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Johan, Filip Rindler Johan Filip. "Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c4736fa2-ab51-4cb7-b1d9-cbab0ede274b.
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Lind, Martin. "Functions of bounded variation." Thesis, Karlstad University, Division for Engineering Sciences, Physics and Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-209.
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The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.
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Lind, Martin. "Functions of Generalized Bounded Variation." Doctoral thesis, Karlstads universitet, Institutionen för matematik och datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-26342.
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This thesis is devoted to the study of different generalizations of the classical conception of a function of bounded variation. First, we study the functions of bounded p-variation introduced by Wiener in 1924. We obtain estimates of the total p-variation (1<p<∞) and other related functionals for a periodic function f in Lp([0,1]) in terms of its Lp-modulus of continuity ω(f;δ)p. These estimates are sharp for any rate of decay of ω(f;δ)p. Moreover, the constant coefficients in them depend on parameters in an optimal way. Inspired by these results, we consider the relationship between the Riesz type generalized variation vp,α(f) (1<p<∞, 0≤α≤1-1/p) and the modulus of p-continuity ω1-1/p(f;δ). These functionals generate scales of spaces that connect the space of functions of bounded p-variation and the Sobolev space Wp1. We prove sharp estimates of vp,α(f) in terms of ω1-1/p(f;δ). In the same direction, we study relations between moduli of p-continuity and q-continuity for 1<p<q<∞. We prove an inequality that estimates ω1-1/p(f;δ) in terms of ω1-1/q(f;δ). The inequality is sharp for any order of decay of ω1-1/q(f;δ). Next, we study another generalization of bounded variation: the so-called bounded Λ-variation, introduced by Waterman in 1972. We investigate relations between the space ΛBV of functions of bounded Λ-variation, and classes of functions defined via integral smoothness properties. In particular, we obtain the necessary and sufficient condition for the embedding of the class Lip(α;p) into ΛBV. This solves a problem of Wang (2009). We consider also functions of two variables. Applying our one-dimensional result, we obtain sharp estimates of the Hardy-Vitali type p-variation of a bivariate function in terms of its mixed modulus of continuity in Lp([0,1]2). Further, we investigate Fubini-type properties of the space Hp(2) of functions of bounded Hardy-Vitali p-variation. This leads us to consider the symmetric mixed norm space Vp[Vp]sym of functions of bounded iterated p-variation. For p>1, we prove that Hp(2) is not embedded into Vp[Vp]sym, and that Vp[Vp]sym is not embedded into Hp(2). In other words, Fubini-type properties completely fail in the class of functions of bounded Hardy-Vitali type p-variation for p>1.Baksidestext The classical concept of the total variation of a function has been extended in several directions. Such extensions find many applications in different areas of mathematics. Consequently, the study of notions of generalized bounded variation forms an important direction in the field of mathematical analysis. This thesis is devoted to the investigation of various properties of functions of generalized bounded variation. In particular, we obtain the following results: sharp relations between spaces of generalized bounded variation and spaces of functions defined by integral smoothness conditions (e.g., Sobolev and Besov spaces); optimal properties of certain scales of function spaces of frac- tional smoothness generated by functionals of variational type; sharp embeddings within the scale of spaces of functions of bounded p-variation; results concerning bivariate functions of bounded p-variation, in particular sharp estimates of total variation in terms of the mixed Lp-modulus of continuity, and Fubini-type properties.
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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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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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Chirikhin, Andrey. "Polynomial distribution functions on bounded closed intervals." Thesis, University of Warwick, 2007. http://wrap.warwick.ac.uk/3678/.
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The thesis explores several topics, related to polynomial distribution functions and their densities on [0,1]M, including polynomial copula functions and their densities. The contribution of this work can be subdivided into two areas. - Studying the characterization of the extreme sets of polynomial densities and copulas, which is possible due to the Choquet theorem. - Development of statistical methods that utilize the fact that the density is polynomial (which may or may not be an extreme density). With regard to the characterization of the extreme sets, we first establish that in all dimensions the density of an extreme distribution function is an extreme density. As a consequence, characterizing extreme distribution functions is equivalent to characterizing extreme densities, which is easier analytically. We provide the full constructive characterization of the Choquet-extreme polynomial densities in the univariate case, prove several necessary and sufficient conditions for the extremality of densities in arbitrary dimension, provide necessary conditions for extreme polynomial copulas, and prove characterizing duality relationships for polynomial copulas. We also introduce a special case of reflexive polynomial copulas. Most of the statistical methods we consider are restricted to the univariate case. We explore ways to construct univariate densities by mixing the extreme ones, propose non-parametric and ML estimators of polynomial densities. We introduce a new procedure to calibrate the mixing distribution and propose an extension of the standard method of moments to pinned density moment matching. As an application of the multivariate polynomial copulas, we introduce polynomial coupling and explore its application to convolution of coupled random variables. The introduction is followed by a summary of the contributions of this thesis and the sections, dedicated first to the univariate case, then to the general multivariate case, and then to polynomial copula densities. Each section first presents the main results, followed by the literature review.
