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1
Chen, Jixin. "Some Domain Decomposition and Convex Optimization Algorithms with Applications to Inverse Problems." Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/271782.
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Domain decomposition and convex optimization play fundamental roles in current computation and analysis in many areas of science and engineering. These methods have been well developed and studied in the past thirty years, but they still require further study and improving not only in mathematics but in actual engineering computation with exponential increase of computational complexity and scale. The main goal of this thesis is to develop some efficient and powerful algorithms based on domain decomposition method and convex optimization. The topicsstudied in this thesis mainly include two classes of convex optimization problems: optimal control problems governed by time-dependent partial differential equations and general structured convex optimization problems. These problems have acquired a wide range of applications in engineering and also demand a very high computational complexity. The main contributions are as follows: In Chapter 2, the relevance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations. To study the optimal control problem, we obtain second order domain decomposition methods by combining Crank-Nicolson scheme with implicit Galerkin method in the sub-domains and explicit flux approximation along inner boundaries in Chapter 3. Parallelism can be easily achieved for these explicit/implicit methods. Time step constraints are proved to be less severe than that of fully explicit Galerkin finite element method. Based on the domain decomposition method in Chapter 3, we propose an iterative algorithm to solve an optimal control problem associated with the corresponding partial differential equation with pointwise constraint for the control variable in Chapter 4. In Chapter 5, overlapping domain decomposition methods are designed for the wave equation on account of prediction-correction" strategy. A family of unit decomposition functions allow reasonable residual distribution or corrections. No iteration is needed in each time step. This dissertation also covers convergence analysis from the point of view of mathematics for each algorithm we present. The main discretization strategy we adopt is finite element method. Moreover, numerical results are provided respectivelyto verify the theory in each chapter.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Winkler, Gunter. "Control constrained optimal control problems in non-convex three dimensional polyhedral domains." Doctoral thesis, Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800626.
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The work selects a specific issue from the numerical analysis of
optimal control problems. We investigate a linear-quadratic optimal
control problem based on a partial differential equation on
3-dimensional non-convex domains. Based on efficient solution methods
for the partial differential equation an algorithm known from control
theory is applied. Now the main objectives are to prove that there is
no degradation in efficiency and to verify the result by numerical
experiments.
We describe a solution method which has second order convergence,
although the intermediate control approximations are piecewise
constant functions. This superconvergence property is gained from a
special projection operator which generates a piecewise constant
approximation that has a supercloseness property, from a sufficiently
graded mesh which compensates the singularities introduced by the
non-convex domain, and from a discretization condition which
eliminates some pathological cases.
Both isotropic and anisotropic discretizations are investigated and
similar superconvergence properties are proven.
A model problem is presented and important results from the regularity
theory of solutions to partial differential equation in non-convex
domains have been collected in the first chapters. Then a collection
of statements from the finite element analysis and corresponding
numerical solution strategies is given. Here we show newly developed
tools regarding error estimates and projections into finite element
spaces. These tools are necessary to achieve the main results. Known
fundamental statements from control theory are applied to the given
model problems and certain conditions on the discretization are
defined. Then we describe the implementation used to solve the model
problems and present all computed results.
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Backlund, Ulf. "Envelopes of holomorphy for bounded holomorphic functions." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 1992. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-141155.
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Some problems concerning holomorphic continuation of the class of bounded holomorphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Gleason’s Problem for H°°(Ω) cannot be solved. Furthermore a proof of the existence of a bounded domain of holomorphy in C2 for which the volume of the H°°-envelope of holomorphy is infinite is given. The idea of the proof is to put a family of so-called ”Sibony domains” into the unit bidisk by a packing procedure and patch them together by thin neighbourhoods of suitably chosen curves. If H°°(Ω) is the Banach algebra of bounded holomorphic functions on a bounded domain Ω in Cn and if p is a point in Ω, then the following problem is known as Gleason’s Problem for Hoo(Ω) : Is the maximal ideal in H°°(Ω) consisting of functions vanishing at p generated by (z1 -p1) , ... , (zn - pn) ? A sufficient condition for solving Gleason’s Problem for 77°° (Ω) for all points in Ω is given. In particular, this condition is fulfilled by a convex domain Ω with Lip1+e boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenson. It is also proved that Gleason’s Problem can be solved for all points in certain unions of two polydisks in C2. One of the ideas in the methods of proof is integration along specific polygonal lines. Certain properties of some open sets defined by global plurisubharmonic functions in Cn are studied. More precisely, the sets Du = {z e Cn : u(z) < 0} and Eh = {{z,w) e Cn X C : h(z,w) < 1} are considered where ti is a plurisubharmonic function of minimal growth and h≠0 is a non-negative homogeneous plurisubharmonic function. (That is, the functions u and h belong to the classes L(Cn) and H+(Cn x C) respectively.) It is examined how the fact that Eh and the connected components of Du are H°°-domains of holomorphy is related to the structure of the set of discontinuity points of the global defining functions and to polynomial convexity. Moreover it is studied whether these notions are preserved under a certain bijective mapping from L(Cn) to H+(Cn x C). Two counterexamples are given which show that polynomial convexity is not preserved under this bijection. It is also proved, for example, that if Du is bounded and if the set of discontinuity points of u is pluripolar then Du is of type H°°. A survey paper on general properties of envelopes of holomorphy is included. In particular, the paper treats aspects of the theory for the bounded holomorphic functions. The results for the bounded holomorphic functions are compared with the corresponding ones for the holomorphic functions.digitalisering@umu.se
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Aksnes, Vegard. "On Fourier Series in Convex Domains." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9517.
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We consider systems of complex exponential functions in spaces of square integrable functions. Some classical one-dimensional theory is reviewed, in particular, we emphasize the duality between the Riesz bases of complex exponential functions in $L^2$-spaces and complete interpolating sequences in $PW^2$-spaces of entire functions of exponential type. Basis properties for $L^2$-spaces over planar convex domains are then studied in detail. The convex domain in question is shown to be crucial for what basis properties the corresponding $L^2$-space possesses. We explain some results related to Fuglede's conjecture about existence of orthonormal bases and then a result by Lyubarskii and Rashkovskii regarding Riesz bases for $L^2$-spaces over convex polygons, symmetric with respect to the origin. Finally, we make a modest attempt to apply the techniques by Lyubarskii and Rashkovskii combined with approximation of plurisubharmonic functions using logarithms of moduli of entire functions, to construct a complete system of exponential functions in the space of square integrable functions over a disk. This work is not completed yet.
