Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we will use the techniques established in [2] to analyze the existence and uniqueness of classical solution to the nonlinear heat equation in ; provided u0 2 Lq() with some conditions on 1 q 1, where RN is a smooth bounded domain and p > 1. / Nesta dissertação, vamos utilizar as técnicas vistas em [2] para analisar a existência e unicidade de solução clássica para a equação do calor não-linear quando uo E Lq com algumas condições sobre 1<q<, onde RN é um domínio limitado suave e p>1.

Context: According to Swedish National Council for Crime Prevention, there is an increase in residential burglary crimes by 2% in 2014 compared to 2013and by 19% in the past decade. Law enforcement agencies could only solve three to five percent of crimes reported in 2012. Multiple studies done in the field of crime analysis report that most of the residential burglaries are committed by relatively small number of offenders. Thus, the law enforcement agencies need toinvestigate the possibility of linking crimes into crime series. Objectives: This study presents the computation of a median crime which is the centre most crime in a crime series calculated using the statistical concept of median. This approach is used to calculate the uniqueness of a crime series consisting of linked residential burglaries. The burglaries are characterised using temporal, spatial features and modus operandi. Methods: Quasi experiment with repeated measures is chosen as research method.The burglaries are linked based on their characteristics(features) by building a statistical model using logistic regression algorithm to formulate estimated crime series. The study uses median crime as an approach for computing the uniqueness of linked burglaries. The measure of uniqueness is compared between estimated series and legally verified known series. In addition, the study compares the uniqueness of estimated and known series to randomly selected crimes. The measure of uniqueness is used to know the feasibility of using the formulated estimated series for investigation by the law bodies. Results: Statistical model built for linking crimes achieved an AUC = 0.964,R 2 = 0.770 and Dxy = 0.900 during internal evaluation and achieved AU C =0.916 for predictions on test data set and AUC = 0.85 for predictions on known series data set. The uniqueness measure of estimated series ranges from 0.526to 0.715, and from 0.359 to 0.442 for known series corresponding to differentseries. The uniqueness of randomly selected crimes ranges from 0.522 to 0.726 for estimated series and from 0.636 to 0.743 for known series. The values obtained are analysed and evaluated using Independent two sample t-test, Cohen’s d and kolmogorov-smirnov test. From this analysis, it is evident that the uniqueness measure for estimated series is high compared to the known series and closely matches with randomly selected crimes. The uniqueness of known series is clearly low compared to both the estimated series and randomly selected crimes. Conclusion: The present study concludes that estimated series formulated using the statistical model has high uniqueness measures and needs to be furtherfiltered to be used by the law bodies.

La tomographie consiste à reconstruire un objet nD à partir de projections (n-1)D. Cette discipline soulève plusieurs questions auxquelles la recherche essaie d’apporter des réponses. On s’intéresse dans cette thèse à trois aspects de cette problématique : 1) la reconstruction de l’image 2D à partir de projections dans un cadre rarement étudié qui est celui des sources ponctuelles ; 2) l’unicité de cette reconstruction ; 3) l'estimation d’informations concernant un objet sans passer par l'étape de reconstitution de son image. Afin d’aborder le problème de reconstruction pour la classe des ensembles convexes, nous définissons une nouvelle classe d’ensembles ayant des propriétés de convexité qu’on appelle convexité par quadrants pour des sources ponctuelles. Après une étude de cette nouvelle classe d’ensembles, nous montrons qu’elle présente des liens forts avec la classe des ensembles convexes. Nous proposons alors un algorithme de reconstruction d’ensemblesconvexes par quadrants qui, si l’unicité de la reconstruction est garantie, permet de reconstruire des ensembles convexes en un temps polynomial. Nous montrons que si une conjecture, que nous avons proposée, est vraie, les conditions de l’unicité pour les ensembles convexes par quadrants sont les mêmes que celles pour les ensembles convexes. Concernant le troisième aspect étudié dans cette thèse, nous proposons une méthode qui permet d’estimer, à partir d’une seule projection, la surface d’un ensemble 2D. Concernant l’estimation du périmètre d’un ensemble 2D, en considérant les projections par une deuxième source d’un ensemble convexe, nous obtenons deux bornes inférieures et une borne supérieure pour le périmètre de l’objet projeté. / Tomography is about reconstructing an nD object from its (n-1)D projections. This discipline addresses many questions to which research tries to provide answers. In this work, we are interested to three aspects: 1) the 2D image reconstruction from projections in a rarely studies framework that is the point sources; 2) the uniqueness of this reconstruction; 3) estimating information about an object without going through the step of reconstructing its image. To approach the problem of tomographic reconstruction for the class of convex sets, we define a new class of sets having properties of convexity called quadrant convexity for point sources. After a study of this new class of sets, we show that it presents strong links with the class of convex sets. Wepropose a reconstruction algorithm for quadrant-convex sets that, if the uniqueness of the reconstruction is guaranteed, allows the reconstruction of convex sets in polynomial time. We also show that if a conjecture we have proposed is true the conditions of uniqueness for quadrant-convex sets are the same as those for convex sets. Regarding the third aspect studied in this thesis, we focus on two quantitative properties that are the surface and the perimeter. We propose a method to estimate, from only one projection, the surface of a 2D set. We obtain two lower bounds and an upper bound for the perimeter of a projected convexobject by considering the projections from a second point source.

