As software and hardware systems grow more complex and we begin to rely more on their correctness and reliability, it becomes exceedingly important to formally verify certain properties of these systems. If done naïvely, verifying a system can easily require exponentially more work than running it, in order to account for all possible executions. However, there are often symmetries or other properties of a system that can be exploited to reduce the amount of necessary work. In this thesis, we present a number of approaches that do this in the context of the CSP model checker FDR. CSP is named for Communicating Sequential Processes, or parallel combinations of state machines with synchronised communications. In the FDR model, the component processes are typically converted to explicit state machines while their parallel combination is evaluated lazily during model checking. Our contributions are motivated by this model but applicable to other models as well. We first address the scalability of the component machines by proposing a lazy compiler for a subset of CSP_M selected to model parameterised state machines. This is a typical case where the state space explosion can make model checking impractical, since the size of the state space is exponential in the number and size of the parameters. A lazy approach to evaluating these systems allows only the reachable subset of the state space to be explored. As an example, in studying security protocols, it is common to model an intruder parameterised by knowledge of each of a list of facts; even a relatively small 100 facts results in an intractable 2¹⁰⁰ states, but the rest of the system can ensure that only a small number of these states are reachable. Next, we address the scalability of the overall combination by presenting novel algorithms for bisimulation reduction with respect to strong bisimulation, divergence- respecting delay bisimulation, and divergence-respecting weak bisimulation. Since a parallel composition is related to the Cartesian product of its components, performing a relatively time-consuming bisimulation reduction on the components can reduce its size significantly; an efficient bisimulation algorithm is therefore very desirable. This thesis is motivated by practical implementations, and we discuss an implementation of each of the proposed algorithms in FDR. We thoroughly evaluate their performance and demonstrate their effectiveness.

[pt] Nesse trabalho, calcula-se a dinâmica de sistemas contínuos unidimensionais. Problemas de barras e vigas com diferentes condições de contorno e condições intermediárias são tratados no contexto da formulação fraca para que seja aplicado o Método de Elementos Finitos; e então seja possível calcular as aproximações das freqüências naturais e dos modos de vibração do sistema. Uma vez conhecidos os modos (exata ou aproximadamente), constrói-se um modelo reduzido de equações diferenciais ordinárias e, então, calcula-se a dinâmica do sistema. Essa dissertação propõe um material didático a ser utilizado no curso de Vibrações, com o intuito de auxiliar os alunos de graduação no estudo de sistemas contínuos, através do desenvolvimento da formulação fraca e aplicação do MEF. / [en] In this work, the dynamic of one-dimensional continuum systems is calculated. Problems of bars and beams with different boundary and intermediate conditions are treated in the context of weak formulation, so the Finite Element Method (FEM) can be applied; and it is possible to calculate the approximation of natural frequencies and vibration modes of the system. Once the modes are known (exactly or approximately), a reduced-model of ordinary differential equations is constructed and the dynamic of the system is calculated. This essay proposes a didactic material to be used at the Vibration course, with the purpose to help undergraduate students in the studies of continuum systems, through the development of the weak formulation and the application of the FEM.

I förskolans uppdrag ingår det att i samspel med barnen främja de grundläggande värden som vårt samhälle vilar på. Dessa är; människolivets okränkbarhet, individens frihet och integritet, alla människors lika värde, jämställdhet mellan könen och solidaritet med svaga och utsatta (Skolverket 2016). I den här studien tittar vi närmare på värdet; "solidaritet med svaga och utsatta". Anledningen till det är att vi i vår egen utbildning till förskollärare, samt på de förskolor vi arbeter på saknar reflekterande diskussioner om vad detta värde innebär i en förskolepedagogisk kontext. Studiens syfte är därför att ur ett didaktiskt perspektiv synliggöra förskollärares beskrivningar av deras värdegrundsarbete med soidaritet med svaga och utsatta.Genom de didaktiska frågorna; Vad (vilket innehåll lärs ut) och Hur (vilka metoder används) söker vi svar på hur förskollärare arbetar med detta värde. För att få svar på detta intervjuar vi sex förskollärare. Resultatet visar att på samtliga förskollärares arbetsplatser finns det inte ett planerat arbete samt att värdet inte lyfts till reflektion om dess innebörd. Dock, framkommer det i resultatet fem olika innehållsområden som förskollärarna kopplar ihop med deras arbete med solidaritet med svaga och utsatta, samt sex metoder som de anser främja detta arbete. Gemensam nämnare för de olika ämnesområdena handlar om att barnen i ord och handling visar att de bryr sig om sina kamrater. Metoder som förskollärare använder sig av är att de i den dagliga verksamheten bäddar i arbetet med solidaritet med svaga och utsatta i de vardagliga situationer som uppstår i barnens samspel.

