Dissertations / Theses on the topic 'Regular and singular curve'
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PeÌrez-VelaÌsquez, Judith. "Singular and regular travelling waves in tumour encapsulation." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435991.
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Oliver, Joseph Michael. "Pairs of geometric foliations of regular and singular surfaces." Thesis, Durham University, 2010. http://etheses.dur.ac.uk/280/.
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We examine some generic features of surfaces in the Euclidean 3-space $\mathbb{R}^3$ related to the Gauss map on the surface. We consider these features on smooth surfaces and on singular surfaces with a cross-cap singularity. We study some symmetries between two classical pairs of foliations defined on smooth surfaces in $\mathbb{R}^3$: the asymptotic curves and the characteristic curves (called harmonic mean curvature lines in \cite{garciasotomayorharmonic}). The asymptotic curves exist in hyperbolic regions of surfaces and have been well studied. The characteristic curves are in certain ways the analogy of the asymptotic curves in elliptic regions. In this thesis we extend this analogy. . We use We produce results on the characteristic curves mirroring those of Uribe-Vargas (\cite{uribevargas}) on the asymptotic curves. By considering cross-ratios of Legendrian lines in the manifold of contact elements to the surface we show that certain properties of the characteristic curves are invariant under projective transformations, and examine their behaviour at cusps of Gauss. We establish an analogy of the Beltrami-Enepper Theorem, which allows us to distinguish between the two characteristic foliations in a natural geometric way. We show that the local properties of characteristic curves may be used to prove certain global results concerning the elliptic regions of smooth surfaces. Motivated by the study of the asymptotic, principal and characteristic curves on surfaces in $\mathbb{R}^3$, we construct a natural one-to-one correspondence between the set of non-degenerate binary differential equations (BDEs) and linear involutions on the real projective line. We show that one may construct pairs of BDEs that have various symmetric properties using a single involution on $\mathbb{R}P^1$. We study the folded singularities of BDEs, and associate an affine invariant to such points. We show that one may associate a complex parameter to folded singularities that determines the relative positions of various curves of interest. We show that the BDEs asymptotic, characteristic, and principal curves are related to other quadratic forms on surfaces. These include the BDE that defines the lines of arithmetic mean curvature which are studied in \cite{garciasotomayorarith}, and the third fundamental form of the surface. We define a new pair of foliations of a surface which we label the minimal orthogonal spherical image (MOSI) curves which are the integral curves of those tangent directions to a surface that have orthogonal images under the Gauss map, and are inclined at an extremal angle. We establish the configurations of the MOSI curves in a neighbourhood of umbilic points, parabolic points and cusps of Gauss. We construct natural 1-parameter families of BDEs that interpolate between the BDEs we have studied, and establish relationships between these families. We exhibit the existence of a curve of points of zero torsion of the characteristic curves, and a curve of points where the tangent plane to the surface is the osculating plane of a characteristic curve. We determine the behaviour of these curves near cusps of Gauss and umbilic points. We study BDEs with coefficients that vanish simultaneously at an isolated point and with discriminant having an $A_2$-singularity at that point. We show that such BDEs can be grouped into three distinct types, and study the differences between these types in terms of their codimension and the linear parts of their coefficients. We establish the topological configurations of the solution curves in each case with codimension $\leq4$. We study the asymptotic and characteristic curves in the neighbourhood of a parabolic cross-cap, that is, on a singular surface with a cross-cap singularity with a parabolic set having a cusp singularity at the singular point. We obtain the topological configurations of these foliations both in the domain of a parametrisation of such a surface, and on the surface itself. We construct a natural one-parameter family of surfaces with cross-cap singularities in which the parabolic cross-cap is the transition from a hyperbolic cross-cap to an elliptic cross-cap. We study the bifurcations of the asymptotic and characteristic curves in this family.
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Nguyen, Van Luong. "On regular and singular points of the minimum time function." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3424058.
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In this thesis, we study the regularity of the minimum time function Τ for both linear and nonlinear control systems in Euclidean space.