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Ford, Robert Kuperberg Krystyna. "Path curvature on a convex roof." Auburn, Ala., 2007. http://repo.lib.auburn.edu/2007%20Fall%20Dissertations/Ford_Robert_45.pdf.
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Abuelela, Waleed Mostafa Kamal Abdelfatah. "Hardy type inequalities for non-convex domains." Thesis, University of Birmingham, 2010. http://etheses.bham.ac.uk//id/eprint/1268/.
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Amiran, Edoh Yosef. "Caustics and evolutes for convex planar domains." Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/80448.
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Fällström, Anders. "Algebras of bounded holomorphic functions." Doctoral thesis, Umeå universitet, Institutionen för matematik, teknik och naturvetenskap, 1994. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-114744.
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Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. If A(f2) is the Banach algebra of functions holomorphic in the bounded domain Q in Cn and continuous on the boundary and if p is a point in Q, then the following problem is known as Gleason’s Problem for A(Q) : Is the maximal ideal in A(Q) consisting of functions vanishing at p generated by (Zl ~Pl) , ■■■ , (Zn - Pn) ? A sufficient condition for solving Gleason’s Problem for A(Q) for all points in Q is given. In particular, this condition is fulfilled by a convex domain Q with Lipi+£-boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenzon. One of the ideas in the methods of proof is integration along specific polygonal lines. If Gleason’s Problem can be solved in a point it can be solved also in a neighbourhood of the point. It is shown, that the coefficients in this case depends holomorphically on the points. Defining a projection from the spectrum of a uniform algebra of holomorphic functions to Cn, one defines the fiber in the spectrum over a point as the elements in the spectrum that projects on that point. Defining a kind of maximum modulus property for domains in Cn, some problems concerning the fibers and the number of elements in the fibers in certain algebras of bounded holomorphic functions are solved. It is, for example, shown that the set of points, over which the fibers contain more than one element is closed. A consequence is also that a starshaped domain with the maximum modulus property has schlicht /y°°-envelope of holomorphy. These kind of problems are also connected with Gleason’s problem. A survey paper on general properties of algebras of bounded holomorphic functions of several variables is included. The paper, in particular, treats aspects connecting iy°°-envelopes of holomorphy and some areas in the theory of uniform algebras.Diss. (sammanfattning) Umeå : Umeå universitet, 1994, härtill 6 uppsatser
digitalisering@umu
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Doto, James William. "Conditional uniform convexity in Orlicz spaces and minimization problems." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27352.
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Thaher, Mohammed. "Efficient Algorithms for the Maximum Convex Sum Problem." Thesis, University of Canterbury. Computer Science and Software Engineering, 2009. http://hdl.handle.net/10092/2102.
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The work of this thesis covers the Maximum Subarray Problem (MSP) from a new
perspective. Research done previously and current methods of finding MSP include
using the rectangular shape for finding the maximum sum or gain. The rectangular
shape region used previously is not flexible enough to cover various data
distributions. This research suggested using the convex shape, which is expected to
have optimised and efficient results.
The steps to build towards using the proposed convex shape in the context of MSP are
as follows: studying the available research in-depth to extract the potential guidelines
for this thesis research; implementing an appropriate convex shape algorithm;
generalising the main algorithm (based on dynamic programming) to find the second
maximum sum, the third maximum sum and up to Kth maximum sum; and finally
conducting experiments to evaluate the outcomes of the algorithms in terms of the
maximum gain, time complexity, and the running time.
In this research, the following findings were achieved: one of the achievements is
presenting an efficient algorithm, which determines the boundaries of the convex
shape while having the same time complexity as other existing algorithms (the prefix
sum was used to speed up the convex shape algorithm in finding the maximum sum).
Besides the first achievement, the algorithm was generalized to find up to the Kth
maximum sum. Finding the Kth maximum convex sum was shown to be useful in
many applications, one of these (based on a study with the cooperation of
Christchurch Hospital in New Zealand) is accurately and efficiently locating brain
tumours. Beside this application, the research findings present new approaches to
applying MSP algorithms in real life applications, such as data mining, computer
vision, astronomy, economics, chemistry, and medicine.
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Cox, Bruce. "Applications of accuracy certificates for problems with convex structure." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39489.
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Applications of accuracy certificates for problems with convex structure This dissertation addresses the efficient generation and potential applications of accuracy certificates in the framework of “black-box-represented” convex optimization problems - convex problems where the objective and the constraints are represented by “black boxes” which, given on input a value x of the argument, somehow (perhaps in a fashion unknown to the user) provide on output the values and the derivatives of the objective and the constraints at x. The main body of the dissertation can be split into three parts. In the first part, we provide our background --- state of the art of the theory of accuracy certificates for black-box-represented convex optimization. In the second part, we extend the toolbox of black-box-oriented convex optimization algorithms with accuracy certificates by equipping with these certificates a state-of-the-art algorithm for large-scale nonsmooth black-box-represented problems with convex structure, specifically, the Non-Euclidean Restricted Memory Level (NERML) method. In the third part, we present several novel academic applications of accuracy certificates. The dissertation is organized as follows: In Chapter 1, we motivate our research goals and present a detailed summary of our results. In Chapter 2, we outline the relevant background, specifically, describe four generic black-box-represented generic problems with convex structure (Convex Minimization, Convex-Concave Saddle Point, Convex Nash Equilibrium, and Variational Inequality with Monotone Operator), and outline the existing theory of accuracy certificates for these problems. In Chapter 3, we develop techniques for equipping with on-line accuracy certificates the state-of-the-art NERML algorithm for large-scale nonsmooth problems with convex structure, both in the cases when the domain of the problem is a simple solid and in the case when the domain is given by Separation oracle. In Chapter 4, we develop several novel academic applications of accuracy certificates, primarily to (a) efficient certifying emptiness of the intersection of finitely many solids given by Separation oracles, and (b) building efficient algorithms for convex minimization over solids given by Linear Optimization oracles (both precise and approximate). In Chapter 5, we apply accuracy certificates to efficient decomposition of “well structured” convex-concave saddle point problems, with applications to computationally attractive decomposition of a large-scale LP program with the constraint matrix which becomes block-diagonal after eliminating a relatively small number of possibly dense columns (corresponding to “linking variables”) and possibly dense rows (corresponding to “linking constraints”).
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Coatney, Ryan D. "Mean Square Estimate for Primitive Lattice Points in Convex Planar Domains." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2501.