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Don, Sebastiano. "Functions of bounded variation in Carnot-Carathéodory spaces." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3426813.
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We study properties of functions with bounded variation in Carnot-Carathéodory spaces. In Chapter 2 we prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative. In Chapter 3 we prove a rank-one theorem à la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes all Heisenberg groups H^n with n ≥ 2. Some important tools for the proof are properties linking the horizontal derivatives of a real-valued function with bounded variation to its subgraph. In Chapter 4 we prove a compactness result for bounded sequences (u_j) of functions with
bounded variation in metric spaces (X, d_j) where the space X is fixed, but the metric may vary with j. We also provide an application to Carnot-Carathéodory spaces. The results of Chapter 4 are fundamental for the proofs of some facts of Chapter 2.Analizziamo alcune proprietà di funzioni a variazione limitata in spazi di Carnot-Carathéodory. Nel Capitolo 2 dimostriamo che esse sono approssimativamente differenziabili quasi ovunque, esaminiamo il loro insieme di discontinuità approssimata e la decomposizione della loro derivata distribuzionale. Assumendo un'ipotesi addizionale sullo spazio, che chiamiamo proprietà R, mostriamo che quasi tutti i punti di discontinuità approssimata sono di salto e studiamo una formula per la parte di salto della derivata. Nel Capitolo 3 dimostriamo un teorema di rango uno à la G. Alberti per la derivata distribuzionale di funzioni vettoriali a variazione limitata in una classe di gruppi di Carnot che contiene tutti i gruppi di Heisenberg H^n con n ≥ 2. Uno strumento chiave nella dimostrazione è costituito da alcune proprietà che legano le derivate orizzontali di una funzione a variazione limitata con il suo sottografico. Nel Capitolo 4 dimostriamo un risultato di compattezza per succesioni (u_j) equi-limitate in spazi metrici (X, d_j) quando lo spazio X è fissato ma la metrica può variare con j. Mostriamo inoltre un'applicazione agli spazi di Carnot-Carathéodory. I risultati del Capitolo 4 sono fondamentali per la dimostrazione di alcuni fatti contenuti nel Capitolo 2.
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Dawson, Dan Paul. "Concerning Integral Approximations of Bounded Finitely Additive Set Functions." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc332650/.
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The purpose of this paper is to generalize a theorem that characterizes absolute continuity of bounded finitely additive set functions in the form of an integral approximation. We show that his integral exists if the condition of absolute continuity is removed.
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Gurney, David R. (David Robert). "Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc332375/.
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In leading up to the proof, methods for constructing fields and finitely additive set functions are introduced with an application involving the Tagaki function given as an example. Also, non-absolutely continuous set functions are constructed using Banach limits and maximal filters.
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Sababheh, Mohammad Suboh. "Constructions of bounded functions related to two-sided Hardy inequalities." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102160.
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We investigate inequalities that can be viewed as generalizations of Hardy's inequality about the Fourier coefficients of a function analytic on the circle. The proof of the Littlewood conjecture opened a wide door in front of questions regarding possible generalizations of Hardy's inequality. The proof of the Littlewood conjecture was based on some constructions of bounded functions having particular properties.In 1993, I. Klemes investigated one of the constructions (we shall call it the algebraic construction) and proved what is called a mixed norm generalization of Hardy's inequality. It turns out that we can work with the same construction and examine more properties of it in order to get more results.
The objectives of the thesis are to give more detailed properties of the algebraic construction and to use these properties in order to prove various versions of two-sided Hardy inequalities.
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Lindner, Marko. "Limit Operators and Applications on the Space of Essentially Bounded Functions." Doctoral thesis, Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200301569.