We first consider nonlinear problems satisfying Petrov condition. In this case, Τ is locally Lipschitz and then is differentiable almost everywhere. In general, Τ fails to be differentiable at points where there are multiple time optimal trajectories and its differentiability at a point does not guarantee continuous differentiability around this point. We show that, under some regularity assumptions, the non-emptiness of proximal subdifferential of the minimum time function at a point x implies its continuous differentiability on a neighborhood of Υ. The technique consists of deriving sensitivity relations for the proximal subdifferential of the minimum time function and excluding the presence of conjugate points when the proximal subdifferential is nonempty.
We then study the regularity the minimum time function Τ to reach the origin under controllability conditions which do not imply the Lipschitz continuity of Τ. Basing on the analysis of zeros of the switching function, we find out singular sets (e.g., non - Lipschitz set, non - differentiable set) and establish rectifiability properties for them. The results imply further regularity properties of Τ such as the SBV regularity, the differentiability and the analyticity. The results are mainly for linear control problems.La presente tesi è dedicata allo studio della regolarità della funzione tempo minimo Τ per sistemi di controllo sia lineari che non lineari in dimensione finita. Si considerano dapprima problemi non lineari in cui la condizione di controllabilità detta di Petrov è soddisfatta. Come è ben noto, in questo caso Τ è localmente Lipschitziana e quindi è differenziabile quasi ovunque. In generale, Τ non è differenziabile nei punti dai quali escono diverse traiettorie ottimali e inoltre il fatto che Τ è differenziabile in un punto non garantisce che lo sia in un intorno (l'insieme dei punti di differenziabilità non è aperto). Imponendo alcune condizioni di regolarità sulla dinamica, si dimostra che se il sottodifferenziale prossimale di Τ è non vuoto in un punto x, allora Τ è differenziabile in tutto un intorno di x. La tecnica usata consiste nel derivare relazioni di sensitività per il sottodifferenziale prossimale di Τ e nell'escludere la presenza di punti coniugati dove tale sottodifferenziale è non vuoto. In secondo luogo si studia la regolarità di Τ sotto condizioni di controllabilità più generali, tali da non imporre la Lipschitzianità. In questo caso il bersaglio è l'origine e la dinamica è -- principalmente -- lineare a coefficienti costanti. Si identificano alcuni insiemi singolari (cioè dove Τ non è differenziabile), ad esempio l'insieme dove Τ non è Lipschitz e l'insieme dei punti dove l'insieme raggiungibile presenta più di un versore normale, e si dimostrano risultati di rettificabilità, in questo modo mostrando che sono ``molto piccoli''. Come conseguenza si ricavano ulteriori risultati di regolarità per Τ, fra i quali la regolarità SBV e la differenziabilità e l'analiticità in aperti il cui complementare ha dimensione inferiore a quella dello spazio degli stati. La tecnica usata è basata principalmente su un'analisi accurata degli zeri della cosiddetta funzione di switching.
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Chang, Ting-Ying. "On Singular Solutions of Weighted Divergence Operators." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16817.
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We give a complete classification of the isolated singularities of positive solutions to a broad class of nonlinear elliptic equations involving a weighted p-Laplacian and absorption terms in the punctured unit ball centred at zero. We work in the framework of regular variation theory. We introduce the notion of a fundamental solution to our operator, the weighted p-Laplacian. We prove a sharp condition for the removability of all singularities at zero for the positive solutions to our problem. We also show that any non-removable singularity at zero for a positive solution to our prescribed problem is either weak (that is, it is behaves asymptotically like the fundamental solution at zero) or strong (where it dominates the fundamental solution at zero). The main difficulty and novelty of this thesis, for which we develop new techniques, come from the explicit asymptotic behaviour of the strong singularity solutions in the critical case, which had previously remained open even for the p-Laplacian. We also study the existence and uniqueness of the positive solution of our problem with a prescribed admissible behaviour at zero and a Dirichlet condition on the boundary of the unit ball. We also classify the behaviour near zero of the positive solutions with isolated singularities for the weighted p-Laplacian equation. We show that all positive solutions of this problem either has a finite limit at the singularity (and, in certain cases, the solution can be extended as a continuous solution in the entire unit ball), or has a weak singularity depending on the range of p. We note there are no solutions with strong singularities here, unlike the case above where absorption terms are introduced.