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The Gauss circle problem in classical number theory concerns the estimation of N(x) = { (m1;m2) in ZxZ : m1^2 + m2^2 <= x }, the number of integer lattice points inside a circle of radius sqrt(x). Gauss showed that P(x) = N(x)- pi * x satisfi es P(x) = O(sqrt(x)). Later Hardy and Landau independently proved that P(x) = Omega_(x1=4(log x)1=4). It is conjectured that inf{e in R : P(x) = O(x^e )}= 1/4. I. K atai showed that the integral from 0 to X of |P(x)|^2 dx = X^(3/2) + O(X(logX)^2). Similar results to those of the circle have been obtained for regions D in R^2 which contain the origin and whose boundary dD satis fies suff cient smoothness conditions. Denote by P_D(x) the similar error term to P(x) only for the domain D. W. G. Nowak showed that, under appropriate conditions on dD, P_D(x) = Omega_(x1=4(log x)1=4) and that the integral from 0 to X of |P_D(x)|^2 dx = O(X^(3/2)). A result similar to Nowak's mean square estimate is given in the case where only "primitive" lattice points, {(m1;m2) in Z^2 : gcd(m1;m2) = 1 }, are counted in a region D, on assumption of the Riemann Hypothesis.
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Deng, Si Wen. "Precondition technique for conservative space-fractional diffusion equations in convex domains." Thesis, University of Macau, 2018. http://umaclib3.umac.mo/record=b3950597.
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Sloane, Craig Andrew. "Hardy-Sobolev-Maz'ya inequalities for fractional integrals on halfspaces and convex domains." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41125.
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This thesis will present new results involving Hardy and Hardy-Sobolev-Maz'ya inequalities for fractional integrals. There are two key ingredients to many of these results. The first is the conformal transformation between the upper halfspace and the unit ball. The second is the pseudosymmetric halfspace rearrangement, which is a type of rearrangment on the upper halfspace based on Carlen and Loss' concept of competing symmetries along with certain geometric considerations from the conformal transformation.
After reducing to one dimension, we can use the conformal transformation to prove a sharp Hardy inequality for general domains, as well as an improved fractional Hardy inequality over convex domains. Most importantly, the sharp constant is the same as that for the halfspace.
Two new Hardy-Sobolev-Maz'ya inequalities will also be established. The first will be a weighted inequality that has a strong relationship with the pseudosymmetric halfspace rearrangement. Then, the psuedosymmetric halfspace rearrangement will play a key part in proving the existence of the standard Hardy-Sobolev-Maz'ya inequality on the halfspace, as well as some results involving the existence of minimizers for that inequality.
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Gonzalez, Espinoza Luis. "The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28640.
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Meas, Len. "Estimations de dispersion et de Strichartz dans un domaine cylindrique convexe." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4038/document.
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Dans ce travail, nous allons établir des estimations de dispersion et des applications aux inégalités de Strichartz pour les solutions de l’équation des ondes dans un domaine cylindrique convexe Ω ⊂ R³ à bord C∞, ∂Ω ≠ ∅. Les estimations de dispersion sont classiquement utilisées pour prouver les estimations de Strichartz. Dans un domaine Ω général, des estimations de Strichartz ont été démontrées par Blair, Smith, Sogge [6,7]. Des estimations optimales ont été prouvées dans [29] lorsque Ω est strictement convexe. Le cas des domaines cylindriques que nous considérons ici généralise les resultats de [29] dans le cas où la courbure positive dépend de l'angle d'incidence et s'annule dans certaines directionsIn this work, we establish local in time dispersive estimates and its application to Strichartz estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains Ω ⊂ R³ with smooth boundary ∂Ω ≠ ∅. Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair, Smith, Sogge [6,7]. Optimal estimates in strictly convex domains have been obtained in [29]. Our case of cylindrical domains is an extension of the result of [29] in the case where the nonnegative curvature radius depends on the incident angle and vanishes in some directions
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Rockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.
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In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the global relation for the Laplace equation on domains with smooth boundary. Using properties of the F_p-transform, we show that the global relation defines a continuously invertible map between the Dirichlet and Neumann data for a given BVP for the Laplace equation. Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.
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Ludwig, André [Verfasser], and Ernst [Akademischer Betreuer] Kuwert. "A relaxed partitioning disk for strictly convex domains = Eine relaxierte Partitionsdisk für strikt konvexe Gebiete." Freiburg : Universität, 2013. http://d-nb.info/1123476918/34.
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Vasiloglou, Nikolaos. "Isometry and convexity in dimensionality reduction." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/28120.
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Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.Committee Chair: David Anderson; Committee Co-Chair: Alexander Gray; Committee Member: Anthony Yezzi; Committee Member: Hongyuan Zha; Committee Member: Justin Romberg; Committee Member: Ronald Schafer.
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Duda, Jakub. "Aspects of delta-convexity /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p3115539.
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Santos, Jo?o Paulo Rodrigues dos. "A concep??o da dupla domina??o em Horkheimer (1930-1940)." PROGRAMA DE P?S-GRADUA??O EM FILOSOFIA, 2017. https://repositorio.ufrn.br/jspui/handle/123456789/24570.
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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES)
O texto tem por objetivo tratar o tema da domina??o, o qual foi muito caro na alta modernidade, por assim dizer, bem como na modernidade tardia e, ao que nos parece, continua a ser de nuclear relev?ncia para maior e melhor entendimento acerca do destino da Civiliza??o Ocidental Hodierna que, de barb?rie em barb?rie, pavimenta sua estrada para o decl?nio. Discorre sobre a hip?tese da dupla domina??o em Max Horkheimer (1898-1973) e segue uma linha de racioc?nio que procurou expor o entendimento o modo como se deu a compreens?o do autor citado acima acerca da domina??o da Natureza e da domina??o do Homem. Procurou-se, no presente trabalho, n?o somente expor o que se entende por dupla domina??o, mas, sobretudo, mostrar de que maneira se deu essa domina??o bifurcada. Dito de modo mais claro procurou-se percorrer um vi?s investigativo que nos sugere que houve uma evolu??o na domina??o duplicada e, portanto, a miss?o prec?pua desse trabalho ? mostrar em que sentido houve essa evolu??o e como identific?-la dentro da obra do autor em estudo, tendo em vista os anos 30 e 40 do s?culo XX, levando-se em considera??o as mudan?as de ordem hist?rica, social, pol?tica, econ?mica e psicol?gica ? uma vez que, na d?cada de trinta t?nhamos uma concep??o de domina??o da natureza efetivada pela ci?ncia e domina??o do homem realizada pela pol?tica, nos idos dos anos quarenta temos uma domina??o da natureza externa que continuo, a ser controlada pela ci?ncia positivista e uma domina??o da natureza interna -, a qual diz respeito ? forma??o do ego do indiv?duo na civiliza??o modernista.