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Die Dissertation untersucht die Invertierbarkeit im Unendlichen fuer Normgrenzwerte von Bandoperatoren - sogenannte band-dominierte Operatoren. Das dazu verwendete Instrument ist die Methode der Limitoperatoren. Es werden grundlegende Eigenschaften von Limitoperatoren bewiesen, Zusammenhaenge zur Invertierbarkeit im Unendlichen hergeleitet, sowie darueber hinaus gehende Anwendungen, z.B. zur Konvergenz von Projektionsverfahren, studiert.
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Lumori, Mikaya Lasuba Delesuk. "Microwave power deposition in bounded and inhomogeneous lossy media." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184389.
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We present Bessel function and Gaussian beam models for a study of microwave power deposition in bounded and inhomogeneous lossy media. The aim is to develop methods that can accurately simulate practical results commonly found in electromagnetic hyperthermic treatment, which is a noninvasive method. The Bessel function method has a closed form solution and can be used to compute accurate results of electromagnetic fields emanating from applicators with cosinusoidal aperture fields. On the other hand, the Gaussian beam method is approximate but has the capability to simplify boundary value problems and to compute fields in three-dimensions with extremely low CPU time (less than 30 sec). Although the Gaussian beam method is derived from geometrical optics theory, it performs very well in domains outside the realm of geometrical optics which stipulates that aperture dimension/λ ≥ 5 in the design of microwave systems. This condition has no relevance to the Gaussian beam method since the method shows that a limit of aperture dimension/ λ ≥ 0.9 is possible, which is a very important achievement in the design and application of microwave systems. Experimental verifications of the two theoretical models are integral parts of the presentation and show the viability of the methods.
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MENEGATTI, GIORGIO. "Sobolev classes and bounded variation functions on domains of Wiener spaces, and applications." Doctoral thesis, Università degli studi di Ferrara, 2018. http://hdl.handle.net/11392/2488305.
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The main thread of this work is the bounded variation (BV) functions in abstract Wiener spaces (a topic in infinite-dimensional analysis).
In the first Part of this work, we present some known results, and we introduce the concepts of Wiener space, of Sobolev space in Wiener spaces, of BV functions (and finite perimeter sets) in Wiener spaces, and of BV functions in convex sets of Wiener spaces (by following the definition in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); moreover, we introduce the trace theory on subsets of a Wiener space (by following P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), and the concept of Mosco convergence.
In the second Part we present some new results.
In Chapter 6, we consider a subset O of a Wiener space which satisfies a regularity condition, and we prove that a function in W^{1,2}(O) has null trace if and only if it is the limit of a sequence of functions with support contained in O.
The main chapter is Chapter 7, which is devoted to the extension in the Wiener spaces setting of a result given in the section 8 of (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): if O is a convex bounded set with regular boundary in R^{d} and L is the Laplace operator in O with null Dirichlet boundary condition, then the normalized resolvent of L is contractive in sense L^1 respect to the gradient.
We extend this result to the case of L Ornstein-Uhlenbeck operator in O with null Dirichlet boundary condition, with Gaussian measure (by using the results of Chapter 6): in this case O must satisfy a condition (which we call Gaussian convexity) which takes the place of the convexity in the Gaussian setting.
Moreover, we extend the result also to the case of: L Laplace operator in an open convex O with null Neumann boundary condition, with Lebesgue measure; L Ornstein-Uhlenbeck operator in an open convex O with null Neumann boundary condition, with Gaussian measure.
In the last part of Chapter 7, we use the preceding results to give an alternative definition of BV function (in the case L^2(O)).
In Chapter 8, let X the set of continuous functions on [0,1] with starting point 0, provided with the measure induced by the Brownian motion with starting point 0; it is a Wiener space. For every A subset of X, we define Ξ_A, set of functions in X with image in A.
In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) it is proved that, if d ≥ 2 and A is an open subset of R^d which satisfies an uniform outer ball condition then Ξ_A has finite perimeter in the sense of Gaussian measure.
