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Education plays a pivotal role in shaping the future of any nation. Researchers, pedagogists, and teachers all over the world are constantly working towards improving the process of teaching at all levels of education in order to help impart knowledge in a more effective way. One of the most fundamental branches of education is mathematics. Unless a strong foundation is laid in childhood, it becomes difficult for adults to apply mathematics to their daily lives. Mathematics is such a field that it is integrated in most of our activities. Fractions, a mathematics topic, pose significant challenges for middle school students Although the students generally understand proper fractions (i.e., the numerator is smaller than the denominator), they find it very difficult to learn improper fractions (i.e., the numerator is greater than the denominator). One cannot do away with parts of mathematics curriculum, just because the concept is hard to grasp. The solution is to come up with alternative methods to teach these concepts, such that they are easier to understand and more fun to learn. This thesis describes a digital game-based solution for teaching fractions to middle school students using iOS mobile devices, i.e., iPad, iPhone, and iPod Touch. We developed a universal iOS game, called Candy Factory, which runs on all iOS mobile devices. The game assigns the student the role of the owner of a Candy Factory and tasks the student to manufacture a candy bar to match the kind and size of a customer order from a whole candy bar that is retrieved from the warehouse. The game is created to teach fractions based on the concept of partitioning and iterating. The student performs various activities such as partitioning, iterating, and measuring to produce the candy bar to satisfy the customer requirements. The game consists of three levels, which help the student progress smoothly from easier problems to more difficult ones. The Candy Factory game, not only helps students learn the fundamentals of fractions, but also makes the learning process enjoyable. / Master of Science

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(工学) / 甲第25292号 / 工博第5251号 / 新制||工||1999(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 松尾 哲司, 教授 萩原 朋道, 教授 阪本 卓也 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DGAM

Nowadays cross platform software development is more expensive than ever before in terms of time and effort. Meantime with increasing number of personal devices, it is harder for local applications to synchronize and connect to the Internet. In terms of educational games, they can be divided into "local educational game" and "web educational game." "Local game" indicates the ones either on tablets, mobile devices or PC, which is an application on the corresponding platform. This kind of game mostly does not have backend support nor cross platform features such as the iPad version of CandyFactory. For one specific game, if the developer wants it to run on iPad and Android tablets, they need to develop two applications based on corresponding development framework, which is time and effort consuming. "Web game" indicates the ones on websites, which support cross platforms, but do not have backend support. Usually they are pure JavaScript or flash games with no backend recording the performances and the achievements. Software development for each individual platform is time and effort consuming. In order to achieve cross platform development, many programming languages and platforms like Java, Python, and JVM appear. Among all the cross platform approaches, cloud-based software development is the most universal solution to this problem. With web browsers built into every operating system, cloud software can be compatible with almost any device. Moreover, "Software-as-a-Service" (SaaS) is becoming a new software engineering paradigm and cloud-based software development is more popular because of its flexible scalability and cross platform features. In this thesis, we create a cloud-based educational game, CandyFactory, based on an iPad version of CandyFactory, and add backend to it to record user performance as well as achievements. Firstly, we re-develop the whole game from the iOS platform to the cloud-based Java EE platform. Secondly, we add new features to improve the game play such as ruler functionality and achievements animation. Thirdly, we add backend support to CandyFactory, including user account creation, course creation and performance report generation. With this functionality, teachers can monitor their students' performances and generate course reports. Moreover, teachers can view a specific student's report in order to provide more specific and effective help to their students. Lastly, with the advantages of cloud-based software development, we can update the whole application at any time without forcing the user to reinstall the update or re-download the game. With the hot update, the cloud-based CandyFactory is highly maintainable. The cloud-based CandyFactory runs on any computer that supports minimum 1024x768 screen resolution. The computer could be iPads, Android or Microsoft tablets, Windows or Mac laptops and desktops, and any other computer with a web browser. The advantages of cloud-based educational games over local educational games and web educational games are: firstly, they have cross platform features; secondly, they have backend data collection support; thirdly, they are consistent even if users log in with different computers, their game record and history will always be the same; lastly, the teacher can always keep track of his/her students' performance and provide more specific help and feedback. / Master of Science / Providing services on the cloud has become universal. The term “Cloud-Based” indicates that the software application runs on a server computer and users access the application by using a web browser anywhere and anytime. This thesis presents a cloud-based educational game called CandyFactory to teach fractions. The users can use CandyFactory under a web browser on an Internet-connected tablet, laptop, or desktop computer with minimum 1024x768 screen resolution. User’s game performance data is recorded on the server computer regardless of which tablet, laptop, or desktop computer the user uses to play the game. Cloud-based CandyFactory has four kinds of users: Individual, Teacher, Student, Administrator. Individual users can play the game to learn fractions as well as generate performance reports. Teachers can create a course, automatically generate student accounts under a course, and generate performance reports for individual students or for the whole class. Students can play the game under the account provided by the teacher and view their performance reports. Administrator is a built-in account user for maintaining the cloud-based software application. By developing the cloud-based CandyFactory educational game, we provide the users a crossplatform and cross-computers solution which helps the teachers and students learn fractions more efficiently and effectively.