Les surfaces de polymères électro-stimulables font partie de la catégorie des surfacesintelligentes. Elles sont capables de modifier leurs propriétés lorsqu’elles sont stimulées par unchamp électrique. Au cours de cette thèse nous avons fabriqué des surfaces de chaines depolyélectrolytes faibles greffées (PAA, P2VP, PDMAEMA), soit par auto-assemblage, soit partransfert via la balance de Langmuir. Nous avons ensuite étudié l’organisation des chaines depolyélectrolytes à la surface en fonction des conditions de pH et de sel de la sous-phase dans labalance de Langmuir. Avant de stimuler ces chaines de polyélectrolytes greffées à l’aide d’unchamp électrique, nous avons étudié leur sensibilité à la variation de pH et à la variation de laconcentration en sel. Pour cela des mesures d’épaisseurs de films de polyélectrolytes et desmesures d’angle de contact ont été effectuées. Ces études préliminaires nous ont permis desélectionner des valeurs de densité de greffage des chaines de polyélectrolytes ainsi que le pH etla concentration en sel de la solution adaptés pour la stimulation des surfaces par un champélectrique. Nous avons alors montré que les chaines greffées de PAA et de PDMAEMA étaienttrès sensibles à la variation de la tension électrique lorsque le pH est proche du pKa ou du pKb dela surface : pour une charge de la surface identique aux charges des chaines de polyélectrolytes,ces dernières vont adopter une conformation de brosse tandis qu’elles seront collapsées lorsque lacharge de la surface est de signe opposé aux charges des chaines. Cette transition réversible deschaines en fonction de la valeur de la tension appliquée permet de contrôler les propriétés demouillage et d’adhésion de ces surfaces. En revanche, pour un pH proche du pKb, les chainesgreffées de P2VP sont peu sensibles à l’application d’un champ électrique. Nous avons supposéque cela était dû à une variation de pH local au sein des chaines lorsque le champ électrique estappliqué. / Electro-responsive polymer surfaces are able to change their properties when they are stimulatedby an electric field. In this work, we grafted weak polyelectrolyte on surfaces by self-assembly orby transferring the molecules using the Langmuir-Schaefer method. First we studied theorganization of the polyelectrolyte chains at the surface for different pH and salt concentration ofthe subphase used in the Langmuir trough. Then we explored the response of the surfaces to pHand salt concentration changes by measuring the thickness variation of the polyelectrolyte filmsand the changes in contact angle. These preliminary studies allowed us to select the graftingdensity of polyelectrolyte chains and the pH and salt concentrations of the aqueous solutionadapted for the stimulation of the surfaces by an electric field. We then demonstrated that PAAand PDMAEMA grafted chains were very sensitive to the variation of the applied voltage whenthe pH is close to the pKa or from the pKb of the surface. If the charge of the surface has the samesign as the charges on the polyelectrolyte chains, the latter would adopt a brush conformation,whereas if the charge of the surface has the opposite sign compared to the sign of the charges onthe polyelectrolyte chains, the chains would collapse. This reversible transition of the chainsconformation with the sign of the applied voltage allowed us to control the wetting and theadhesion properties of these surfaces. Nevertheless, for a pH close to the pKb, the P2VP graftedchains are almost unresponsive to the application of an electric field. We supposed that this is theconsequence of a local pH variation inside the grafted chains when the electric field is applied.