This paper aims to address the issue of domination that for us is very dear in high modernity and late modernity and, that it seems, relevant to a bigger and better understanding about Western civilization from barbarism in barbarism as a destiny paving his road to the decline. Our dissertation will discuss about the double domination hypothesis in Max Horkheimer (1898-1973) theoretical knowledgement about the issue. This research has taken a path that tried to conduct us to a comprehension on how the author did understand nature and man?s domination. We tried, in this work, not only to expose what it is meant by double domination, however, and above all, we had exposed how that bifurcated domination has happened continually since the beginning of the civilization. To be clear, we tried to follow a path that suggests us that there has been an evolution in duplicated domination, and this has made the difference on how our work was written to show what was the way that this evolution has occurred and how to identify it in our author works during the years 30tieth and 40tieth of the twentieth century, taking into account the historical, social, political, economic and psychological changes ? climate in the thirties, we had started out by politics, in the forties we have an external nature domination that keeps itself on course controlled by positivist science and an inner nature domination, which concerns the formation of the individual ego in the civilization. Finally, we conclude that research exposing our particular view point at the side of short commentaries which we do believe that is properly the culmination of our thoughts above the theme and that it will serve to close with a personal opinion on the work as a whole.
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Marx, Didier. "Contribution à l'étude de la stabilité des systèmes électrotechniques." Thesis, Vandoeuvre-les-Nancy, INPL, 2009. http://www.theses.fr/2009INPL078N/document.
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Dans cette thèse différents outils issus de l'automatique non linéaire ont été mis en œuvre et ont permis d'apporter une première solution au problème de stabilité large signal des dispositifs électriques. A l'aide de modèles flous de type Takagi-Sugeno, on a montré qu'il était possible de résoudre le problème de stabilité dans le cas de deux applications électrotechniques à savoir un hacheur contrôlé en tension et l'alimentation par l'intermédiaire un filtre d'entrée d'un dispositif électrique fonctionnant à puissance constante. Dans le cas du hacheur, la taille estimée des bassins d'attraction reste modeste. Les raisons essentielles à l'échec obtenu dans la recherche de bassin de grande taille peut résulter dans le fait que d'une part , la mise sous forme TS du système n'est pas unique et que d'autre part les matrices du sous modèle TS du système ne sont de Hurwitz que dans une gamme très restreinte de variations du rapport cyclique. Dans le cas de l'alimentation par l'intermédiaire d'un filtre d'entrée d'un dispositif fonctionnant à puissance constante, on a montré que l'utilisation d'un modèle flou de type Takagi-Sugeno permettait d'exhiber un domaine d'attraction de taille significative. On a fourni des outils permettant de borner la plage de variations des pôles du système dans un domaine donné de l'espace d'état, domaine dans lequel la stabilité du modèle TS est prouvée. L'utilisation de la D-stabilité permet de connaitre les dynamiques maximales du système. La notion de stabilité exponentielle permet de connaître les dynamiques minimales du système. L'approche utilisée pour prouver la stabilité du système en présence de variations paramétriques, pour les deux systèmes étudiés, n'autorise que des variations extrêmement faibles de la valeur du paramètre autour de sa valeur nominaleIn this thesis, various tools resulting from the nonlinear automatic were implemented and made it possible to bring a first solution to the problem of large signal stability of the electric systems. Using Takagi-Sugeno fuzzy models, one showed that it was possible to in the case of solve the problem of stability two electrotechnical applications to knowing a Boost converter controlled in tension and an electric system constituted by an input filter connected to an actuator functioning at constant power. In the case of the Boost converter, the estimated size of attraction domain remains modest. The reasons essential with the failure obtained in the search for domain of big size can result in the fact that on the one hand, the setting TS fuzzy models of the system is not single and that on the other hand the matrices of local model of TS model of the system are of Hurwitz only in one very restricted range of variations of the cyclic ratio. In the case of the electric system via a filter of entry of a functioning device at constant power, one showed that the use of a Takagi-Sugeno fuzzy model allowed exhibit a attraction domain of significant size. One provided tools allowing to limit the variations of the poles of the system in a given field of the state space, domain in which the stability of model TS is proven. The use of D-stability makes it possible to know dynamic maximum system. The concept of exponential stability makes it possible to know dynamic minimal system. The approach used to prove the stability of the system in the presence of parametric variations, for the two studied systems, authorizes only extremely weak variations of the value of the parameter around its maximal value
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Otto, Michael. "Symplectic convexity theorems and applications to the structure theory of semisimple Lie groups." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1084986339.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains v, 88 p. Includes bibliographical references (p. 87-88). Available online via OhioLINK's ETD Center
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Lê, Hoài Nam. "Influence des défauts de forme sur le comportement des liaisons : étude expérimentale et théorique." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00961201.
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L'objectif de l'étude est d'identifier le comportement des liaisons d'un mécanisme du point de vue des déplacements en fonction des défauts de forme et des jeux. Le sujet est abordé selon une approche théorique et une approche expérimentale.La partie théorique montre la dualité entre les deux concepts utilisés : le domaine jeu et la surface convexe des différences. Elle montre également la typologie des domaines et l'influence des incertitudes de forme sur ces domaines.En parallèle, un dispositif expérimental est développé. Il permet, non seulement, de réaliser la mesure des déplacements dans la liaison avec l'exactitude nécessaire, mais aussi, de valider les résultats par une simulation de l'assemblage à partir de la mesure 3D des surfaces en contact. L'expérimentation porte sur plusieurs couples de surfaces comportant des défauts de forme de différents types. L'influence d'un chargement mécanique est étudiée afin de quantifier les déformations locales de surfaces de contact et l'évolution des écarts de position entre les pièces.
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Kluge, Silvia Franziska [Verfasser]. "The transmembrane domain of HIV-1 Vpu is sufficient to confer anti-tetherin activity to SIVcpz and SIVgor V pus / Silvia Franziska Kluge." Ulm : Universität Ulm. Medizinische Fakultät, 2014. http://d-nb.info/105793853X/34.
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Mouysset, Vincent. "Une méthode de sous-domaines pour la résolution des équations de Maxwell instationnaires en présence d'un ensemble non-connexe d'objets diffractant." Phd thesis, Université Paul Sabatier - Toulouse III, 2006. http://tel.archives-ouvertes.fr/tel-00136029.