L'anneau $\Diff(n)$ des opérateurs différentiels $\h$-déformés apparaît dans la théorie des algèbres de réduction.Dans cette thèse, nous construisons les anneaux des opérateurs différentiels généralisés sur les espaces vectoriels $\h$-déformés de type $\gl$. Contrairement aux espaces vectoriels $q$-déformés pour lequel l'anneau des opérateurs différentiels est unique \`a isomorphisme pr\`es, l'anneau généralisé des opérateurs différentiels $\h$-déformés $\Diffs(n)$ est indexée par une fonction rationnelle $\sigma$ en $n$ variables, solution d'un syst\`eme d\'eg\'en\'er\'e d'\'equations aux diff\'erences finies. Nous obtenons la solution g\'en\'erale de ce syst\`eme. Nous montrons que le centre de $\Diffs(n)$ est un anneau des polynômes en $n$ variables. Nous construisons un isomorphisme entre des localisations de l'anneau $\Diffs(n)$ et de l’algèbre de Weyl $\text{W}_n$ l’étendue par $n$ indéterminés. Nous présentons des conditions irréductibilité des modules de dimension fini de $\Diffs(n)$. Finalement, nous discutons des difficultés a trouver les constructions analogues pour l'anneau $\Diff(n,N)$ correspondant \`a $N$ copies de $\Diff(n)$. / The ring $\Diff(n)$ of $\h$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\h$-deformed vector spaces of $\gl$-type. In contrast to the $q$-deformed vector spaces for which the ring of differential operators is unique up to an isomorphism, the general ring of $\h$-deformed differential operators $\Diffs(n)$ is labeled by a rational function $\sigma$ in $n$ variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system. We show that the center of $\Diffs(n)$ is a ring of polynomials in $n$ variables. We construct an isomorphism between certain localizations of $\Diffs(n)$ and the Weyl algebra $\W_n$ extended by $n$ indeterminates. We present some conditions for the irreducibility of the finite dimensional $\Diffs(n)$-modules. Finally, we discuss difficulties for finding analogous constructions for the ring $\Diff(n, N)$ formed by several copies of $\Diff(n)$.