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Cai, Yulin. "Integral Points on Modular Curves, Singular Moduli and Conductor-Discriminant Inequality." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0098.
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Cette thèse traite de trois sujets en trois parties. Dans la première partie, nous étudions les points S-entiers de la courbe modulaire X0(p). Yuri Bilu a montré qu’en utilisant la méthode de Baker, on peut donner une borne effective de la hauteur de ces points en fonction de p, du corps de base et de l’ensemble de places S. Min Sha a rendu ce résultat explicite. avec une borne doublement exponentielle en dans p. Nous améliorons considérablement dans cette thèse le résultat de Sha, en obtenant une borne simplement exponentielle. Cela se fait en utilisant une version très explicite du principe de Chevalley-Weil basée sur des travaux de Qing Liu et Dino Lorenzini. Notre borne est non seulement plus nette que celle de Sha, mais également explicite en tous les paramètres. Dans la deuxième partie, nous considérons des modules singuliers de courbes elliptiques. Pour un module singulier fixe a, nous donnons une borne supérieure effective de la norme de x - a pour un autre module singulier x avec un grand discriminant. Dans la troisième partie, nous donnons une relation entre les conducteurs d’Artin d’un modèle Werestrass Y et ceux de deux modèles de Weierstrass donnés Y1,Y2. Avec cette relation, nous déduisons que l’inégalité conducteur-discriminant est valable pour Y si elle est valable pour Y1 et Y2This thesis discusses three topics, so it includes three parts. In the first part, we study S-integral points on the modular curve X0(p). Bilushowed that, using Baker’s method, they can be effectively bounded in terms of p, the base field and the set of places S. Sha made this result explicit, but the bound he obtained is double exponential in p. We drastically improve upon the result of Sha, obtaining a simple exponential bound. This is done using a very explicit version of the Chevalley-Weil principle based on the work of Liu and Lorenzini. Our bound is not only sharper than that of Sha, but is also explicit in all parameters. In the second part, we consider singular moduli. For a fixed singular modulus a, we give an effective upper bound of norm of x - a for another singular modulus x with large discriminant. In the third part, we give a relation between Artin conductors of a Weierstrass model Y and the ones of two given Weierstrass models Y1,Y2. With this relation, we know that the conductor-discriminant inequality holds for Y if it holds for Y1 and Y2
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Yang, Xiaojing. "Nonlinear Control System Stability Metrics via A Singular Perturbation Approach." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364466371.
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Kindler, Lars Verfasser], Hélène [Akademischer Betreuer] Esnault, Phung Ho Hai [Akademischer Betreuer], and Alexander [Akademischer Betreuer] [Beilinson. "Regular singular stratified bundles in positive characteristic / Lars Kindler. Gutachter: Phung Ho Hai ; Alexander A. Beilinson. Betreuer: Hélène Esnault." Duisburg, 2012. http://d-nb.info/1029288453/34.
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Ouoba, Mahamadi. "Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-26100.
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In this Master thesis, we use a singular and regular perturbation theory to derive an analytic approximation formula for the expected discounted penalty function. Our model is an extension of Cramer–Lundberg extended classical model because we consider a more general insurance risk model in which the compound Poisson risk process is perturbed by a Brownian motion multiplied by a stochastic volatility driven by two factors- which have mean reversion models. Moreover, unlike the classical model, our model allows a ruin to be caused either by claims or by surplus’ fluctuation. We compute explicitly the first terms of the asymptotic expansion and we show that they satisfy either an integro-differential equation or a Poisson equation. In addition, we derive the existence and uniqueness conditions of the risk model with two stochastic volatilities factors.
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Fedina, Jekaterina. "Statistiniai stegoanalizės metodai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2012~D_20140704_172603-70609.
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Pagrindinis šio darbo tikslas susipažinti su steganografijos mokslu bei statistiniais stegoanalizės metodais, kurių dėka slepiama ir atrandama informacija įvairiuose failuose. Šitame magistro darbe išnagrinėti, aprašyti bei įgyvendinti du steganografijos ir du stegoanalizės metodai. Visi metodai realizuoti JAVA programavimo kalba, daliai matematiniams skaičiavimams atlikti panaudota MAPLE programa. Darbo pabaigoje pateikta metodų analizė.The main goal of the thesis is to review the methods of steganography and steganalysis and to experiment with them. Steganography helps to embed hidden messages in such way that anyone except the intended recipient is unaware of the existence of the message but with the use of statistical steganalysis methods those hidden messages can be detected. This thesis consists of two steganography (LSB and LSBH) and two steganalysis methods (RS and PoV) description and implementation. All methods were implemented with JAVA code. Thesis is concluded with a comparison of these methods' quality.