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A partir de l'établissement d'une approximation in stationnaires en 3D des potentiels retardés pour des courants électromagnétiques sur des polyèdres non-nécessairement convexes, une méthode de résolution pour la simulation de la diffraction par un ensemble non-connexe d'objets est formulée. Une partition de ce dernier est effectuée suivant les inhomogénéités présentes. Le problème est alors traduit en un système d'équations de Maxwell couplées, chacune étant homogène hors d'un élément correspondant de la partition, qui induit la construction d'une solution du problème initial. Par approximation des termes de couplage, il s'en suit une méthode naturellement hybride et parallèle sur un système stable et bien-posé. La restriction de chaque sous-système à un voisinage du support de ses inhomogénéités est obtenue par introduction de conditions aux limites absorbantes de type "PML" dont un formalisme généralisé est étudié. Des exemples numériques illustrent l'ensemble de ces développements.
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Leguina, Ruzzi Adrian Antonio. "Multidimensional facets of cultural distinction in the music domain : context, methods, and meanings." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/multidimensional-facets-of-cultural-distinction-in-the-music-domain-context-methods-and-meanings(731d7382-5a11-4689-a790-96fef6a77e60).html.
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From different traditions, research in the field of sociology of cultural taste and consumption has argued that contemporary societies are symbolically stratified through cultural engagement. These theoretical frameworks differ mainly in their explanations of the mechanisms that shape the relationship between culture and social stratification. Motivated by concepts from Pierre Bourdieu, Richard A. Peterson, and other key scholars, this thesis is focused on addressing the relationship between music consumption and social stratification. Due to its peculiar characteristics, music provides a good illustration of how people, through cultural engagement, draw boundaries that symbolically differentiate social groups. Although literature in the area has made great progress, there are still theoretical and empirical gaps. It is possible to find some passionate views which deny the relevance of some operationalisations and methods over others (Wuggenig, 2007; Chan, 2010a). From a comparative point of view it is questioned whether different dimensions of cultural practices can deliver consistent results (Peterson, 2005; Purhonen, Gronow and Rahkonen, 2011; Yaish and Katz-Gerro, 2012). Research which focuses on comparisons between societies frequently lacks detailed theoretical conceptualisations regarding how cultural items are distributed in different social settings (Katz-Gerro, 2011; Purhonen and Wright, 2013). Other important gap in the literature is the lack of understanding about how technologies act as an element of social distinction (López-Sintas, Cebollada, Filimon and Gharhaman, 2014). The main objective of this research is therefore to review how research has defined and studied the relationship between culture and society across several perspectives and to offer new insights which significantly contribute to the advancement of knowledge of the sociology of cultural taste and consumption. This is motivation for the development of four research articles which use several quantitative methods to analyse survey data from Austria, England, Chile, Finland, Israel and Serbia. This thesis shows that musical engagement, regardless of how and where it is measured, remains socially stratified. Age is the primary stratifying factor for musical engagement, highlighting the distinction between popular music preferred by the younger age cohorts, and the classical or traditional music of the older. Both are reinforced by educational level and social class. Individuals displaying broader musical preferences are more likely to be in advantageous positions. This concurs with arguments about omnivorism as a manifestation of cultural homology in the classic Bourdieusian sense (Lizardo and Skiles, 2012). Thanks to the innovative analysis of available data and the use of more specific cultural indicators it is possible to elaborate research questions to address the study of musical engagement and its place in society, integrating research methods, theory of practices, local and global contexts, and technologies as salient analytical dimensions.
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Ghorbal, Khalil. "Analyse Statique de Programmes Numériques: Ensembles Affines Contraints." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00643442.
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Nous nous plaçons dans le cadre de l'analyse statique de programmes, et nous nous intéressons aux propriétés numériques, c'est a dire celles qui concernent les valeurs numériques des variables de programmes. Nous essayons en particulier de déterminer une sur-approximation garantie de l'ensemble de valeurs possibles pour chaque variable numérique utilisée dans le programme à analyser. Cette analyse statique est faite dans le cadre de la théorie de l'interprétation abstraite, théorie présentant un compromis entre les limites théoriques d'indécidabilite et de calculabilite et la précision des résultats obtenus. Nous sommes partis des travaux d'Eric Goubault et Sylvie Putot, que nous avons étendus et généralisés. Notre nouveau domaine abstrait, appelé ensembles affines contraints, combine à la fois l'efficacite de calcul des domaines à base de formes affines et le pouvoir ex- pressif des domaines relationnels classiques tels que les octogones ou les polyèdres. Le nouveau domaine a été implémenté pour mettre en évidence l'intérêt de cette combinaison, ses avantages, ses performances et ses limites par rapport aux autres domaines numériques déjà existants. Le formalisme ainsi que les résultats pra- tiques ont fait l'objet de plusieurs publications [CAV 2009, CAV 2010].
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Liu, Liwei. "The implication of context and criteria information in recommender systems as applied to the service domain." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/the-implication-of-context-and-criteria-information-in-recommender-systems-as-applied-to-the-service-domain(c3b8e170-8ae0-4e5c-a9b1-508f9c54316a).html.
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Recommender systems support online customers by suggesting products and services of likely interest to them. Research in recommender systems is now starting to recognise the importance of multiple selection criteria and the role of customer context in improving the recommendation output. This thesis investigates the inclusion of criteria and context information in the recommendation process. Firstly, a novel technique for multi-criteria recommendation is proposed. It assumes that some selection criteria for an item (product or a service) will dominate the overall rating, and that these dominant criteria will be different for different users. Following this assumption, users are clustered based on their criteria preferences, creating a “preference lattice”. The recommendation output for a user is then based on ratings by other users from the same or nearby clusters. Secondly, a context similarity metric for context aware recommendation is presented. This metric can help improve the prediction accuracy in two ways. On the one hand, the metric can guide the aggregation of the feedback from similar context to improve the prediction accuracy. This aggregation is important because the recommendation generation based on prior feedback by similar customers reduces the quantum of feedback used, resulting in a reduction in recommendation quality. On the other hand, the value returned by the context similarity metric can also be used to indicate the importance of the context information in the prediction process for a context aware recommendation.The validation of the two proposed techniques and their applications are conducted in the service domain because the relatively high degree of user involvement attracts users to provide detailed feedback from multiple perspectives, such as from criteria and context perspectives. In particular, hotel services and web services areas are selected due to their different levels of maturity in terms of users’ feedback. For each area, this thesis proposes a different recommendation approach by combining the proposed techniques with a traditional recommendation approach. The thesis concludes with experiments conducted on the datasets from the two aforementioned areas to evaluate the proposed techniques, and to demonstrate the process and the effectiveness of the techniques-based recommendation approaches.