Title: Robust Monitoring Procedures for Dependent Data Author: Ondřej Chochola Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Marie Hušková, DrSc. Supervisor's e-mail address: huskova@karlin.mff.cuni.cz Abstract: In the thesis we focus on sequential monitoring procedures. We extend some known results towards more robust methods. The robustness of the procedures with respect to outliers and heavy-tailed observations is introduced via use of M-estimation instead of classical least squares estimation. Another extension is towards dependent and multivariate data. It is assumed that the observations are weakly dependent, more specifically they fulfil strong mixing condition. For several models, the appropriate test statistics are proposed and their asymptotic properties are studied both under the null hypothesis of no change as well as under the alternatives, in order to derive proper critical values and show consistency of the tests. We also introduce retrospective change-point procedures, that allow one to verify in a robust way the stability of the historical data, which is needed for the sequential monitoring. Finite sample properties of the tests need to be also examined. This is done in a simulation study and by application on some real data in the capital asset...

The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)

Title: Mathematical analysis of equations describing the flow of compressible heat conducting fluids Author: Šimon Axmann Department: Mathematical Institute of Charles University Supervisor: doc. Mgr. Milan Pokorný, Ph.D., Mathematical Institute of Charles University Abstract: The present thesis is devoted to the mathematical analysis of equa- tions describing the flow of viscous compressible newtonian fluid in various time regimes. In particular, we present existence results for three problems arising as special cases of a general model derived in the introductory part. The first chap- ter deals with time-periodic solutions to the full Navier-Stokes-Fourier system for heat-conducting fluid. The second chapter contains the proof of existence of steady solutions to a system arising from phase field model for two-phase com- pressible fluid. Finally, in the last section we study steady strong solutions to the Navier-Stokes equations under the additional assumption that the fluid is suffi- ciently dense. For each problem a different concept of the solution is considered, on the other hand in all cases an essential role is played by the crucial quantity effective viscous flux. Keywords: compressible Navier-Stokes system; weak solution; entropy variational solution; large data

Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...

Magister Artium - MA / Social networking sites are used on a daily basis, to communicate with friends we have known for quite some time as well as make new friends from all over the globe - a global phenomenon. According to Aparicio (2011) the use of social networking sites have given way to a new “social dynamic” where friendships are formed with individuals from diverse backgrounds and geographical locations. Larsen (2007) continues to state that social network sites make for the creation of new friendships and the maintenance of new relationships. Using social networking sites to develop relationships provides us with new social skills, but through constant use of these sites we lose valuable interpersonal skills learnt through the use of face to face interaction (Aparicio, 2011). This thesis investigated the notion of social networking sites, specifically focusing on interpersonal relationships and language use within the networking context. The social networking site in question is that of Twitter, as majority of existing studies in this area focuses on the more popular Facebook. The main objective was to determine whether social networking sites, specifically Twitter, influence the development and maintenance of interpersonal relationships and language use. Participants included a group of 11 males and 11 females (22 in total), ranging from the ages of 17 to 33 and from different geographical locations (e.g. United Kingdom, South Africa, Tokyo, and so on). These participants frequently keep in contact with each other. Four ways in which Twitter has been adapted to emulate face to face communication have been found, namely: (1) the use of Paralinguistic and Prosodic Features to imitate speech, (2) Ustream, although not prominent within the data collected, is used to make up for the lack of face to face communication.This, however, is one-way; only one user provides a video link while those communicating with him or her (as there can be more than one) would type messages, (3) as expected a variety of shortenings can be found within the data collected. Shortenings imitate speech among the younger generation, and (4) participants make use of an informal register, as the most common type of relationship found on Twitter is that of friendships. Both strong and weak ties exist in the collected data; with weak ties being the majority. It is possible for weak ties to become strong ties. All online relationships start off as weak and gradually, over time, become strong ties. This is done through establishing trust between participants and communicating on a regular basis. Paolillo (1999) found that online relationships manifests as both weak and strong. However, “online ties are not ‘branded’ as weak ties” and these ties differ in quality; “those who have regular contact have strong ties and those with less frequent contact have weaker ties weak”. Social support is evident in the collected data and possible in online, textbased communication. In is manifested in four types of support, namely: instrumental, emotional, informational, and appraisal. The most common type of support found in the collected data is that of informational support. With regards to support activation strategies, most tweet fall under the ‘ask’ and ‘cry’ types of strategies. Also, considering the amount of emoticons found in the data, little or no emoticons were found in the activation strategies. There are also more indirect support activation strategies as opposed to direct. This could possibly be due to the fact that majority of the ties are ‘in the weak stage’. Textese has not been adapted in anyway; the same elements used by texters and IMers are used by tweeters, such as initialisms, phonetic spellings and contractions. Although present in the Twitter data, elements of textese did not occur as frequently as that found in e.g. Bieswanger’s (2007) and Thurlow’s (2003) studies; however more elements of Twitter language was found. If anything, the characteristics of textese are well-suited for Twitter; as shortened forms of words would make it easier for users to maintain a character count below the imposed limitation and it promotes the idea of writing quick and concise messages instead of filling message space with irrelevant content. With regards to the difference in the way male and female participants use language in terms of the linguistic characteristics of textese and the language unique to Twitter and the use of paralinguistic and prosodic features, it can be said that females tend to use these characteristics more than males do.