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Alabdallah, Suleiman. "Development of a nonlinear equations solver with superlinear convergence at regular singularities." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/17045.
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In dieser Arbeit präsentieren wir eine neue Art von Newton-Verfahren mit Liniensuche, basierend auf Interpolation im Bildbereich nach Wedin et al. [LW84]. Von dem resultierenden stabilisierten Newton-Algorithmus wird theoretisch und praktisch gezeigt, dass er effizient ist im Falle von nichtsingulären Lösungen. Darüber hinaus wird beobachtet, dass er eine superlineare Rate von Konvergenz bei einfachen Singularitäten erhält. Hingegen ist vom Newton-Verfahren ohne Liniensuche bekannt, dass es nur linear von fast allen Punkten in der Nähe einer singulären Lösung konvergiert. In Hinsicht auf Anwendungen auf Komplementaritätsprobleme betrachten wir auch Systeme, deren Jacobimatrix nicht differenzierbar sondern nur semismooth ist. Auch hier erreicht unser stabilisiertes und beschleunigtes Newton- Verfahren Superlinearität bei einfachen Singularitäten.In this thesis we present a new type of line-search for Newton’s method, based on range space interpolation as suggested by Wedin et al. [LW84]. The resulting stabilized Newton algorithm is theoretically and practically shown to be efficient in the case of nonsingular roots. Moreover it is observed that it maintains a superlinear rate of convergence at simple singularities. Whereas Newton’s method without line-search is known to converge only linearly from almost all points near the singular root. In view of applications to complementarity problems we also consider systems, whose Jacobian is not differentiable but only semismooth. Again, our stabilized and accelerated Newton’s method achieves superlinearity at simple singularities.
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Rêgo, Thiago Luiz de Oliveira do. "Sobre o número máximo de retas em superfícies não singular de grau 4 em P3." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9302.
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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In 1943 Beniamino Segrebelievedtohaveshownthatthemaximumnumberof lines containedinasmoothquarticsurfacein P3 is 64, ([16]).Butrecently,therewasa majoroverturnonthatthemewhenthemathematiciansRamsandSchuttfoundthat Segre hadmadeamistakeinhisworktoforgetthequartic'sfamily Z , ([14]),which essentiallycorrespondstothosequarticscontainingalinesthatcanbeincidenttomore than 18 lines containedinthesurface.Inthiswork,basedon([14]),weshowthatevery smoothquarticsurface,whichdoesnotbelongtofamily Z containsamaximumof 64 lines. Oneofthemostimportanttoolstoshowthisresult,isthestudyof_brations _l induced byaline l containedonthesurface,andtherelationshipbetweentheEuler characteristicofthebase(P1 in ourcase),the_bersandthesurfaceconcerned.
Em 1943,BeniaminoSegreacreditouterdemonstradoqueonúmeromáximo de retascontidasnumasuperfíciequárticanãosingularem P3 é 64; ([16]). Mas recentemente,houveumareviravoltanessetema,quandoosmatemáticosSªawomir Rams eMatthiasSchüttconstataramqueSegretinhacometidoumerroemseutrabalho ao esquecerasquárticasdafamília Z; ([14]), quecorrespondemessencialmenteas quárticas quepossuemretasquepodemserincidentesamaisde 18 retas contidas na superfície.Nestetrabalho,tendocomobase[14],mostramosquetodaquártica não singular,quenãopertenceafamília Z; contémnomáximo 64 retas. Umadas ferramentasmaisimportantes,paramostraresseresultado,éoestudodas_brações _l induzida porumareta l contidanasuperfície,earelaçãoqueexisteentrea característica deEulerdabase(emnossocaso P1), das_brassingulareseadasuperfície em questão.