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Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.
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L'objectif de cette thèse est l'étude de la représentation probabiliste des différentes classes d'EDPSs non-linéaires(semi-linéaires, complètement non-linéaires, réfléchies dans un domaine) en utilisant les équations différentielles doublement stochastiques rétrogrades (EDDSRs). Cette thèse contient quatre parties différentes. Nous traitons dans la première partie les EDDSRs du second ordre (2EDDSRs). Nous montrons l'existence et l'unicité des solutions des EDDSRs en utilisant des techniques de contrôle stochastique quasi- sure. La motivation principale de cette étude est la représentation probabiliste des EDPSs complètement non-linéaires. Dans la deuxième partie, nous étudions les solutions faibles de type Sobolev du problème d'obstacle pour les équations à dérivées partielles inteégro-différentielles (EDPIDs). Plus précisément, nous montrons la formule de Feynman-Kac pour l'EDPIDs par l'intermédiaire des équations différentielles stochastiques rétrogrades réfléchies avec sauts (EDSRRs). Plus précisément, nous établissons l'existence et l'unicité de la solution du problème d'obstacle, qui est considérée comme un couple constitué de la solution et de la mesure de réflexion. L'approche utilisée est basée sur les techniques de flots stochastiques développées dans Bally et Matoussi (2001) mais les preuves sont beaucoup plus techniques. Dans la troisième partie, nous traitons l'existence et l'unicité pour les EDDSRRs dans un domaine convexe D sans aucune condition de régularité sur la frontière. De plus, en utilisant l'approche basée sur les techniques du flot stochastiques nous démontrons l'interprétation probabiliste de la solution faible de type Sobolev d'une classe d'EDPSs réfléchies dans un domaine convexe via les EDDSRRs. Enfin, nous nous intéressons à la résolution numérique des EDDSRs à temps terminal aléatoire. La motivation principale est de donner une représentation probabiliste des solutions de Sobolev d'EDPSs semi-linéaires avec condition de Dirichlet nul au bord. Dans cette partie, nous étudions l'approximation forte de cette classe d'EDDSRs quand le temps terminal aléatoire est le premier temps de sortie d'une EDS d'un domaine cylindrique. Ainsi, nous donnons les bornes pour l'erreur d'approximation en temps discret. Cette partie se conclut par des tests numériques qui démontrent que cette approche est effectiveThe objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
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Ye, Jian. "Régularité de l'application du transport optimal sur des variétés riemanniennes compactes." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30354.
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Dans cette thèse on s'intéressons à la régularité de l'application du transport optimal sur des variétés riemanniennes compactes. Dans le premier chapitre, on rappelle certaines définitions sur une variété riemannienne. Dans le deuxième chapitre, on décrit la variation de la courbure sur des géodésiques. Dans le troisième chapitre, on étudie le tenseur de MTW sur une variété riemannienne compacte. On montre qune condition de MTW améliorée est satisfaite sur une variété presque sphérique. La preuve consiste à une analyse minutieuse, combinée avec les arguments de perturbation sur des sphères. Dans le quatrième chapitre, on étudie le comportement de l'inverse de la matrice Hessienne de la distance au carré. Dans le cinquième chapitre, on prouve la régularité du transport optimale sur deux classes des variétés riemanniennes compactes- des variétés presque sphériques et des produits riemanniens des variétés presque sphériques. Dans le dernier chapitre, on déscrit quelques perspectives sur le transport optimal dans la littératureIn this thesis, we are concerned with the regularity of optimal transport maps on compact Riemannian manifolds. In the first chapter, we give some definitions and recall some facts in Riemannian geometry. In the second chapter, we examine the variation of the curvature on the geodesics. In the third chapter, we study the MTW tensor on compact Riemannian manifold. We show that an improved MTW condition is satisfied on nearly spherical manifold. The proof goes by a careful analysis combined with the perturbative arguments on the spheres. In the fourth chapter, we study the inverse of the Hessian matrix of the squared distance. In the fifth chapter, we prove the smoothness of the optimal transport maps on two classes of compact Riemannian manifold-nearly spherical manifolds and Riemannian products of nearly spherical manifolds. In the last chapter, we provide some perspectives about the optimal transportation in the literature
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Assmann, Caroline Maria. "O problema de Dirichlet para a equacão dos gráficos mínimos com dado no bordo lipschitz contínuo." Universidade Federal de Santa Maria, 2016. http://repositorio.ufsm.br/handle/1/11974.
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In this work, we study existence and non existence for the Dirichlet problem for the minimal
graph equation in non convex domains of the plane. We search for conditions on the boundary
data which be the less restricted possible for the solubility of the Dirichlet problem.Neste trabalho estudamos existência e não existência do problema de Dirichlet para a equação dos gráficos mínimos em domínios não convexos do plano. Procuramos por condições sobre o dado no bordo que sejam as menos restritivas possíveis para que o problema de Dirichlet em questão tenha solução
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Gutt, Jean. "On the minimal number of periodic Reeb orbits on a contact manifold." Phd thesis, Université de Strasbourg, 2014. http://tel.archives-ouvertes.fr/tel-01016954.
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Le sujet de cette thèse est la question du nombre minimal d'orbites de Reeb distinctes sur une variété de contact qui est le bord d'une variété symplectique compacte. L'homologie symplectique $S^1$-équivariante positive est un des outils principaux de cette thèse; elle est construite à partir d'orbites périodiques de champs de vecteurs hamiltoniens sur une variété symplectique dont le bord est la variété de contact considérée. Nous analysons la relation entre les différentes variantes d'homologie symplectique d'une variété symplectique exacte compacte (domaine de Liouville) et les orbites de Reeb de son bord. Nous démontrons certaines propriétés de ces homologies. Pour un domaine de Liouville plongé dans un autre, nous construisons un morphisme entre leurs homologies. Nous étudions ensuite l'invariance de ces homologies par rapport au choix de la forme de contact sur le bord. Nous utilisons l'homologie symplectique $S^1$-équivariante positive pour donner une nouvelle preuve d'un théorème de Ekeland et Lasry sur le nombre minimal d'orbites de Reeb distinctes sur certaines hypersurfaces dans $\R^{2n}$. Nous indiquons comment étendre au cas de certaines hypersurfaces dans certains fibrés en droites complexes négatifs. Nous donnons une caractérisation et une nouvelle façon de calculer l'indice de Conley-Zehnder généralisé, défini par Robbin et Salamon pour tout chemin de matrices symplectiques. Ceci nous a mené à développer de nouvelles formes normales de matrices symplectiques.