Made available in DSpace on 2016-04-27T16:58:19Z (GMT). No. of bitstreams: 1 alexandre notari.pdf: 286199 bytes, checksum: 591269af2d5afccbd3071b0fac3cc7e1 (MD5) Previous issue date: 2002-10-30 / This research has as objective to get a systematic diagnosis of the main errors and difficulties revealed for pupils of Basic Ensino and Average Ensino in the simplification of arithmetical and algebraic fractions. They had been selected, for the inquiry, one 8ª series of Basic Ensino and one 1ª series of Average Ensino of two public schools of the Region West, of the city of São Paulo. We assume as referencial theoretician the happened ones of research where Algebra, in these levels of education, must search its beddings in the laws of the Arithmetic. However, it does not reduce it to a generalization of these laws, a time that algebraic the conceptual system incorporates elements and Inter-relations with proper characteristics. The data had been gotten by means of period of training in a classroom of each one of the mentioned series, application of a test and interviews. The main conclusions point with respect to one high number of errors in the simplification of algebraic fractions that disclose a incompreensão of the formal rules that regulate these transformations. Between these, a predominance of errors due to a generalization of rules of a situation for another one occurs, without an analysis of the conditions that validate this generalization. They disclose in the treatment of the arithmetical expressions a predominance of automatically carried through computational procedures, without a reflection on the nature of the task proposal; they indicate, still, an absence of integration between the arithmetical and algebraic conceptual domínios / Esta pesquisa tem como objetivo obter um diagnóstico sistemático dos principais erros e dificuldades manifestados por alunos do Ensino Fundamental e do Ensino Médio na simplificação de frações aritméticas e algébricas. Foram selecionadas, para a investigação, uma 8ª série do Ensino Fundamental e uma 1ª série do Ensino Médio de duas escolas públicas da Região Oeste, da cidade de São Paulo. Assumimos como referencial teórico os advindos de pesquisas em que a Álgebra, nesses níveis de ensino, deve buscar seus fundamentos nas leis da Aritmética. Entretanto, não o reduz a uma generalização dessas leis, uma vez que o sistema conceitual algébrico incorpora elementos e inter-relações com características próprias. Os dados foram obtidos por meio de estágio em uma classe de cada uma das séries mencionadas, de aplicação de uma prova e de entrevistas. As principais conclusões apontam para um elevado número de erros na simplificação de frações algébricas que revelam uma incompreensão das regras formais que regulamentam essas transformações. Entre esses, ocorre uma predominância de erros devidos a uma generalização de regras de uma situação para outra, sem uma análise das condições que validam essa generalização. Revelam no tratamento das expressões aritméticas um predomínio de procedimentos computacionais realizados automaticamente, sem uma reflexão sobre a natureza da tarefa proposta; indicam, ainda, uma ausência de integração entre os domínios conceituais aritméticos e algébricos

Ce travail porte sur le comportement du Ra au sein d’un écosystème forestier (Montiers, Meuse). Il s’appuie sur la mesure de plusieurs traceurs isotopiques (déséquilibres radioactifs, rapports 228Ra/226Ra et 87Sr/86Sr) dans les différents compartiments du système eau-sol-plante. Les objectifs étaient : 1) d’étudier la mobilité du Ra et ses ascendants radioactifs entre les fractions minérales séparées d’un profil de sol, 2) d’évaluer le transfert du Ra vers les compartiments eau-plante de l’écosystème, 3) de caractériser le transfert du Ra et son temps de résidence dans la végétation, 4) de réaliser le bilan du cycle biogéochimique du Ra. Ce travail montre une forte redistribution de U, Th et Ra en fonction de leurs affinités respectives avec les différentes fractions minérales du sol. Bien que le Ra soit très fortement associé à la fraction fine (< 2µm) du sol, la végétation (hêtres) semble prélever le Ra des oxydes de fer du sol. Le transfert ultérieur de ce nucléide depuis les racines vers les parties aériennes de l’arbre est moins important que celui des autres alcalino-terreux, aboutissant à un temps de résidence dans la végétation de l’ordre de quelques années (2.6 ± 1.6 ans). Enfin, le cycle biogéochimique du Ra est caractérisé par un flux de dégradation de la litière souterraine plus important que celui lié à la litière de surface, par un apport atmosphérique en Ra négligeable et par un flux d'altération très important, ce dernier ne transitant pas par les solutions de sols gravitaires. Le Ra présent dans ces dernières provient presque exclusivement de la dégradation de la litière. / This work investigates the behaviour of Ra within a forest ecosystem (Montiers, Meuse). It is based on the quantification of several isotopic tracers (U- and Th- series disequilibria, isotopic ratios of 228Ra/226Ra and 87Sr/86Sr) in the different compartments of the water-soil-plant system. The research goals were : 1) to study the mobility of Ra and its radioactive ascendants in the separated mineral fractions of a soil profile, 2) to evaluate the transfer of Ra to the water-plant system, 3) to characterise the transfer of Ra and its residence time onto the vegetation, 4) to realise an account of the biogeochemical cycle of Ra. This work shows a strong redistribution of U, Th and Ra depending on their respective affinities with the different mineral fractions of the soil. Despite being predominantly concentrated in the clay fraction (<2 µm) of the soil, our findings indicate that trees (beeches) mostly extract Ra from the soil’s iron oxides. The subsequent transfer of this nuclide from the roots to the foliage is lesser than that of other alkaline-earth metals, leading to a vegetal residence time on the order of a few years (2.6 ± 1.6 years). Finally, the biogeochemical cycle of Ra is characterised by the degradation flux of fine-roots rather than that of leaves, by a negligible atmospheric input and by a strong weathering rate. Ra presents in the latter originates almost uniquely from litter degradation and does not pass through gravitational soil solutions.