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Iezzi, Annamaria. "Nombre de points rationnels des courbes singulières sur les corps finis." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4027/document.
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On s'intéresse, dans cette thèse, à des questions concernant le nombre maximum de points rationnels d'une courbe singulière définie sur un corps fini, sujet qui, depuis Weil, a été amplement abordé dans le cas lisse. Cette étude se déroule en deux temps. Tout d'abord on présente une construction de courbes singulières de genres et corps de base donnés, possédant un grand nombre de points rationnels : cette construction, qui repose sur des notions et outils de géométrie algébrique et d'algèbre commutative, permet de construire, en partant d'une courbe lisse X, une courbe à singularités X', de telle sorte que X soit la normalisée de X', et que les singularités ajoutées soient rationnelles sur le corps de base et de degré de singularité prescrit. Ensuite, en utilisant une approche euclidienne, on prouve une nouvelle borne sur le nombre de points fermés de degré deux d'une courbe lisse définie sur un corps fini.La combinaison de ces résultats, à priori indépendants, permet notamment d'étudier le problème de savoir quand la borne d'Aubry-Perret, analogue de la borne de Weil dans le cas singulier, est atteinte. Cela nous amène de façon naturelle à l'étude des propriétés des courbes maximales et, lorsque la cardinalité du corps de base est un carré, à l'analyse du spectre des genres de ces dernièresIn this PhD thesis, we focus on some issues about the maximum number of rational points on a singular curve defined over a finite field. This topic has been extensively discussed in the smooth case since Weil's works. We have split our study into two stages. First, we provide a construction of singular curves of prescribed genera and base field and with many rational points: such a construction, based on some notions and tools from algebraic geometry and commutative algebra, yields a method for constructing, given a smooth curve X, another curve X' with singularities, such that X is the normalization of X', and the added singularities are rational on the base field and with the prescribed singularity degree. Then, using a Euclidian approach, we prove a new bound for the number of closed points of degree two on a smooth curve defined over a finite field.Combining these two a priori independent results, we can study the following question: when is the Aubry-Perret bound (the analogue of the Weil bound in the singular case) reached? This leads naturally to the study of the properties of maximal curves and, when the cardinality of the base field is a square, to the analysis of the spectrum of their genera
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Flores, Quiroz Martín. "Descriptive analysis of the acquisition of the base form, third person singular, present participle regular past, irregular past, and past participle in a supervised artificial neural network and an unsupervised artificial neural network." Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/115653.
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Tesis para optar al grado de Magíster en Lingüistica mención Lengua InglesaStudying children’s language acquisition in natural settings is not cost and time effective. Therefore, language acquisition may be studied in an artificial setting reducing the costs related to this type of research. By artificial, I do not mean that children will be placed in an artificial setting, first because this would not be ethical and second because the problem of the time needed for this research would still be present. Thus, by artificial I mean that the tools of simulation found in artificial intelligence can be used. Simulators as artificial neural networks (ANNs) possess the capacity to simulate different human cognitive skills, as pattern or speech recognition, and can also be implemented in personal computers with software such as MATLAB, a numerical computing software. ANNs are computer simulation models that try to resemble the neural processes behind several human cognitive skills. There are two main types of ANNs: supervised and unsupervised. The learning processes in the first are guided by the computer programmer, while the learning processes of the latter are random.
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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.
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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrödinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
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Aagaard, Fransson Erik Johannes, and Tobias Wall-Horgen. "Building and Evaluating a 3D Scanning System for Measurementsand Estimation of Antennas and Propagation Channels." Thesis, KTH, Elektroteknisk teori och konstruktion, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-104802.
