Three problems are being investigated in this thesis. The first two relate to the modelling and analysis of martensitic phase transitions, while the third is concerned with some mathematical tools used in this setting. After a short introduction (Chapter 1) and overviews of the calculus of variations and martensitic phase transformations (Chapter 2), the research part of this thesis is divided into three chapters. We show in Chapter 3 that for the two wells $\mathrm{SO}(3)U$ and $\mathrm{SO}(3)V$ to be rank-one connected, where the $3\times 3$ symmetric positive definite $U$ and $V$ have the same eigenvalues, it is necessary and sufficient that $\mathrm{det}(U-V)=0$, a result that does not hold in higher dimensions. Using this criterion and a result of Gurtin, formulae for the twinning plane and the shearing vector are obtained, which yield an extremely simple condition for the occurrence of so-called compound twins. Our results also provide a simple classification of the twinning mode of the two wells by looking at the crystallographic properties of the eigenvectors of the difference $U-V$. As an illustration, we apply our results to cubic-to-tetra gonal,tetragonal-to-monoclinic and cubic-to-monoclinic transitions. Chapter 4 focuses on the mathematical analysis of biaxial loading experiments in martensite, more particularly on how hysteresis relates to metastability. These experiments were carried out by Chu and James and their mathematical treatment was initiated by Ball, Chu and James. Experimentally it is observed that a homogeneous deformation $y_1(x)= U_1x$ is the stable state for `small' loads while $y_2(x)=U_2x$ is stable for `large' loads. A model was proposed by Ball, Chu and James which, for a certain intermediate range of loads, predicts crucially that $y_1(x)=U_1x$ remains metastable i.e., a local - as opposed to global - minimiser of the energy). This result explains convincingly the hysteresis that is observed experimentally. It is easy to get an upper bound for when metastability finishes. However, it was also noticed that this bound (the Schmid Law) may not be sharp, though this required some geometric conditions on the sample. In this chapter, we rigorously justify the Ball-Chu-James model by means of De Giorgi's $\Gamma$-convergence, establish some properties of local minimisers of the (limiting) energy and prove the metastability result mentioned above. An important part of the chapter is then devoted to establishing which geometric conditions are necessary and sufficient for the counter-example to the Schmid Law to apply. Finally, Chapter 5 investigates the structure of the solutions to the two-well problem. Restricting ourselves to the subset $K=\{H\}\cup \mathrm{SO}(2)V \subset\mathrm{SO}(2)U\cup\mathrm{SO}(2)V$ and assuming the two wells to be compatible, we let $T_1$ and $T_2$ denote the two (not necessarily distinct) twins of $H$ on $\mathrm{SO}(2)V$ and ask the following question: if $\nu_x$ is a non-trivial gradient Young measure almost everywhere supported on $K$, does its support necessarily contain a pair of rank-one connected matrices on a set of positive measure? Although we do not provide a solution for the general case, we show that this is true whenever (a) $\nu_x\equiv \nu$ is homogeneous and $\mathrm{supp}\nu\cap \mathrm{SO}(2)V$ is connected, (b) $\nu_x\equiv \nu$ is homogeneous and $T_1=T_2$ i.e., when the two wells are trivially rank-one connected) or (c) $\mathrm{supp}\nu_x \subset F$ a.e., for some finite set $F$. We also establish a more general case provided a strong `rigidity' conjecture holds.

This work investigates the use of formal logic as a practical tool for describing the syntax and semantics of a subset of English, and building a computer program to answer data base queries expressed in that subset. To achieve an intimate connection between logical descriptions and computer programs, all the descriptions given are in the definite clause subset of the predicate calculus, which is the basis of the programming language Prolog. The logical descriptions run directly as efficient Prolog programs. Three aspects of the use of logic in natural language analysis are covered: formal representation of syntactic rules by means of a grammar formalism based on logic, extraposition grammars;. formal semantics for the chosen English subset, appropriate for data base queries; informal semantic and pragmatic rules to translate analysed sentences into their formal semantics. On these three aspects, the work improves and extends earlier work by Colmerauer and others, where the use of computational logic in language analysis was first introduced.

