Artificial vision is the problem of creating systems capable of processing visual information. A fundamental sub-problem of artificial vision is image segmentation, the problem of detecting a structure from a digital image. Examples of segmentation problems include the detection of a road from an aerial photograph or the determination of the boundaries of the brain's ventricles from medical imagery. The extraction of structures allows for subsequent higher-level cognitive tasks. One of them is shape comparison. For example, if the brain ventricles of a patient are segmented, can their shapes be used for diagnosis? That is to say, do the shapes of the extracted ventricles resemble more those of healthy patients or those of patients suffering from schizophrenia? This thesis deals with the problem of image segmentation and shape comparison in the mathematical framework of partial differential equations. The contribution of this thesis is threefold: 1. A technique for the segmentation of regions is proposed. A cost functional is defined for regions based on a non-parametric functional of the distribution of image intensities inside the region. This cost is constructed to favor regions that are homogeneous. Regions that are optimal with respect to that cost can be determined with limited user interaction. 2. The use of direction information is introduced for the segmentation of open curves and closed surfaces. A cost functional is defined for structures (curves or surfaces) by integrating a local, direction-dependent pattern detector along the structure. Optimal structures, corresponding to the best match with the pattern detector, can be determined using efficient algorithms. 3. A technique for shape comparison based on the Laplace equation is proposed. Given two surfaces, one-to-one correspondences are determined that allow for the characterization of local and global similarity measures. The local differences among shapes (resulting for example from a segmentation step) can be visualized for qualitative evaluation by a human expert. It can also be used for classifying shapes into, for example, normal and pathological classes.

In the thesis, we propose a newly-developed method called the method of Connected Local Fields (CLF) to analyze opto-electromagnetic passive devices. The method of CLF somewhat resembles a hybrid between the finite difference and pseudo-spectral methods. For opto-electromagnetic passive devices, our primary concern is their steady state behavior, or narrow-band characteristics, so we use a frequency-domain method, in which the system is governed by the Helmholtz equation. The essence of CLF is to use the intrinsic general solution of the Helmholtz equation to expand the local fields on the compact stencil. The original equation can then be transformed into the discretized form called LFE-9 (in 2-D case), and the intrinsic reconstruction formulae describing each overlapping local region can be obtained. Further, we present rigorous analysis of the numerical dispersion equation of LFE-9, by means of first-order approximation, and acquire the closed-form formula of the relative numerical dispersion error. We are thereby able to grasp the tangible influences brought both by the sampling density as well as the propagation direction of plane wave on dispersion error. In our dispersion analysis, we find that the LFE-9 formulation achieves the sixth-order accuracy: the theoretical highest order for discretizing elliptic partial differential equations on a compact nine-point stencil. Additionally, the relative dispersion error of LFE-9 is less than 1%, given that sampling density greater than 2.1 points per wavelength. At this point, the sampling density is nearing that of the Nyquist-Shannon sampling limit, and therefore computational efforts can be significantly reduced.

This research was done to develop tools to predict parametric roll motion of ships in regular and irregular sea and provide guidelines to avoid parametric roll during initial design stage. A post Panamax hull form (modified C11 Hull form, Courtesy of MARIN) was used to study parametric roll in ships. The approach of the study has been to simplify the roll equation of motion to a single degree of freedom equation so as to utilize the tools available to analyze the system retaining the non-linear character of the system. The Hill’ equation is used to develop highly accurate stability boundaries in the Ince-Strutt Diagram. The effect of non-linear damping has also been incorporated into the chart for the first time providing a simple method to predict the bounded roll motion amplitude. Floquet theory is also extended to predict parametric roll motion amplitude. Forward speed of the vessel has been treated as a bifurcation parameter and its effects studied both in head and following sea condition. In the second half of the research, parametric roll of the vessel in irregular sea is investigated using the Volterra Quadratic model. GM variation in irregular sea was obtained using transfer functions of the Volterra model. Heave and pitch coupling to roll motion was also studied using this approach. Sensitivity studies of spectral peak period and significant wave height on roll motion amplitude were also carried out. Forward speed effects were also evaluated using the Volterra approach. Based on the study, the Hill’s equation approach was found to give more accurate prediction of parametric roll in regular sea. The boundaries in the stability chart were more accurately defined by the Hill’s equation. The inclusion of non-linear damping in the stability chart gave reasonably accurate bounded motion amplitude prediction. The Volterra approach was found to be a good analytical prediction tool for parametric roll motion in irregular sea. Using the Volterra model, it was found that there is a high probability of parametric roll when the spectral modal period is close to twice the natural period of roll.