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Wireless communications rely, among other things, on theunderstanding of the properties of the radio propagationchannel, the antennas and their interplay. Adequate measurementsare required to verify theoretical models and togain knowledge of the channel behavior and antenna performance.As a result of this master thesis we built a 3D fieldscanner measurement system to predict multipath propagationand to measure antenna characteristics. The 3Dscanner allows measuring a signal at the point of interestalong a line, on a surface or within a volume in space. In orderto evaluate the system, we have performed narrowbandchannel sounding measurements of the spatial distributionof waves impinging at an imaginary spherical sector. Datawas used to estimate the Angle-of-Arrivals (AoA) and amplitudeof the waves. An estimation method is presented tosolve the resulting inverse problem by means of regularizationwith truncated singular value decomposition. The regularizedsolution was then further improved with the helpof a successive interference cancellation algorithm. Beforeapplying the method to measurement data, it was testedon synthetic data to evaluate its performance as a functionof the noise level and the number of impinging waves. Inorder to minimize estimation errors it was also required tofind the phase center of the horn antenna used in the channelmeasurements. The task was accomplished by directmeasurements and by the regularization method, both resultsbeing in good agreement.
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Bacha, Inès. "Traitement symbolique des systèmes d'équations différentielles non linéaires au voisinage des singularités." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10078.
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Cette these se rattache a l'etude locale des equations differentielles, elle est composee de trois parties dependantes. Dans la premiere partie, nous presentons differentes theories telles que les formes normales, les transformations quasi-monomiales ainsi que celle du polygone de newton afin de mettre en place un algorithme pour simplifier les systemes planaires d'equations differentielles au voisinage des singularites isolees. Cet algorithme se base essentiellement sur les travaux d'a. Bruno sur les solutions locales des systemes d'equations differentielles. Quelques exemples d'application sont donnes afin d'illustrer ce travail. Dans la deuxieme partie, les differentes theories precedentes ainsi que l'etude des courbes algebriques nous permettent d'etendre cet algorithme dans l'espace. Dans la partie finale, nous proposons une methode de reduction de l'ordre des systemes differentiels en dimension n.
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Badaoui, Noad. "Dynamique et estimation paramétrique pour les gyroscopes laser à milieu amplificateur gazeux." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEM058/document.
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Les gyroscopes laser à gaz constituent une solution technique de haute performances dans les problématiques de navigation inertielle. Néanmoins, pour de très faibles vitesses de rotation, les petites imperfections des miroirs de la cavité optique font que les deux faisceaux contra-propageant sont verrouillés en phase. En conséquence, les mesures en quadrature de leur différence de phase ne permettent plus de remonter directement aux vitesses de rotation à l'intérieur d'une zone autour de zéro, dite zone aveugle statique, ou, si l'on utilise une procédure d'activation mécanique, dite zone aveugle dynamique. Ce travail montre qu'il est néanmoins possible, en utilisant des méthodes issues du filtrage et de l'estimation, de remonter aux vitesses de rotation mêmes si ces dernières sont en zone aveugle. Pour cela, on part d'une modélisation physique de la dynamique que l'on simplifie par des techniques de perturbations singulières pour en déduire une généralisation des équations de Lamb. Il s'agit de quatre équations différentielles non-linéaires qui décrivent la dynamique des intensités et des phases des deux faisceaux contra-propageant. Une étude qualitative par perturbations régulières, stabilité exponentielle des points d'équilibre et applications de Poincaré permet de caractériser les zones aveugles statiques et dynamiques en fonction des imperfections dues aux miroirs. Il est alors possible d'estimer en ligne avec un observateur asymptotique fondé sur les moindre carrés récursifs ces imperfections en rajoutant aux deux mesures en quadrature celles des deux intensités. La connaissance précise de ces imperfections permet alors de les compenser dans la dynamique de la phase relative, et ainsi d'estimer les rotations en zone aveugle. Des simulations numériques détaillées illustrent l'intérêt de ces observateurs pour augmenter la précision des gyroscopes à gazGaz ring laser gyroscopes provide a high performance technical solution for inertial navigation. However, for very low rotational speeds, the mirrors imperfections of the optical cavity induce a locking phenomena between the phases of the two counter-propagating Laser beams. Hence, the measurements of the phase difference can no longer be used when the speed is within an area around zero, called lock-in zone, or,if a procedure of mechanical dithering is implemented, dithering lock-in zone. Nevertheless, this work shows that it is possible using filtering and estimation methods to measure the speed even within the lock-in zones. To achieve this result, we exploit a physical modeling of the dynamics that we simplify, using singular perturbation techniques, to obtain a generalization of Lamb's equations. There are four non-linear differential equations describing the dynamics of the intensities and phases of the two counter-propagating beams. A qualitative study by regular perturbation theory, exponential stability of the equilibrium points and Poincaré maps allows a characterisation of the lock-in zones according to the mirrors imperfections. It is then possible to estimate online, with an asymptotic observer based on recursive least squares, these imperfections by considering the additional measurements of the beam intensities. Accurate knowledge of these imperfections enables us to compensate them in the dynamic of the relative phase, and thus to estimate rotational speeds within the lock-in zones. Detailed numerical simulations illustrate the interest of those observers to increase the accuracy of gas ring laser gyroscopes
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Wehbe, Charbel. "Étude asymptotique de modèles en transition de phase." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2311/document.