Veterinarinė odontologija – tai nauja greitai besivystanti veterinarinės medicinos sritis. Daugelyje šalių veterinarinė odontologija jau egzistuoja kaip atskira disciplina, tirianti dantų ir burnos ertmės ligas, profilaktiką bei gydymą. Remiantis statistiniais duomenimis, dantų, žandikaulio ir burnos ertmės ligos gyvūnų tarpe - labai paplitusios visame pasaulyje. Daugiau nei 95 proc. kačių ir šunų per visą jų gyvenimą pasireiškia dantų ir burnos ertmės patologijos. Kadangi kačių dantų ligų gydymas yra gana sudėtingas ir skausmingas gyvūnui procesas, geriau tinka taikyti profilaktikos priemones, nei gydymą. Todėl nuo mažens gyvūną reikia pratinti prie burnos ertmės higienos. Lietuvoje dar labai mažai dėmesio skiriama šiai problemai. Deja, tik 8 proc. gyvūnų savininkų laiku pastebi dantų ligų požymius. Šeimininkai neskiria reikalingo dėmesio savo augintinio burnos ertmės priežiūrai, nesusimąstydami, kad dantų ligos gali būti bendros gyvūno savijautos pablogėjimo ir daugelio ligų priežastimi. Darbo tikslas – nustatyti kačių sergamumą dantų ligomis, bei apžvelgti jų gydymą ir profilaktikos priemonių taikymą. Darbo uždaviniai: 1. išanalizuoti ir apžvelgti literatūros šaltinius, susijusius su šia tema; 2. išnagrinėti dantų ligų diagnozavimo ir gydymo metodus; 3. išsiaiškinti ar kačių lytis turi įtakos dantų ligų pasireiškimui; 4. nustatyti kokiomis dantų ligomis dažniausiai serga katės; 5. nustatyti kokios ligos kokiose amžiaus grupėse paplitusios dažniausiai; 6. nustatyti... [toliau žr. visą tekstą] / The aim of this work is to determine morbidity of feline dental disease,and review the treatment and prevention measures. The objectives: 1. To examine and review literature sources and information concerning the work objectives. 2. To review dental disease diagnostic and treatment methods. 3. To detemine whether cat gender has an effect on dental diseases. 4. To determine which dental diseases are the most popular in cats. 5. To determine what kind of dental diseases are the most popular in age groups. 6. To determine which breed of cats most likely have dental diseases. 7. To analyze prevention measures of dental disease. The research results and conclusions are: Cat sex does not have an effect on dental diseases. Dental diseases are most likely to develop in mixed breed cats. The most popular dental disease in cats is calculus. Mostly dental diseases affect cats which are older than 10 years. Periodontitis usually affects cats at age of 7 to 9 and those older than 10 years. Dental diseases mostly occur in the Siamese – oriental group of cat, and less longhaired cat group. The most common prevention measure is the specific cat food for teeth. Most cat owners do not clean their cat teeth in veterinary clinic. In conclusion, the cat owners do not have enough knowledge about dental diseases, its treatment and prevention factors.

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This thesis analyzes the solution attempts of Zeno&rsquo / s paradoxes and its related problems in a historical context. The evolution of calculus and its critiques will also be examined regarding the rigor problem in mathematics. As a conclusion a compound method is proposed.

This thesis presents the prediction algorithm for the price of the share of risky asset. The price of the share is presented by dynamic model and observation is presented by the measurement model. Dynamic model is derived by using Stochastic Calculus. The algorithm is simulated by using Matlab.