Abstract The objective of this study was to explore the feasibility of using the One-Variable Linear Equation Situational Test to investigate the development of the concept of one-variable linear equation for middle school students. The conduct of the first stage of this study was as follows: first, a thorough literature review was made; which was followed by interviews with middle and high school math teachers; finally a survey of the eighth-grade students was made using the ¡§One-Variable Linear Equation Concept Unstructured Questionnaire¡¨. The second stage of this study was to devise the One-Variable Linear Equation Situational Test. First, a detailed concept map of the one-variable linear equation was made based on the results obtained in the first stage of this study. Then, a situational test of one-variable linear equation was constructed according to the map. This test was to be used later in the one-to-one interviews with twelve seventh-grade students from a middle school in Kaohsiung, who did not learn the one-variable linear equation before. These twelve subjects were randomly devided into two groups: with guidance and without guidance. The data of the math achievement tests were also collected for these subjects. The results of the test interviews were analyzed and the feasibility of using the One-Variable Linear Equation Situational Test to investigate the development of the concept of one-variable linear equation was discussed. The analysis results of individual questions of the situational test of one-variable linear equation indicated that the concepts of one-variable linear equation for middle school students were detectable. This suggested that it was feasible to use the One-Variable Linear Equation Situational Test to investigate the development of the concept of one-variable linear equation for middle school students. All subjects who participated in this study already had some preliminary ideas of the one-variable linear equation. The factor of providing guidance would enhance the development of the concept of one-variable linear equation and it would reduce the differences in numbers of various concepts of one-variable linear equation developed among the high, medium and low achievement students. Therefore, the variable of with- or without-guidance would have some effects on the detectable concepts of one-variable linear equation by the One-Variable Linear Equation Situational Test.

Non-isothermal crystallization of the PET/PTT copolyesters was studied at five different cooling rates over 1-20oC/min by means of differential scanning calorimetry (DSC). Both the Ozawa equation and the modified Avrami equation have been used to analyze the crystallization kinetics. The non-isothermal kinetics of most copolymers cannot be described by the Ozawa analysis, except the copolyester with a composition of 66.3% trimethylene- (TT) and 33.7 %ethylene- terephthalates (ET). It may be due to the inaccuracy of the Ozawa assumptions, such as the secondary crystallization is neglected. From the kinetic analysis using the modified Avrami equation, the Avrami exponents, n, were found to be in the range of 2.43-4.67 that are dependent on the composition of the copolyesters. The results indicated that the primary crystallization of the PET/PTT copolymers followed a heterogeneous nucleation and a spherulitic growth mechanism during the non-isothermal crystallization. In the cases of the copolyesters with either TT or ET less than 10%, we found the molten temperature is a key factor to decide whether the Ozawa equation can be succeeded in analyzing the dynamic crystallization. For the non-isothermal crystallization, a single exothermic peak was detected in each DSC curve regardless of the composition and the cooling rate. It indicated that a single-mode distribution of the crystallite sizes was formed during the cooling process. After the non-isothermal crystallization, the melting behavior of the specimens was monitored by temperature modulated DSC (TMDSC) in the conventional mode and the modulated mode. Multiple endothermic peaks were observed in both modes. The wide-angle X-ray diffraction (WAXD) patterns of these copolymers showed that the peak height became sharper and sharper as the crystallization temperature increased, but the position of the diffraction peaks did not change apparently. It indicated that the multiple melting behaviors did not originate from the melting of the crystals with different structures. The melting behavior of these PET/PTT copolyesters can be explained logically by using the melt-recrystallization model. From the reversing and non-reversing signals of TMDSC, the melting-recrystallization-remelting phenomena were further verified. In addition, a small endothermic peak was found at the highest melting temperature in the reversing thermogram for TT-enriched copolyesters. It is reasonably to believe that this endotherm is attributed to the melting of the crystals that are formed in regime I during the heating scan. The cocrystallization of the PET/PTT copolyesters was studied using DSC and WAXD. A clear endothermic peak in the DSC thermogram was detected over the entire range of copolymer composition. A minimum melting temperature was found for the copolyester with 50% ET. The WAXD patterns of these copolymers can be divided into two groups with sharp diffraction peaks, i.e., PET type and PTT type crystals. The transition of crystal structure between PET type and PTT type occurred around the eutectic composition (50 % ET and TT), determined from the variation of the melting temperature with the composition. In addition, the fiber diagram and the WAXD pattern of the copolyester with the eutectic composition showed a different crystalline structure. These results indicated that the cocrystallization behavior of the PET/PTT copolyesters was isodimorphic.

Cette thèse est consacrée à l'étude du comportement asymptotique de solutions d'une classe d'équations aux dérivées partielles avec des coefficients fortement oscillants. Dans un premier temps, on s'intéresse à une famille d'équations non linéaires, des lois de conservation scalaires hétérogènes, qui interviennent dans divers problèmes de la mécanique des fluides ou de l'électromagnétisme non linéaire. On suppose que le flux de cette équation est périodique en espace, et que la période des oscillations tend vers zéro. On identifie alors les profils asymptotiques microscopique et macroscopique de la solution, et on démontre un résultat de convergence forte; en particulier, on montre que lorsque la condition initiale ne suit pas le profil microscopique dicté par l'équation, il se forme une couche initiale en temps durant laquelle les solutions s'adaptent à celui-ci. Dans un second temps, on considère une équation de transport linéaire, qui modélise l'évolution de la densité d'un ensemble de particules chargées dans un potentiel électrique aléatoire et très oscillant. On établit l'apparition d'oscillations microscopiques en temps et en espace dans la densité, en réponse à l'excitation par le potentiel électrique. On donne également des formules explicites pour l'opérateur de transport homogénéisé lorsque la dimension de l'espace est égale à un.