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Ce rapport de thèse est consacré à l'étude de modèles de champ de phase de type Caginalp. Nous considérons ici, deux parties : la première étant une généralisation du modèle de champ de phase de Caginalp basée sur la loi de Maxwell-Cattaneo et la seconde traite le même modèle dans sa version conservative. L'étude dans les deux parties est faite dans un domaine borné. De plus, dans la première partie on distingue les cas de conditions aux bords de type Dirichlet ainsi que Neumann, tandis que dans la deuxième partie le modèle est étudié uniquement avec les conditions Dirichlet (avec un potentiel régulier puis un potentiel singulier). Tout d'abord, l'existence, l'unicité, et la régularité des solutions sont analysées aux moyens d'arguments classiques. Ensuite, l'existence d'ensembles bornés absorbants est établie. Enfin, dans certains cas, l'existence de l'attracteur global et d'attracteurs exponentiels sont analysésThis thesis report is devoted to the study of Caginalp type phase-field Models. Here, we consider two parts : the first is a generalization of the Caginalp type phase-field model based on a generalization of the Maxwell-Cattaneo law and the second with the same model in its conservative version. The study in the two parts is made in a bounded domain. In addition, in the first part we distinguish cases of boundary conditions of Dirichlet and Neumann, while in the second part the model is studied only with Dirichlet conditions (with a regular potential and a singular potential). First, the existence, uniqueness, and regularity of solutions are analyzed by means of classical arguments. Then, the existence of bounded absorbing sets is established. Finally, in some cases, the existence of the global attractor and exponential attractors are analyzed
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Kratz, Marie. "Some contributions in probability and statistics of extremes." Habilitation à diriger des recherches, Université Panthéon-Sorbonne - Paris I, 2005. http://tel.archives-ouvertes.fr/tel-00239329.
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Giovannardi, Gianmarco. "Variations for submanifolds of fixed degree." Doctoral thesis, 2020. https://hdl.handle.net/2158/1287865.
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The aim of this PhD thesis is to study the area functional for submanifolds immersed in an equiregular graded manifold. This setting, extends the sub-Riemannian one, removing the bracket generating condition. However, even in the sub-Riemannian setting only sub-manifolds of dimension or codimension one have been extensively studied. We will study the general case and observe that in higher codimension new phenomena arise, which can not show up in the Riemannian case. In particular, we will prove the existence of isolated surfaces, which do not admit degree preserving variation: a phenomena observed by now only for curves, related to the notion of abnormal geodesics.
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Lo, Ja-Yaw, and 羅嘉耀. "Singular Surfaces and Regular Domains of Tridiagonal Matrices." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/57229348429464493498.
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碩士國立清華大學
數學研究所
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This paper is concerned with tridiagonal matrices of the form ┌ ┐ │g(1) 1 │ │ 1 g(2) 1 │ A(g)=│ . . . │. │ 1 g(n-1) 1 │ │ 1 g(n)│ └ ┘ where g=(g(1),g(2),...,g(n)) is a real vector in Rn. We treat such a matrix as a function of its diagonal vector g=(g(1),g(2),...,g(n)) and investigate, by means of a three-term recurrence relation, the properties of a partition of Rn which consists of "regular domains" and "singular surfaces" with respect to A(g). In particular, properties related to geometrical, topological, symmetry and oscillatory properties of a general partition are given, and analytic estimates of the sizes of the regular domains, as well as existence and localization of eigenvalues related to linear and nonlinear difference eigenvalue problems are derived as application.