Nous considérons certaines séries de Fourier liées à la théorie des formes modulaires. Nous étudions leurs propriétés analytiques : la dérivabilité, le module de continuité et l'exposant de Hölder. Nous utilisons deux méthodes différentes. La première revient à trouver et itérer une équation fonctionnelle de la fonction étudiée (méthode d'Itatsu) et la deuxième provient de l'analyse en ondelettes (méthode de Jaffard). L'étape essentielle de chacune dépend de la modularité sous-jacente. Nous trouvons que les propriétés analytiques de ces séries aux points irrationnels sont liées aux propriétés diophantiennes de ces points. Ce travail a été motivé par l'étude de la fonction de Riemann. / We consider certain Fourier series which arise from modular or automorphicforms. We study their analytic properties: differentiability, modulus of continuity and theH¨older regularity exponent. We use two different methods. One is based on finding anditerating a functional equation for the function studied (Itatsu’s method), the second onecomes from wavelet analysis (Jaffard’s method). The crucial steps in both of them arebased on the underlined modularity. We find that the analytic properties of these seriesat an irrational x are related to the fine diophantine properties of x, in a very precise way.The work was motivated by the study of the Riemann series.

La présence d'hétéroatomes et métaux dans des fractions lourdes de pétrole brut peuvent entraîner la désactivation des catalyseurs d’hydrotraitement et d’hydrocraquage. Les composés contenant ces éléments sont connus pour être inclus dans des agrégats macromoléculaires d’asphaltènes, qui sont considérées comme les composants les plus problématiques des produits pétroliers. Ces travaux ont pour objectif d’apporter une meilleure compréhension de l’environnement chimique de ces espèces et des phénomènes d’agrégation pour optimiser les processus de raffinage. Des techniques de séparation comme la chromatographie de perméation de gel ou Gel Permeation Chromatography (GPC), Advanced Polymer chromatographie (APC) et la chromatographie sur couche mince d’haute performance ou High Performance Thin Layer Chromatography (HPTLC) ont été combinées avec des techniques d’analyse élémentaire comme la spectrométrie de masse à plasma à couplage inductif ou Inductively Coupled Plasma Mass Spectrometry (ICP-MS) et la spectrométrie de masse moléculaire d’haute résolution pour la caractérisation des fractions pétrolières lourdes. Les profils de distribution en taille d’espèces qui contiennent du vanadium, du nickel et du soufre, les hétéroatomes et métaux les plus abondants dans les produits pétroliers, ont été déterminés par GPC couplé à une détection élémentaire par ICP MS. Les paramètres ayant le plus d’impact sur la distribution en taille et l’évolution des agrégats dans les solutions de différentes coupes pétrolières ont été optimisés. Cela nous a permis de faire différentes comparaisons, entre de nombreuses charges et effluents de procédés, ainsi que d’autres séries d’échantillons ou de mélanges provenant d’unités-pilotes d’hydrotraitement. Les résultats obtenus ont pu être mis en regard de caractéristiques macroscopiques comme la viscosité. Le couplage du nouveau système APC avec l’ICP MS a été mis au point avec succès. Cette technique a permis de réaliser des cartographies d’échantillons pétroliers plus rapides qu’en GPC tout en consommant moins de solvant. Cependant, les différences des chromatogrammes APC obtenus par rapport aux profils GPC suggèrent des interactions indésirables avec la phase stationnaire, qui ont été l’objet d’une évaluation approfondie.Enfin, un dernier type de séparation a été évaluée. L’HPTLC, qui utilise des plaques à usage unique, peut être appliquée à la séparation de produits lourds par polarité, et ce sans étapes de déasphaltage