Résumé: Limits of work of copyright in visual art This diploma thesis primarily deals with the concept of copyright work in the current Czech law and its relation towards works of contemporary visual art. The main aim of this thesis is to carry out a complex analysis of conceptual features of work of copyright under the Czech Copyright Act No. 121/2000 Coll. (including key and not always properly interpreted terms such as work of art, originality, or creativity) and then to apply these features to examples of the world's major works of visual art from the twentieth and twenty-first century. Author of this thesis tries to find out whether even specific works of visual art "meet legal requirements" imposed on works of copyright and thus may enjoy the copyright protection in the Czech legal system. It is the effort to identify boundaries between works of copyright and objects which are not under the protection of copyright law what is reflected in the title of this diploma thesis. Text of this thesis is divided into two main units. The first unit, which is the core of the thesis, is called "Limits of work of copyright", the second unit is called "Limits of appropriation". In the general part of the first unit the author tries to focus deeply on theoretical inquiry about the concept of work of copyright under...

Nonnegative matrix factorization (NMF) is an important data-analysis problem which concerns factoring a given d n matrix A with nonnegative entries into matrices B and C where B and C are d k and k n with nonnegative entries. It has numerous applications including Object recognition, Topic Modelling, Hyper-spectral imaging, Music transcription etc. In general, NMF is intractable and several heuristics exists to solve the problem of NMF. Recently there has been interest in investigating conditions under which NMF can be tractably recovered. We note that existing attempts make unrealistic assumptions and often the associated algorithms tend to be not scalable. In this thesis, we make three major contributions: First, we formulate a model of NMF with assumptions which are natural and is a substantial weakening of separability. Unlike requiring a bound on the error in each column of (A BC) as was done in much of previous work, our assumptions are about aggregate errors, namely spectral norm of (A BC) i.e. jjA BCjj2 should be low. This is a much weaker error assumption and the associated B; C would be much more resilient than existing models. Second, we describe a robust polynomial time SVD-based algorithm, UTSVD, with realistic provable error guarantees and can handle higher levels of noise than previous algorithms. Indeed, experimentally we show that existing NMF models, which are based on separability assumptions, degrade much faster than UTSVD, in the presence of noise. Furthermore, when the data has dominant features, UTSVD significantly outperforms existing models. On real life datasets we again see a similar outperformance of UTSVD on clustering tasks. Finally, under a weaker model, we prove a robust version of uniqueness of NMF, where again, the word \robust" refers to realistic error bounds.

A firm’s brand image has to stand the test of time and be durable through different trends and changes, which emphasize the importance of following developments in the marketplace such as the emerging relevance of firm generated content on social media. With attitudes towards a product being lower in relation to the involvement regarding a product, the importance of establishing brand image for low-involvement product brands increases. With this in mind the purpose of this thesis was to explore how consumers’ brand image of low involvement products was affected by firm generated content on social media. This research provides insights on how brand image of a brand of a low involvement products is affected by firm generated content on social media. The study is based on existing research within brand image and was conducted through the use of a qualitative research approach using in-depth interviews as data collection method. The findings of this thesis suggest that consumers brand image is influenced by symbolic benefits where the benefits around the product are emphasized. A pattern could be seen where consumers emphasized symbolic benefits communicated through firm generated content on social media in a higher regard when the perceived functional benefits between brands were similar. This suggests that firm generated content of brands of low involvement products communicated on social media often seem to influence consumers perception of symbolic benefits in regards to favorability, strength and uniqueness of associations which in turn influence brand image.