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Zamani, Mohsen. "Modeling multivariable time series using regular and singular autoregressions." Phd thesis, 2014. http://hdl.handle.net/1885/151565.
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The primary aim of this thesis is to study the modeling of high-dimensional time series with periodic missing observations. This study is very important in different branches of science and technology such as: econometric modeling, signal processing and systems and control. For instance, in the field of econometric modeling, it is crucial to provide proper models for national economies to help policy makers with decision making and policy adjustments. These models are built upon available high-dimensional data sets, which are not usually collected at the same rate. For example, some data such as, the employment rate are available on a monthly basis while some others like the gross domestic product (GDP) are collected quarterly. Motivated by applications in econometric modeling, we mainly consider systems, which have two sets of measurement streams, one stream being available at all times and the other one is observed every N-th time. There are two major issues involved with modeling of high-dimensional time series with periodic missing observations, namely, the curse of dimensionality and missing observations. Generalized dynamic factor models (GDFMs), which have been recently introduced in the field of econometric modeling, are exploited to handle the curse of dimensionality phenomenon. Furthermore, the blocking technique from systems and control is used to tackle issues associated with the missing observations. In this thesis, we consider a class of GDFMs and assume that there exists an underlying linear time-invariant system operating at the highest sample rate and our task is to identify this model from the available mixed frequency measurements. To this end, we first provide a very detailed study about zeros of linear systems with alternate missing measurements. Zeros of this class of linear systems are examined when the parameter matrices of a minimal state space representation of a transfer function matrix corresponding to the underlying high frequency system assume generic values. Under this setting, we then illustrate situations under which linear systems with missing observations are completely zero-free. It is worthwhile noting that the obtained condition is very common in an econometric modeling context. Then we apply this result and assume that the underlying high frequency system has an autoregressive (AR) structure. Next, we study identifiability of AR systems from those population second order moments, which can be observed in principle. We propose the method of modified extended Yule-Walker equations to show that the set of identifiable AR systems is an open and dense subset of the associated parameter space i.e. AR systems are generically identifiable.
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Carriazo, A., M. C. Marquez, and Hassan Ugail. "Normal Approximations of Regular Curves and Surfaces." 2015. http://hdl.handle.net/10454/8162.
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YesBezier curves and surfaces are two very useful tools in Geometric Modeling, with many applications. In this paper, we will offer a new method to provide approximations of regular curves and surfaces by Bezier ones, with the corresponding examples.
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范志鵬. "The decoupling design and control of regular and singular systems." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/84169131491912558148.
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Hsiu, Teng Kuo, and 鄧國修. "The research of the automatic measurement on regular curve by." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/00084266656797862200.
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Blažková, Eva. "Struktura a aproximace reálných rovinných algebraických křivek." Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-389639.
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Finding a topologically accurate approximation of a real planar algebraic curve is a classic problem in Computer Aided Geometric Design. Algorithms describing the topology search primarily the singular points and are usually based on algebraic techniques applied directly to the curve equation. In this thesis we propose a more geometric approach, taking into account the subsequent high-precision approximation. Our algorithm is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. To find the characteristic points we use not only the primary algebraic equation of the curve but also, and more importantly, its implicit support function representation. Using the rational Puiseux series, we describe local properties of curve branches at the points of interest and exploit them to find their connectivity. The support function representation is also used for an approximation of the segments. In this way, we obtain an approximate graph of the entire curve with several nice properties. It approximates the curve within a given Hausdorff distance. The actual error can be measured efficiently. The ap- proximate curve and its offsets are piecewise rational. And the question of topological equivalence of the...
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Kálnai, Peter. "Kompaktní moduly nad nesingulárními okruhy." Doctoral thesis, 2020. http://www.nusl.cz/ntk/nusl-434348.
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This doctoral thesis provides several new results in which we leverage the inner structure of non-singular rings, in particular of self-injective von Neumann regular rings. First, we describe categorical and set-theoretical conditions under which all products of compact objects remain compact, where the notion of compactness is relativized with respect to a fixed subclass of objects. A special instance when such closure property holds are the classic module categories over rings of our interest. Moreover, we show that a potential counterexample for Köthe's Conjecture might be in the form of a countable local subring of a suitable simple self-injective von Neumann regular ring. 1