We present a weaker condition on A (in dimension sufficiently great) such that Ξ_A has finite perimeter: in particular, A can be the complement of a convex unbounded symmetric cone.L’argomento principale di questo lavoro sono le funzioni a variazione limitata (BV) in spazi di Wiener astratti (un argomento di analisi infinito-dimensionale). Nella prima parte di questo lavoro, presentiamo alcuni risultati noti, e introduciamo i concetti di spazi di Wiener, di classi di Sobolev su spazi di Wiener, di funzioni BV (e insiemi di perimetro finito) in spazi di Wiener, e di funzioni BV in sottoinsiemi convessi di Spazi di Wiener (seguendo la definizione in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); inoltre, introduciamo la teoria delle tracce su sottoinsiemi di uno spazio di Wiener( seguendo P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), e il concetto di convergenza di Mosco. Nella seconda parte presentiamo alcuni risultati originali. Nel capitolo 6, consideriamo un sottoinsieme O di uno spazio di Wiener che soddisfa a una condizione di regolarità, e proviamo che una funzione in W^{1,2} (O) ha traccia nulla se e solo se è il limite di una sequenza di funzioni con supporto contenuto in O. Il capitolo principale è il 7, che è dedicato all'estensione all'ambito degli spazi di Wiener di un risultato dato nella sezione 8 di (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): se O è un insieme convesso limitato con frontiera regolare in R^{d} e L è l'operatore di Laplace in O con condizione al bordo di Dirichlet nulla, allora il risolvente normalizzato di L è contrattivo nel senso L^1 rispetto al gradiente. Estendiamo questo risultato al caso di L operatore di Ornstein-Uhlenbeck in O con condizione al bordo di Dirichlet nulla, con misura gaussiana (usando i risultati del Capitolo 6): in questo caso O deve soddisfare una condizione (che chiamiamo convessità Gaussiana) che nel caso gaussiano prende il posto della convessità. Inoltre, estendiamo il risultato anche al caso di: L operatore di Laplace in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura di Lebesgue; L operatore in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura gaussiana. Nell'ultima parte del Capitolo 7, usiamo i precedenti risultati per dare una definizione alternativa di funzione BV in O (nel caso L^2(O) ). Nel Capitolo 8, sia X l'insieme delle funzioni continue in R^d su [ 0,1 ] con punti di partenza nell’origine fornito della misura indotta dal moto browniano con punto di partenza nell’origine; è uno spazio di Wiener. Per ogni A sottoinsieme di X, definiamo Ξ_A, insieme delle funzioni in X con immagine in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) viene dimostrato che, se d ≥ 2 e A è un insieme aperto in R^d che soddisfa una condizione di uniforme palla esterna, allora Ξ_A ha perimetro finito nel senso della misura gaussiana. Presentiamo una condizione più debole su A (in dimensione sufficientemente grande) tale che Ξ_A ha perimetro finito: in particolare, A può essere il complementare di un cono convesso illimitato simmetrico.
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Tombari, Francesca. "Deformation of surfaces in 2D persistent homology." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15809/.
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In the context of 2D persistent homology a new metric has been recently introduced, the coherent matching distance. In order to study this metric, the filtering function is required to present particular “regularity” properties, based on a geometrical construction of the real plane, called extended Pareto grid. This dissertation shows a new result for modifying the extended Pareto grid associated to a filtering function defined on a smooth closed surface, with values in the real plane. In future, the technical result presented here could be used to prove the genericity of the regularity conditions assumed for the filtering function.
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Hokamp, Samuel A. "Weak*-Closed Unitarily and Moebius Invariant Spaces of Bounded Measurable Functions on a Sphere." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562943150719334.
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Chan, Kung-ho, and 陳公豪. "On the deformation of holomorphic bundles of projective spaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224015.
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Chan, Kung-ho. "On the deformation of holomorphic bundles of projective spaces." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22823864.
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Quinn, Eugene P. "On the boundedness character of third-order rational difference equations /." View online ; access limited to URI, 2006. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/AAI3225327.
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Rivetti, Sabrina. "Bounded variation solutions of capillarity-type equations." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10161.
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2012/2013We investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
XXV Ciclo
1985
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Bellavia, Mark R. "Long term behavior or the positive solutions of the non-autonomous difference equation : x [subscript] n+1 = A [subscript] n [superscript] x [subscript] n-1 [divided by] 1+x [subscript] n, n=0,1,2... /." Link to online version, 2005. https://ritdml.rit.edu/dspace/handle/1850/1117.