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Bakgrund och problem: Konsumenter värderar individualism vilket leder till hög efterfrågan av unika produkter. Massproducerade produkter anses inte längre vara lika värdefulla vilket har utvecklat drop till en vanligt förekommande affärsstrategi. Modeföretag kan tillämpa drop i syfte att signalera unikhet genom att begränsa dess tillgänglighet. Marknadsföringen inom drop handlar om att framhäva produktens knapphet och på så sätt förstärka dess unika attribut. Modeföretag väljer att använda sig av sociala medier som marknadsföringsplattform för att stärka varumärkets community och skapa en hype kring lanseringen. I samband med att produkter behöver ha en förmåga att särskilja sig samtidigt som de kan tillfredsställa konsumenternas behov av att vara unika, behövs effektiva marknadsföringsstrategier som betonar produkternas knapphet, framkallar efterfrågan och skapar en känsla av gemenskap för konsumenten. Syfte: Studiens syfte är att undersöka och kartlägga vad affärsstrategin drop innebär och hur det utvalda modeföretaget anpassar strategin i sin verksamhet, samt undersöka i vilken utsträckning knapphet, sociala medier som marknadsföringsplattform och unikhet kan utnyttjas i samband med drop. Avsikten med studien är att öka förståelsen för drop som strategi samt bidra med att berika forskningsområdet genom nya effektiva analyser och slutsatser kring vilka effekter limiterade produkter inom drop har på efterfrågan. Metod: Studien bygger på en kvalitativ forskningsmetod där tre semistrukturerade intervjuer samt en observation har genomförts. Datainsamlingen har utgått ifrån fyra teman och frågeställningar som har förankring till studiens teoretiska referensramen. Resultat och slutsats: Resultatet i denna studie indikerar på att drop generellt ökar produktens exklusivitet och efterfrågan genom att skapa en illusion av knapphet. Vidare visar resultatet på att företag med hjälp av knapphet kan upprätthålla konsumenters uppmärksamhet och därmed öka lönsamheten. Studien indikerar på att det är väsentligt att begränsa antalet drop samt att det är viktigt att ständigt uppdatera produkterna så de upprätthåller sina unika attribut. Marknadsföring via sociala medieplattformar har en förmåga att höja värdet av varumärket och skapa en hype bland konsumenterna innan ett drop. Sociala medier är dessutom lönsamt att tillämpa då det inte kräver stora investeringar samtidigt som det möjliggör att nå ut till en bredare räckvidd konsumenter. / Background: Consumer value individualism which leads to a higher demand for unique products. Mass produced products are no longer considered as valuable which has developed drop into a common occurring business strategy. Fashion companies can apply drop in order to indicate uniqueness by limiting it’s availability. Marketing within drop is about emphasising the products scarcity and thus enhancing its unique attribute. Fashion companies choose to use social media as a marketing platform in order to strengthen the brand community and create a hype around the launch. As well as products need to be able to differentiate and at the same time satisfy the consumers need for uniqueness, it requires effective marketing strategies that emphasizes the products scarcity, provokes demand and creates a feeling of a community for the consumer. Aim: The aim of this study is to examine and map what the business strategy drop means and how the chosen fashion company adopts the strategy into their business, also examine to what extent scarcity, social media as a marketing platform and uniqueness can be utilized within drop. The intention of this study is to increase the understanding about drop as a business strategy as well as contribute to the research area through new effective analyses and conclusions about the effects limited products within drop have on the demand. Methodology: This study is based on a qualitative research method where three semi-structured interviews and one observation have been done. The data collection derives from four themes and the questions which are anchored from the theoretical framework. Findings and conclusion: The result of this study indicated that drop generally enhances the products exclusivity and demand by creating an illusion of scarcity. Furthermore the results show that companies can by scarcity gain the ability to maintain consumers attention and thereby increase the profitability. The study indicates that it is significant to limit the amount of drops as well as it is important to constantly develop the products in order to maintain their unique attributes. Marketing through social media platforms have the ability to increase the value of the brand and create a hype among the consumers before a drop. Social media is also profitable to apply because it doesn't need large investments even though it is possible to reach a wider range of consumers.

Hlavním zájmem diplomové práce je studium zobecněné nabla Laplaceové transformace na časových škálach a její jednoznačnosti, včetně důkazu jednoznačnosti a aplikace jednoznačnosti v zlomkovém kalkulu na časových škálach.

“History matching” (model calibration, parameter identification) is an established method for determination of representative reservoir properties such as permeability, porosity, relative permeability and fault transmissibility from a measured production history; however the uniqueness of selected model is always a challenge in a successful history matching. Up to now, the uniqueness of history matching results in practice can be assessed only after individual and technical experience and/or by repeating history matching with different reservoir models (different sets of parameters as the starting guess). The present study has been used the stochastical theory of Kullback & Leibler (K-L) and its further development by Akaike (AIC) for the first time to solve the uniqueness problem in reservoir engineering. In addition - based on the AIC principle and the principle of parsimony - a penalty term for OF has been empirically formulated regarding geoscientific and technical considerations. Finally a new formulation (Penalized Objective Function, POF) has been developed for model selection in reservoir history matching and has been tested successfully in a North German gas field. / „History Matching“ (Modell-Kalibrierung, Parameter Identifikation) ist eine bewährte Methode zur Bestimmung repräsentativer Reservoireigenschaften, wie Permeabilität, Porosität, relative Permeabilitätsfunktionen und Störungs-Transmissibilitäten aus einer gemessenen Produktionsgeschichte (history). Bis heute kann die Eindeutigkeit der identifizierten Parameter in der Praxis nicht konstruktiv nachgewiesen werden. Die Resultate eines History-Match können nur nach individueller Erfahrung und/oder durch vielmalige History-Match-Versuche mit verschiedenen Reservoirmodellen (verschiedenen Parametersätzen als Startposition) auf ihre Eindeutigkeit bewertet werden. Die vorliegende Studie hat die im Reservoir Engineering erstmals eingesetzte stochastische Theorie von Kullback & Leibler (K-L) und ihre Weiterentwicklung nach Akaike (AIC) als Basis für die Bewertung des Eindeutigkeitsproblems genutzt. Schließlich wurde das AIC-Prinzip als empirischer Strafterm aus geowissenschaftlichen und technischen Überlegungen formuliert. Der neu formulierte Strafterm (Penalized Objective Function, POF) wurde für das History Matching eines norddeutschen Erdgasfeldes erfolgreich getestet.