préalable, contrairement aux colonnes de chromatographie liquide qui peuvent être détériorées à cause de l'adsorption irréversible et de la précipitation des asphaltènes. Différents types de plaques et éluants ont été testés afin de développer une méthode simple pour la séparation des fractions SAR (Saturés, Aromatiques et Résines) des échantillons de distillat sous vide ou Vacuum Gas Oil (VGO). Ce travail avait pour but des migrations en une seule étape et analyse UV qui pourrait être mis en œuvre pour l’analyse de routine dans les laboratoires de contrôle avec une adsorption irréversible réduite. Des résultats très prometteurs ont été obtenus avec l’utilisation de plaques de cellulose pour la séparation des familles de polarité différentes au sein des agrégats d’asphaltènes. Des tests sur l'analyse directe des plaques par Désorption-Ionisation par Électronébulisation (DESI) MS, l'analyse directe en temps réel ou Direct Analysis in Real Time (DART) MS et Ablation Laser (LA) ICP MS ont été effectués. / The presence of heteroatoms and metals in heavy fractions of crude oil can cause the deactivation of hydrotreatment and hydrocracking catalysts. Compounds containing these elements are known to be included in macromolecular asphaltene aggregates, which are considered the most problematic components of heavy oil. This thesis aimed for a better understanding of the chemical environment of these species and on the aggregation phenomenon to optimize refining processes. Separation techniques such as Gel Permeation Chromatography (GPC), Advanced Polymer Chromatography (APC) and High Performance Thin Layer Chromatography (HPTLC) were combined with elementary analysis techniques such as Inductively Coupled Plasma Mass Spectrometry (ICP MS) or high-resolution molecular mass spectrometry for the characterization of heavy fractions of crude oil. Here, the size profiles of species that contain vanadium, nickel and sulfur, the most abundant heteroatoms and metals present in petroleum products, were determined by GPC online with elemental detection by ICP MS. The parameters having the most significant impact on size distribution and the evolution over time of aggregates from solutions of different petroleum cuts were optimized. This allowed the comparison between various feeds and effluents and other series of samples and mixtures from pilot units of refining processes by GPC ICP MS. Results obtained could be related to macroscopic characteristics such as viscosity. Hyphenation of the new APC System to ICP MS has been successfully completed. It allowed the mapping of petroleum samples faster than GPC, therefore with less solvent consumption. However, the differences of the APC chromatograms obtained with respect to the GPC profiles suggested significant unwanted interactions of the highly polar compounds of the petroleum samples with the stationary phase, which have been thoroughly studied. Finally, another type of separation was evaluated. HPTLC, of single-use plates, can be applied to the analysis of heavy petroleum products by polarity without prior deasphalting steps while chromatography columns can be deteriorated because of the irreversible adsorption and asphaltene precipitation. To this end, various types of plates and eluents were tested to develop straightforward SAR (Saturates, Aromatics and Resins) separations of Vacuum Gas Oil (VGO) samples. This method, based on single-step migrations with reduced irreversible adsorption and UV monitoring, could be implemented for routine analysis in control laboratories. Very promising results were obtained by the use of cellulose plates for the separation of different families within asphaltene aggregates. Tests on Desorption ElectroSpray Ionization (DESI) MS, Direct Analysis in Real Time (DART) MS and Laser Ablation (LA) ICP MS analyses of the plates have been performed.