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Reinwand, Simon [Verfasser], Jürgen [Gutachter] Appell, Daria [Gutachter] Bugajewska, and Gianluca [Gutachter] Vinti. "Functions of Bounded Variation: Theory, Methods, Applications / Simon Reinwand ; Gutachter: Jürgen Appell, Daria Bugajewska, Gianluca Vinti." Würzburg : Universität Würzburg, 2021. http://d-nb.info/1232647632/34.
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Handy, Jonathan Michael. "Bounded analytic functions on the complements of square cantor sets the corona problem and related problems /." Diss., Restricted to subscribing institutions, 2007. http://proquest.umi.com/pqdweb?did=1464114061&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Porritt, R. W., and S. Yoshioka. "Evidence of Dynamic Crustal Deformation in Tohoku, Japan, From Time-Varying Receiver Functions." AMER GEOPHYSICAL UNION, 2017. http://hdl.handle.net/10150/626288.
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Temporal variation of crustal structure is key to our understanding of Earth processes on human timescales. Often, we expect that the most significant structural variations are caused by strong ground shaking associated with large earthquakes, and recent studies seem to confirm this. Here we test the possibility of using P receiver functions (PRF) to isolate structural variations over time. Synthetic receiver function tests indicate that structural variation could produce PRF changes on the same order of magnitude as random noise or contamination by local earthquakes. Nonetheless, we find significant variability in observed receiver functions over time at several stations located in northeastern Honshu. Immediately following the Tohoku-oki earthquake, we observe high PRF variation clustering spatially, especially in two regions near the beginning and end of the rupture plane. Due to the depth sensitivity of PRF and the timescales over which this variability is observed, we infer this effect is primarily due to fluid migration in volcanic regions and shear stress/strength reorganization. While the noise levels in PRF are high for this type of analysis, by sampling small data sets, the computational cost is lower than other methods, such as ambient noise, thereby making PRF a useful tool for estimating temporal variations in crustal structure.
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Childers, Adam Fletcher. "Parameter Identification and the Design of Experiments for Continuous Non-Linear Dynamical Systems." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/28236.
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Mathematical models are useful for simulation, design, analysis, control, and optimization of complex systems. One important step necessary to create an effective model is designing an experiment from which the unknown model parameter can be accurately identified and then verified. The strategy which one approaches this problem is dependent on the amount of data that can be collected and the assumptions made about the behavior of the error in the statistical model. In this presentation we describe how to approach this problem using a combination of statistical and mathematical theory with reliable computation. More specifically, we present a new approach to bounded error parameter validation that approximates the membership set by solving an inverse problem rather than using the standard forward interval analysis methods. For our method we provide theoretical justification, apply this technique to several examples, and describe how it relates to designing experiments. We also address how to define infinite dimensional designs that can be used to create designs of any finite dimension. In general, finding a good design for an experiment requires a careful investigation of all available information and we provide an effective approach to dthe problem.Ph. D.
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Rosenberg, Steven Jay. "On some conjectures in Mazur's deformation theory with supplementary results onp-adic L-functions /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487942476405832.
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Kleyn, Judith. "The performance of the preliminary test estimator under different loss functions." Thesis, University of Pretoria, 2014. http://hdl.handle.net/2263/43132.
Full textAbstract:
In this thesis different situations are considered in which the preliminary test estimator is applied and
the performance of the preliminary test estimator under different proposed loss functions, namely
the reflected normal , linear exponential (LINEX) and bounded LINEX (BLINEX) loss functions is
evaluated. In order to motivate the use of the BLINEX loss function rather than the reflected
normal loss or the LINEX loss function, the risk for the preliminary test estimator and its component
estimators derived under BLINEX loss is compared to the risk of the preliminary test estimator and
its components estimators derived under both reflected normal loss and LINEX loss analytically (in
some sections) and computationally. It is shown that both the risk under reflected normal loss and
the risk under LINEX loss is higher than the risk under BLINEX loss. The key focus point under
consideration is the estimation of the regression coefficients of a multiple regression model under two
conditions, namely the presence of multicollinearity and linear restrictions imposed on the regression
coefficients. In order to address the multicollinearity problem, the regression coefficients were
adjusted by making use of Hoerl and Kennard’s (1970) approach in ridge regression. Furthermore,
in situations where under- or overestimation exist, symmetric loss functions will not give optimal
results and it was necessary to consider asymmetric loss functions. In the economic application,
it was shown that a loss function which is both asymmetric and bounded to ensure a maximum
upper bound for the loss, is the most appropriate function to use. In order to evaluate the effect
that different ridge parameters have on the estimation, the risk values were calculated for all three
ridge regression estimators under different conditions, namely an increase in variance, an increase
in the level of multicollinearity, an increase in the number of parameters to be estimated in the
regression model and an increase in the sample size. These results were compared to each other
and summarised for all the proposed estimators and proposed loss functions. The comparison of the
three proposed ridge regression estimators under all the proposed loss functions was also summarised
for an increase in the sample size and an increase in variance.Thesis (PhD)--University of Pretoria, 2014.