La principal contribución de esta Tesis es la propuesta de un modelo de agente BDI graduado (g-BDI) que permita especificar una arquitetura de agente capaz de representar y razonar con actitudes mentales graduadas. Consideramos que una arquitectura BDI más exible permitirá desarrollar agentes que alcancen mejor performance en entornos inciertos y dinámicos, al servicio de otros agentes (humanos o no) que puedan tener un conjunto de motivaciones graduadas. En el modelo g-BDI, las actitudes graduadas del agente tienen una representación explícita y adecuada. Los grados en las creencias representan la medida en que el agente cree que una fórmula es verdadera, en los deseos positivos o negativos permiten al agente establecer respectivamente, diferentes niveles de preferencias o de rechazo. Las graduaciones en las intenciones también dan una medida de preferencia pero en este caso, modelan el costo/beneficio que le trae al agente alcanzar una meta. Luego, a partir de la representación e interacción de estas actitudes graduadas, pueden ser modelados agentes que muestren diferentes tipos de comportamiento. La formalización del modelo g-BDI está basada en los sistemas multi-contextos. Diferentes lógicas modales multivaluadas se han propuesto para representar y razonarsobre las creencias, deseos e intenciones, presentando en cada caso una axiomática completa y consistente. Para tratar con la semántica operacional del modelo de agente, primero se definió un calculus para la ejecución de sistemas multi-contextos, denominado Multi-context calculus. Luego, mediante este calculus se le ha dado al modelo g-BDI semántica computacional. Por otra parte, se ha presentado una metodología para la ingeniería de agentes g-BDI en un escenario multiagente. El objeto de esta propuesta es guiar el diseño de sistemas multiagentes, a partir de un problema del mundo real. Por medio del desarrollo de un sistema recomendador en turismo como caso de estudio, donde el agente recomendador tiene una arquitectura g-BDI, se ha mostrado que este modelo es valioso para diseñar e implementar agentes concretos. Finalmente, usando este caso de estudio se ha realizado una experimentación sobre la flexibilidad y performance del modelo de agente g-BDI, demostrando que es útil para desarrollar agentes que manifiesten conductas diversas. También se ha mostrado que los resultados obtenidos con estos agentes recomendadores modelizados con actitudes graduadas, son mejores que aquellos alcanzados por los agentes con actitudes no-graduadas. / The central contribution of this dissertation is the proposal of a graded BDI agent model (g-BDI), specifying an architecture capable of representing and reasoning with graded mental attitudes. We consider that making the BDI architecture more exible will allow us to design and develop agents capable of improved performance in uncertain and dynamic environments, serving other agents (human or not) that may have a set of graded motivations.In the g-BDI model, the agent graded attitudes have an explicit and suitable representation. Belief degrees represent the extent to which the agent believes a formula to be true. Degrees of positive or negative desires allow the agent to set di_erent levels of preference or rejection respectively. Intention degrees also give a preference measure but, in this case, modelling the cost/benefit trade off of achieving an agent's goal. Then, agents having different kinds of behaviour can be modelled on the basis of the representation and interaction of their graded attitudes. The formalization of the g-BDI agent model is based on Multi-context systems and in order to represent and reason about the beliefs, desires and intentions, we followed a many-valued modal approach. Also, a sound and complete axiomatics for representing each graded attitude is proposed. Besides, in order to cope with the operational semantics aspects of the g-BDI agent model, we first defined a Multi-context calculus for Multi-context systems execution and then, using this calculus we give this agent model computational meaning.Furthermore, a software engineering process to develop graded BDI agents in a multiagent scenario is presented. The aim of the proposed methodology is to guide the design of a multiagent system starting from a real world problem. Through the development of a Tourism recommender system, where one of its principal agents is modelled as a g-BDI agent, we show that the model is useful to design and implement concrete agents.Finally, using the case study we have made some experiments concerning the exibility and performance of the g-BDI agent model, demonstrating that this agent model is useful to develop agents showing varied and rich behaviours. We also show that the results obtained by these particular recommender agents using graded attitudes improve those achieved by agents using non-graded attitudes.

Let G be a compact Lie group and let π be an irreducible representation of G of highest weight λ. We study the operator-valued Fourier transform of the product of the j-function and the pull-back of ?? by the exponential mapping. We show that the set of extremal points of the convex hull of the support of this distribution is the coadjoint orbit through ?? + ??. The singular support is furthermore the union of the coadjoint orbits through ?? + w??, as w runs through the Weyl group. Our methods involve the Weyl functional calculus for noncommuting operators, the Nelson algebra of operants and the geometry of the moment set for a Lie group representation. In particular, we re-obtain the Kirillov-Duflo correspondence for compact Lie groups, independently of character formulae. We also develop a "noncommutative" version of the Kirillov character formula, valid for noncentral trigonometric polynomials. This generalises work of Cazzaniga, 1992.

This is a study of the semantics and proof theory of the logic of bunched implications (BI), which is promoted as a logic of (computational) resources, and is a foundational component of separation logic, an approach to program analysis. BI combines an additive, or intuitionistic, fragment with a multiplicative fragment. The additive fragment has full use of the structural rules of weakening and contraction, and the multiplicative fragment has none. Thus it contains two conjunctive and two implicative connectives. At various points, we illustrate a resource view of BI based upon the Kripke resource semantics. Our first original contribution is the formulation of a proof system for BI in the newly developed proof-theoretical formalism of the calculus of structures. The calculus of structures is distinguished by its employment of deep inference, but we already see deep inference in a limited form in the established proof theory for BI. We show that our system is sound with respect to the elementary Kripke resource semantics for BI, and complete with respect to a formulation of the partially-defined Kripke resource semantics. Our second contribution is the development from a semantic standpoint of preliminary ideas for a hybrid logic of bunched implications (HBI). We give a Kripke semantics for HBI in which nominal propositional atoms can be seen as names for resources, rather than as names for locations, as is the case with related proposals for BI-Loc and for intuitionistic hybrid logic.

Thesis (M.S.) -- Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.