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Yaouanq, Tamby Emilie. "L’indétermination générique dans la prose poétique du symbolisme et du modernisme (domaines francophone et hispanophone, 1885-1914)." Thesis, Paris 4, 2011. http://www.theses.fr/2011PA040001/document.
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Cette thèse étudie les ressorts de l’indétermination générique dans les proses poétiques du symbolisme et du modernisme hispanophone, de 1885 à 1914. L’indéfinition et l’hybridité génériques se manifestent d’abord dans les représentations des formes et des genres, transparaissant dans les discours des écrivains et des critiques. La redéfinition du poétique entraîne la perception d’un continuum entre les formes et entre les genres. La chanson poétique et narrative symboliste et les recueils hétéroclites, associant différentes formes et différents genres illustrent ces phénomènes. Dans ce contexte, le genre du poème en prose tend à se confondre avec un genre limitrophe comme le conte. Cette indéfinition générique s’observe dans les textes, à travers différentes voies de poétisation du récit : la discontinuité, le statisme et la répétition, qui permettent d’explorer d’autres modes de représentation du temps, et de jouer sur l’ambiguïté référentielleThis thesis seeks to examine the mechanisms of generic indetermination in the poetic prose of francophone symbolists and hispanic modernists from 1885 to 1914. Generic indetermination and hybridity tend to appear at first in representations of forms and genres, and in the discourse of writers and critics. The new definition of the poetic category leads to the perception of a continuum between different forms and genres. The narrative poetic symbolist song and the heterogeneous collections mixing different types are an example of this tendency. In this case, the genre of prose poem tends to merge with contiguous genres such as the tale. The absence of generic definition may be observed in discontinuity, immobility and repetition which allow the exploration of other modes of time representation and the play on referential ambiguity
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Soumana, Hima Abdoulaye. "Équations différentielles stochastiques sous G-espérance et applications." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S007/document.
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Depuis la publication de l'ouvrage de Choquet (1955), la théorie d'espérance non linéaire a attiré avec grand intérêt des chercheurs pour ses applications potentielles dans les problèmes d'incertitude, les mesures de risque et le super-hedging en finance. Shige Peng a construit une sorte d'espérance entièrement non linéaire dynamiquement cohérente par l'approche des EDP. Un cas important d'espérance non linéaire cohérente en temps est la G-espérance, dans laquelle le processus canonique correspondant (B_{t})_{t≥0} est appelé G-mouvement brownien et joue un rôle analogue au processus de Wiener classique. L'objectif de cette thèse est d'étudier, dans le cadre de la G-espérance, certaines équations différentielles stochastiques rétrogrades (G-EDSR) à croissance quadratique avec applications aux problèmes de maximisation d'utilité robuste avec incertitude sur les modèles, certaines équations différentielles stochastiques (G-EDS) réfléchies et équations différentielles stochastiques rétrogrades réfléchies avec générateurs lipschitziens. On considère d'abord des G-EDSRs à croissance quadratique. Dans le Chapitre 2 nous fournissons un resultat d'existence et unicité pour des G-EDSRs à croissance quadratique. D'une part, nous établissons des estimations a priori en appliquant le théorème de type Girsanov, d'où l'on en déduit l'unicité. D'autre part, pour prouver l'existence de solutions, nous avons d'abord construit des solutions pour des G-EDSRs discretes en résolvant des EDPs non-linéaires correspondantes, puis des solutions pour les G-EDSRs quadratiques générales dans les espaces de Banach. Dans le Chapitre 3 nous appliquons les G-EDSRs quadratiques aux problèmes de maximisation d'utilité robuste. Nous donnons une caratérisation de la fonction valeur et une stratégie optimale pour les fonctions d'utilité exponentielle, puissance et logarithmique. Dans le Chapitre 4, nous traitons des G-EDSs réfléchies multidimensionnelles. Nous examinons d'abord la méthode de pénalisation pour résoudre des problèmes de Skorokhod déterministes dans des domaines non convexes et établissons des estimations pour des fonctions α-Hölder continues. A l'aide de ces résultats obtenus pour des problèmes déterministes, nous définissons le G-mouvement Brownien réfléchi et prouvons son existence et son unicité dans un espace de Banach. Ensuite, nous prouvons l'existence et l'unicité de solution pour les G-EDSRs multidimensionnelles réfléchies via un argument de point fixe. Dans le Chapitre 5, nous étudions l'existence et l'unicité pour les équations différentielles stochastiques rétrogrades réfléchies dirigées par un G-mouvement brownien lorsque la barrière S est un processus de G-ItôSince the publication of Choquet's (1955) book, the theory of nonlinear expectation has attracted great interest from researchers for its potential applications in uncertainty problems, risk measures and super-hedging in finance. Shige Peng has constructed a kind of fully nonlinear expectation dynamically coherent by the PDE approach. An important case of time-consistent nonlinear expectation is G-expectation, in which the corresponding canonical process (B_{t})_{t≥0} is called G-Brownian motion and plays a similar role to the classical Wiener process. The objective of this thesis is to study, in the framework of the G-expectation, some backward stochastic differential equations (G-BSDE) under a quadratic growth condition on their coefficients with applications to robust utility maximization problems with uncertainty on models, Reflected stochastic differential equations (reflected G-SDE) and reflected backward stochastic differential equations with Lipschitz coefficients (reflected G-BSDE). We first consider G-BSDE with quadratic growth. In Chapter 2 we provide a result of existence and uniqueness for quadratic G-BSDEs. On the one hand, we establish a priori estimates by applying the Girsanov-type theorem, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first constructed solutions for discrete G-BSDEs by solving corresponding nonlinear PDEs, then solutions for the general quadratic G-BSDEs in the spaces of Banach. In Chapter 3 we apply quadratic G-BSDE to robust utility maximization problems. We give a characterization of the value function and an optimal strategy for exponential, power and logarithmic utility functions. In Chapter 4, we discuss multidimensional reflected G-SDE. We first examine the penalization method to solve deterministic Skorokhod problems in non-convex domains and establish estimates for continuous α-Hölder functions. Using these results for deterministic problems, we define the reflected G-Brownian motion and prove its existence and its uniqueness in a Banach space. Then we prove the existence and uniqueness of the solution for the multidimensional reflected G-SDE via a fixed point argument. In Chapter 5, we study the existence and uniqueness of the reflected backward stochastic differential equations driven by a G-Brownian motion when the obstacle S is a G-Itô process
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Briceno-Arias, Luis M. "Problèmes d'inclusions couplées : Éclatement, algorithmes et applications." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00600967.