lk2014
Statistics
PhD
Unrestricted
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Tewodrose, David. "Some functional inequalities and spectral properties of metric measure spaces with curvature bounded below." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85734.
Full textAbstract:
[from the introduction]: The aim of this thesis is to study metric measure spaces with a synthetic notion of Ricci
curvature bounded below. We study them from the point of view of Sobolev/Nash type
functional inequalities in the non-compact case, and from the point of view of spectral
analysis in the compact case. The heat kernel links the two cases: in the first one, the goal
is to get new estimates on the heat kernel of some associated weighted structure; in the
second one, the heat kernel is the basic tool to establish our results.
The topic of synthetic Ricci curvature bounds has known a constant development over
the past few years. In this introduction, we shall give some historical account on this
theory, before explaining in few words the content of this work. The letter K will refer
to an arbitrary real number and N will refer to any finite number greater or equal than 1.
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Pau, Plana Jordi. "Ideals finitament generats i decreixement de funcions analítiques i acotades." Doctoral thesis, Universitat Autònoma de Barcelona, 2001. http://hdl.handle.net/10803/3090.
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Mohsen, Omar. "Deformation groupoids and applications." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC200/document.
Full textAbstract:
Cette thèse est consacrée à l’étude de trois questions différentes concernant les groupoïdes de Lie et leurs applications. Le premier chapitre présente quelques préliminaires sur les groupoïdes de Lie. Dans le chapitre 2, on exprime la déformation de Witten à l’aide d’une déformation au cone normal et la théorie de C∗-modules ce qui nous permet de retrouver les inégalités de Morse. Notre méthode se généralise au cas des feuilletages. Dans le chapitre 3, on donne une construction simple du groupoïde de déformation construit par Choi-Pönge et Van Erp-Yuncken. Rappelons que celui-ci décrit le calcule pseudo-différentiel inhomogène grâce au travail de Debord-Skandalis et Van Erp- Yuncken. Notre construction montre que le groupoïde de déformation est en fait une déformation au cone normal classique itérée. Dans le chapitre 4, suivant le travail de Antonini, Azzali et Skandalis, on construit un élément en KK-théorie équivariante qui permet d’exprimer directement les invariants de Chern-Simons en K-théorie. Dans l’appendice on donne quelques rappels sur la KK-théorie équivariante et la KK-théorie réelle introduite par Antonini, Azzali et SkandalisThis thesis is devoted to the study of three different questions concerning Lie groupoids and their applications. The first chapter presents some preliminaries on Lie groupoids. In Chapter 2, Witten’s deformation is expressed using deformation to the normal cone construction and the theory of C∗-modules, which allows us to reprove the Morse inequalities. Our method is generalised to the case of foliations. In Chapter 3, we give a simple construction of the deformation groupoid built by Choi-Pönge and Van Erp-Yuncken. Recall that this groupoid describes the inhomogeneous pseudo-differential calculus thanks to the work of Debord-Skandalis and Van Erp-Yuncken. Our construction shows that the deformation groupoid is actually an iterated classical deformation to the normal cone. In Chapter 4, following the work of Antonini, Azzali and Skandalis, we construct an element in equivariant KK-theory that allows us to express the Chern-Simons invariants directly in K-theory. In the appendix we give some reminders about the equivariant KK-theory and the real KK-theory introduced by Antonini, Azzali and Skandalis
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Debrecht, Johanna M. "Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278501/.
Full textAbstract:
We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is convex if and only if the curvature does not change sign, and we prove the Isoperimetric Inequality, which gives a bound on the area of a closed curve with fixed length. Finally, we study the deformation of plane curves developed by M. Gage and R. S. Hamilton. We observe that convex curves under deformation remain convex, and simple curves remain simple.