De nombreux problèmes algorithmiques sont « difficiles », dans le sens où on ne sait pas les résoudre en temps polynomial par rapport à la taille de l’entrée, soit parce qu’ils sont NP-difficiles, soit, pour certains problèmes d’énumération, à cause du nombre exponentiel d'objets à énumérer. Depuis une quinzaine d’années on trouve un intérêt grandissant dans la littérature pour la conception d'algorithmes exacts sophistiqués afin de les résoudre le plus efficacement possible. Dans le cadre de cette thèse, nous nous intéressons à la conception d'algorithmes exacts exponentiels autour de trois problèmes difficiles. Nous étudions tout d'abord le problème d'optimisation Ensemble Connexe Tropical pour lequel nous décrivons un algorithme afin de le résoudre en général, puis un algorithme de branchement plus rapide pour le résoudre sur les arbres, ce problème restant difficile même dans ce cas. Nous nous intéressons ensuite au problème d'énumération Ensembles Dominants Minimaux, pour lequel nous donnons des algorithmes résolvant ce problème dans les graphes splits, cobipartis, ainsi que dans les graphes d'intervalles. Nous déduisons des bornes supérieures sur le nombre d'ensembles dominants minimaux admis par de tels graphes. La dernière étude de cette thèse concerne le problème d'optimisation Domination Romaine Faible dans lequel, étant donné un graphe nous cherchons à construire une fonction de pondération selon certaines propriétés. Le problème est NP-difficile en général, mais nous donnons un algorithme glouton linéaire calculant une telle fonction pour les graphes d'intervalles. / Many algorithmic problems are « hard », in the sense of we do not know how to solve them in polynomialtime, either because they are NP-hard, or, for some enumeration problems, because the number of objectsto be produced is exponential. During the last fifteen years there was a growing interest in the design of exact algorithms to solve such problems as efficiently as possible. In the context of this thesis, we focus on the design of exponential exact algorithms for three hard problems. First, we study the optimisation problem Tropical Connected Set for which we describe an algorithm to solve it in the general case, then a faster branch-and-reduce algorithm to solve it on trees; the problem remains difficult even in this case. Secondly we focus on the Minimal Dominating Sets enumeration problem, for which we give algorithms to solve it on split, cobipartite and intervals graphs. As a byproduct, we establish upper bounds on the number of minimal dominating sets in such graphs. The last focus of this thesis concerns the Weak Roman Domination optimisation problem for which, given a graph, the goal is to build a weight function under some properties. The problem is NP-hard in general, but we give a linear greedy algorithm which computes such a function on interval graphs.