avdragsgilla vilket framgår av 9 kap. 2 § IL. Bestämmel-sen om representation i 16 kap. 2 § IL är inte heller tillämpbar på det som ses som person-liga levnadskostnader då ett strikt krav på omedelbart samband med näringsverksamheten fordras. Vad som anses utgöra omedelbart samband med näringsverksamheten bedöms ut-ifrån omständigheterna i det enskilda fallet. Vid denna bedömning tas hänsyn till skillnader mellan företag, bedriven verksamhet, formen av representation samt vid hur många tillfäl-len som representation har skett. Representation kan anta formen av mutor eller andra otillbörliga belöningar då det ligger i representationens natur att fungera som ekonomiskt smörjmedel vid affärsförhandlingar. Enligt 9 kap. 10 § IL får utgifter för mutor eller andra otillbörliga belöningar inte dras av. Vad som avses med otillbörligt framgår inte vidare av de skatterättsliga reglerna. Praxis bakom de straffrättsliga bestämmelserna i 17 kap. 7 § BrB och 20 kap. 2 § BrB får istället användas för att förklara begreppet. En samlad bedömning av omständigheterna i det en-skilda fallet måste göras vid bedömningen av otillbörlighet.

Tidigare forskning har visat samband mellan språkanvändning och den uppfattning som kvinnor själva och samhället har om våld och övergrepp. Kvinnor som har blivit utsatta för våld och övergrepp möter ofta misstro och skuldbeläggande från omgivningen, vilket leder till att de inte blir trodda och att förövaren i många fall inte döms. I detta arbete undersöks hur en viss språkanvändning framställer våld och övergrepp på ett sätt som bland annat skuldbelägger offret, och vilka konsekvenser den språkanvändningen får. Metoden för arbetet är diskursanalys, och består av en textgranskning av domar från en svensk tingsrätt. Resultaten visar att rätten beskriver våld och övergrepp på ett sätt som leder till konsekvenser som att våldet döljs, förövarens ansvar minskas samt att offret skuldbeläggs. Resultatet leder till förslag på hur rätten istället ska beskriva våld och övergrepp, för att undvika ovan nämnda konsekvenser. Resultatet mynnar också ut i ett förslag till förändring av svensk lagstiftning, men det konstateras även att denna lagändring möjligtvis måste föregås av en samhällelig förändring i stort. / Earlier research has demonstrated a link between language and the view that women themselves and society have of violence and abuse. Women who have experienced violence and abuse often face suspicion and blame from society, which leads to that they are not believed and that the perpetrator in many cases, is not convicted. This study focuses on how the language used in a Swedish court describes violence and abuse in ways that leads to the blaming of the victim, and the further consequences of that specific use of language. The method used in this thesis is discourse analysis, and the empirical study consists of a text review of court judgements by a Swedish court. Findings are that the court describes violence and abuse in a way that leads to that violence is hidden, the perpetrator's responsibility is reduced and the victim gets blamed. The result leads to suggestions on how the court could describe violence and abuse differently, in order to avoid these negative consequences. The result also points towards a proposal for a change in Swedish law, although this change in the law might possibly be preceded by a change in society in general.