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Cette thèse est consacrée à la résolution de problèmes d'analyse non linéaire multivoque dans lesquels plusieurs variables interagissent. Le problème générique est modélisé par une inclusion vis-à-vis d'une somme d'opérateurs monotones sur un espace hilbertien produit. Notre objectif est de concevoir des nouveaux algorithmes pour résoudre ce problème sous divers jeux d'hypothèses sur les opérateurs impliqués et d'étudier le comportement asymptotique des méthodes élaborées. Une propriété commune aux algorithmes est le fait qu'ils procèdent par éclatement en ceci que les opérateurs monotones et, le cas échéant, les opérateurs linéaires constitutifs du modèle agissent indépendamment au sein de chaque itération. Nous abordons en particulier le cas où les opérateurs monotones sont des sous-différentiels de fonctions convexes, ce qui débouche sur de nouveaux algorithmes de minimisation. Les méthodes proposées unifient et dépassent largement l'état de l'art. Elles sont appliquées aux inclusions monotones composites en dualité, aux problèmes d'équilibre, au traitement du signal et de l'image, à la théorie des jeux, à la théorie du trafic, aux équations d'évolution, aux problèmes de meilleure approximation et à la décomposition de domaine dans les équations aux dérivées partielles.
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Winkler, Gunter. "Control constrained optimal control problems in non-convex three dimensional polyhedral domains." Doctoral thesis, 2007. https://monarch.qucosa.de/id/qucosa%3A18908.
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The work selects a specific issue from the numerical analysis of
optimal control problems. We investigate a linear-quadratic optimal
control problem based on a partial differential equation on
3-dimensional non-convex domains. Based on efficient solution methods
for the partial differential equation an algorithm known from control
theory is applied. Now the main objectives are to prove that there is
no degradation in efficiency and to verify the result by numerical
experiments.
We describe a solution method which has second order convergence,
although the intermediate control approximations are piecewise
constant functions. This superconvergence property is gained from a
special projection operator which generates a piecewise constant
approximation that has a supercloseness property, from a sufficiently
graded mesh which compensates the singularities introduced by the
non-convex domain, and from a discretization condition which
eliminates some pathological cases.
Both isotropic and anisotropic discretizations are investigated and
similar superconvergence properties are proven.
A model problem is presented and important results from the regularity
theory of solutions to partial differential equation in non-convex
domains have been collected in the first chapters. Then a collection
of statements from the finite element analysis and corresponding
numerical solution strategies is given. Here we show newly developed
tools regarding error estimates and projections into finite element
spaces. These tools are necessary to achieve the main results. Known
fundamental statements from control theory are applied to the given
model problems and certain conditions on the discretization are
defined. Then we describe the implementation used to solve the model
problems and present all computed results.
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Xu, Jia-Ren, and 許嘉仁. "Existence results of capillary surfaces over convex domains." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/47886333637563213405.
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"A fast and efficient algorithm for finding boundary points of convex and non-convex datasets by interpoint distances." 2013. http://library.cuhk.edu.hk/record=b5884340.
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Lam, Hiu Fung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 58-60).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.
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Lin, Qun Gen, and 林群根. "Invariant metrics and measures on convex domains in Cn." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/18272075473259577407.
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Klein, Richard. "Surface and volumetric parametrisation using harmonic functions in non-convex domains." Thesis, 2013. http://hdl.handle.net/10539/12917.
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A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, in
fulfillment of the requirements for the degree of Master of Science.
Johannesburg, 2013Many of the problems in mathematics have very elegant solutions. As complex, real–world geometries come into play, however, this elegance is often lost. This is particularly the case with meshes of physical, real–world problems. Domain mapping helps to move problems from some geometrically complex domain to a regular, easy to use domain. Shape transformation, specifically, allows one to do this in 2D domains where mesh construction can be difficult. Numerical methods usually work over some mesh on the target domain. The structure and detail of these meshes affect the overall computation and accuracy immensely. Unfortunately, building a good mesh is not always a straight forward task. Finite Element Analysis, for example, typically requires 4–10 times the number of tetrahedral elements to achieve the same accuracy as the corresponding hexahedral mesh. Constructing this hexahedral mesh, however, is a difficult task; so in practice many people use tetrahedral meshes instead. By mapping the geometrically complex domain to a regular domain, one can easily construct elegant meshes that bear useful properties. Once a domain has been mapped to a regular domain, the mesh can be constructed and calculations can be performed in the new domain. Later, results from these calculations can be transferred back to the original domain. Using harmonic functions, source domains can be parametrised to spaces with many different desired properties. This allows one to perform calculations that would be otherwise expensive or inaccurate. This research implements and extends the methods developed in Voruganti et al. [2006 2008] for domain mapping using harmonic functions. The method was extended to handle cases where there are voids in the source domain, allowing the user to map domains that are not topologically equivalent to the equivalent dimension hypersphere. This is accomplished through the use of various boundary conditions as the void is mapped to the target domains which allow the user to reshape and shrink the void in the target domain. The voids can now be reduced to arcs, radial lines and even shrunk to single points. The algorithms were implemented in two and three dimensions and ultimately parallelised to run on the Centre for High Performance Computing clusters. The parallel code also allows for arbitrary dimension genus-0 source domains. Finally, applications, such as remeshing and robot path planning were investigated and illustrated.
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Duh, Shing Jia, and 杜幸家. "Topics on fixed points for multifunctions on non-compact and non-convex domains." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/91658522356779706795.
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An, Lin Shin, and 林信安. "Convexity of the first eigenfunction of convex domains in S^{n}& ^{n}." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/42850197735413703145.
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碩士國立師範大學
數學系
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In this paper , we want find suitable condictions on f such that v=f(u) is a convex function on a convex domain , while u is the first eigenfunction of the convex domain in n dimensional Spheredimensional Pseudosphere.
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Winkler, Gunter [Verfasser]. "Control constrained optimal control problems in non-convex three dimensional polyhedral domains / vorgelegt von Gunter Winkler." 2008. http://d-nb.info/989721779/34.
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Eberhard, A. C. "Some results in the area of generalized convexity and fixed point theory of multi-valued mappings / Andrew C. Eberhard." 1985. http://hdl.handle.net/2440/20758.
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Author's `Characterization of subgradients: 1` (31 leaves) in pocketBibliography: leaves 229-231
231 leaves : 1 port ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
Thesis (Ph.D.)--University of Adelaide, 1986