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Roche, Thomas [Verfasser], Martin [Akademischer Betreuer] Brokate, Pavel [Akademischer Betreuer] Krejčí, and Alexander [Akademischer Betreuer] Mielke. "Rate independent evolution processes on functions of bounded variation / Thomas Roche. Gutachter: Pavel Krejci ; Alexander Mielke ; Martin Brokate. Betreuer: Martin Brokate." München : Universitätsbibliothek der TU München, 2012. http://d-nb.info/1047883473/34.
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CAMFIELD, CHRISTOPHER SCOTT. "Comparison of BV Norms in Weighted Euclidean Spaces and Metric Measure Spaces." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1211551579.
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Beltrán, Meneu María José. "Operators on wighted spaces of holomorphic functions." Doctoral thesis, Universitat Politècnica de València, 2014. http://hdl.handle.net/10251/36578.
Full textAbstract:
The Ph.D. Thesis ¿Operators on weighted spaces of holomorphic functions¿ presented
here treats different areas of functional analysis such as spaces of holomorphic
functions, infinite dimensional holomorphy and dynamics of operators.
After a first chapter that introduces the notation, definitions and the basic results
we will use throughout the thesis, the text is divided into two parts. A first one,
consisting of Chapters 1 and 2, focused on a study of weighted (LB)-spaces of entire
functions on Banach spaces, and a second one, corresponding to Chapters 3 and
4, where we consider differentiation and integration operators acting on different
classes of weighted spaces of entire functions to study its dynamical behaviour. In
what follows, we give a brief description of the different chapters:
In Chapter 1, given a decreasing sequence of continuous radial weights on a Banach
space X, we consider the weighted inductive limits of spaces of entire functions
VH(X) and VH0(X). Weighted spaces of holomorphic functions appear naturally
in the study of growth conditions of holomorphic functions and have been investigated
by many authors since the work of Williams in 1967, Rubel and Shields
in 1970 and Shields and Williams in 1971. We determine conditions on the family
of weights to ensure that the corresponding weighted space is an algebra or
has polynomial Schauder decompositions. We study Hörmander algebras of entire
functions defined on a Banach space and we give a description of them in terms of
sequence spaces. We also focus on algebra homomorphisms between these spaces
and obtain a Banach-Stone type theorem for a particular decreasing family of
weights. Finally, we study the spectra of these weighted algebras, endowing them
with an analytic structure, and we prove that each function f ¿ VH(X) extends
naturally to an analytic function defined on the spectrum. Given an algebra homomorphism,
we also investigate how the mapping induced between the spectra
acts on the corresponding analytic structures and we show how in this setting
composition operators have a different behavior from that for holomorphic functions
of bounded type. This research is related to recent work by Carando, García,
Maestre and Sevilla-Peris. The results included in this chapter are published by
Beltrán in [14]. Chapter 2 is devoted to study the predual of VH(X) in order to linearize this space
of entire functions. We apply Mujica¿s completeness theorem for (LB)-spaces to
find a predual and to prove that VH(X) is regular and complete. We also study
conditions to ensure that the equality VH0(X) = VH(X) holds. At this point,
we will see some differences between the finite and the infinite dimensional cases.
Finally, we give conditions which ensure that a function f defined in a subset
A of X, with values in another Banach space E, and admitting certain weak
extensions in a space of holomorphic functions can be holomorphically extended
in the corresponding space of vector-valued functions. Most of the results obtained
have been published by the author in [13].
The rest of the thesis is devoted to study the dynamical behaviour of the following
three operators on weighted spaces of entire functions: the differentiation operator
Df(z) = f (z), the integration operator Jf(z) = z
0 f(¿)d¿ and the Hardy
operator Hf(z) = 1
z z
0 f(¿)d¿, z ¿ C.
In Chapter 3 we focus on the dynamics of these operators on a wide class of
weighted Banach spaces of entire functions defined by means of integrals and
supremum norms: the weighted spaces of entire functions Bp,q(v), 1 ¿ p ¿ ¿,
and 1 ¿ q ¿ ¿. For q = ¿ they are known as generalized weighted Bergman
spaces of entire functions, denoted by Hv(C) and H0
v (C) if, in addition, p = ¿.
We analyze when they are hypercyclic, chaotic, power bounded, mean ergodic
or uniformly mean ergodic; thus complementing also work by Bonet and Ricker
about mean ergodic multiplication operators. Moreover, for weights satisfying
some conditions, we estimate the norm of the operators and study their spectrum.