Dans cette thèse, nous présentons des méthodes asymptotiques <br />mathématiquement justifiées permettant de connaître les champs <br />électromagnétiques dans des milieux à couches minces hétérogènes. <br />La motivation de ce travail est le calcul du champ électrique dans des <br />cellules biologiques composées d'un cytoplasme conducteur entouré <br />d'une fine membrane très isolante. <br />Nous remplaçons la membrane, lorsque son épaisseur est infiniment <br />petite, par des conditions de transmission ou des conditions aux <br />limites appropriées et nous estimons l'erreur commise par ces <br />approximations.<br /> Pour les basses fréquences, nous considérons l'équation quasistatique<br />donnant le potentiel dont dérive le champ. A l'aide d'un <br />calcul en géométrie circulaire nous obtenons les expressions explicites<br /> du potentiel et nous en déduisons les asymptotiques du champ <br />électrique, en fonction de l'épaisseur de la couche mince, avec des <br />estimations de l'erreur. Nous estimons ensuite la différence entre le <br />champ réel et le champ statique. Puis nous généralisons notre <br />développement asymptotique à une géométrie quelconque. <br /> La deuxième partie de cette thèse traite des moyennes fréquences : <br />nous donnons le développement asymptotique de la solution de <br />l'équation de Helmholtz lorsque l'épaisseur de la membrane tend vers <br />0. Tous ces précédents résultats sont illustrés par des calculs par <br />éléments finis.<br /> Enfin, pour les hautes fréquences, nous construisons une condition <br />d'impédance pseudodifférentielle permettant de concentrer l'effet de <br />la couche sur son bord intérieur. Nous concluons cette thèse par un <br />problème de diffraction à haute fréquence d'une onde incidente par <br />un disque de petite taille. A l'aide d'une analyse pseudodifférentielle, <br />nous bornons la norme de la trace du champ diffracté à distance fixe <br />de l'inhomogénéité en fonction de la taille de l'objet et de l'onde <br />incidente.

The main purpose of this thesis is to use modern goal-oriented adaptive methods of Lie group analysis to construct the optimal sys- tem of Black-Scholes equation. We will show in this thesis how to obtain all invariant solutions by constructing what has now become so popular, optimal system of sub-algebras, the main Lie algebra admit- ted by the Black-Scholes equation. First, we obtain the commutator table of already calculated symmetries of the Black-Scholes equation. We then followed with the calculations of transformation of the gen- erators with the Lie algebra L6 which provides one-parameter group of linear transformations for the operators. Here we make use of the method of Lie equations to solve the partial di®erential equations. Next, we consider the construction of optimal systems of the Black- Scholes equation where the method requires a simpli¯cation of a vector to a general form to each of the transformations of the generators. Further, we construct the invariant solutions for each of the op- timal system. This study is motivated by the analysis of Lie groups which is being taken to another level by ALGA here in Blekinge In- stitute Technology, Sweden. We give a practical and in-depth steps and explanation of how to construct the commutator table, the calcu- lation of the transformation of the generators and the construction of the optimal system as well as their invariant solutions. Keywords: Black-Scholes Equation, commutators, commutator table, Lie equa- tions, invariant solution, optimal system, generators, Airy equation, structure constant, / It was an accolade for us to work with Professor Nail.H. Ibrgimov. +46762600953

The experiment performed by Itano, Heinzen, Bollinger and Wineland on the quantum Zeno effect is analyzed in detail through a quantum map derived by conventional quantum mechanics based on the Schrodinger equation. The analysis shows that a slight modification of their experiment leads to a significantly different result from the one that is predicted through von Neumann's hypothesis of collapse of the wave function in the quantum measurement theory. This may offer a possibility of an experimental test of von Neumann's quantum measurement theory. / text

Dans ce travail, on étudier, au voisinage d'un point d'équilibre, l'existence et l'unicité et la dépendance régulière des solutions presque-périodique (p.p.), présqu'automorphe (p.a.), asymptotiquement p.p., asymptotiquement p.a., pseudo p.p., pseudo p.a., pseudo p.p. avec poids, pseudo p.a. avec poids de la famille d'équations de Liénard forcée suivantes x''(t) + f(x(t), p). x'(t) + g(x(t), p) = ep(t), (1) où le terme ep est de la même nature que la solution, et p est un paramètre dans un espace de Banach. On utilise le théorème des fonctions implicites au voisinage de l'équilibre. On étudier aussi deux cas particuliers de la famille (1) qui sont x''(t) + f1(x(t)). x'(t) + g1(x(t))= e(t), x''(t) + f2(x(t), q). x'(t) + g2(x(t), q) = e(t). On établit aussi un nouveau résultat sur la dépendance différentielle des solutions S-asymptotiquement presque-périodique du problème de Cauchy x'(t)=A(t) x(t)+f(t, x(t),u(t) ) x(0) = ζ , par rapport à la condition initial et le contrôle u. On applique cet résultat sur une équation parabolique avec coefficients périodique par rapport au temps.