Special emphasis is made on exponential weights. The content of this chapter is
published in [17] and [15].
For differential operators ¿(D) : Bp,q(v) ¿ Bp,q(v), whenever D : Bp,q(v) ¿
Bp,q(v) is continuous and ¿ is an entire function, we study hypercyclicity and
chaos. The chapter ends with an example provided by A. Peris of a hypercyclic
and uniformly mean ergodic operator. To our knowledge, this is the first example
of an operator with these two properties. We thank him for giving us permission
to include it in our thesis.
The last chapter is devoted to the study of the dynamics of the differentiation and
the integration operators on weighted inductive and projective limits of spaces of
entire functions. We give sufficient conditions so that D and J are continuous on
these spaces and we characterize when the differentiation operator is hypercyclic,
topologically mixing or chaotic on projective limits. Finally, the dynamics of these
operators is investigated in the Hörmander algebras Ap(C) and A0
p(C). The results
concerning this topic are included by Bonet, Fernández and the author in [16].Beltrán Meneu, MJ. (2014). Operators on wighted spaces of holomorphic functions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/36578
TESIS
Premiado
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Trienis, Michael Joseph. "Computational convex analysis : from continuous deformation to finite convex integration." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/2799.
Full textAbstract:
After introducing concepts from convex analysis, we study how to continuously transform one convex
function into another. A natural choice is the arithmetic average, as it is pointwise continuous;
however, this choice fails to average functions with different domains. On the contrary, the proximal
average is not only continuous (in the epi-topology) but can actually average functions with
disjoint domains. In fact, the proximal average not only inherits strict convexity (like the arithmetic
average) but also inherits smoothness and differentiability (unlike the arithmetic average).
Then we introduce a computational framework for computer-aided convex analysis. Motivated
by the proximal average, we notice that the class of piecewise linear-quadratic (PLQ) functions is
closed under (positive) scalar multiplication, addition, Fenchel conjugation, and Moreau envelope.
As a result, the PLQ framework gives rise to linear-time and linear-space algorithms for convex
PLQ functions. We extend this framework to nonconvex PLQ functions and present an explicit
convex hull algorithm.
Finally, we discuss a method to find primal-dual symmetric antiderivatives from cyclically monotone
operators. As these antiderivatives depend on the minimal and maximal Rockafellar functions
[5, Theorem 3.5, Corollary 3.10], it turns out that the minimal and maximal function in [12,
p.132,p.136] are indeed the same functions. Algorithms used to compute these antiderivatives can
be formulated as shortest path problems.
35
Brannath, Werner, and Walter Schachermayer. "A bipolar theorem for $L^0_+(\Om, \Cal F, \P)$." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1688/1/document.pdf.
Full textAbstract:
A consequence of the Hahn-Banach theorem is the classical bipolar theorem which states that the bipolar of a subset of a locally convex vector pace equals its closed convex hull. The space $\L$ of real-valued random variables on a probability space $\OF$ equipped with the topology of convergence in measure fails to be locally convex so that - a priori - the classical bipolar theorem does not apply. In this note we show an analogue of the bipolar theorem for subsets of the positive orthant $\LO$, if we place $\LO$ in duality with itself, the scalar product now taking values in $[0, \infty]$. In this setting the order structure of $\L$ plays an important role and we obtain that the bipolar of a subset of $\LO$ equals its closed, convex and solid hull. In the course of the proof we show a decomposition lemma for convex subsets of $\LO$ into a "bounded" and "hereditarily unbounded" part, which seems interesting in its own right. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
36
Zolfaghari, Reza. "Large Deformation Diffeomorphic Metric Mapping Provides New Insights into the Link Between Human Ear Morphology and the Head-Related Transfer Functions." Thesis, The University of Sydney, 2016. http://hdl.handle.net/2123/16701.
Full textAbstract:
The research findings presented in this thesis is composed of four sections. In the first section of this thesis, it is shown how LDDMM can be applied to deforming head and ear shapes in the context of morphoacoustic study. Further, tools are developed to measure differences in 3D shapes using the framework of currents and also to compare and measure the differences between the acoustic responses obtained from BEM simulations for two ear shapes. Finally this section introduces the multi-scale approach for mapping ear shapes using LDDMM. The second section of the thesis estimates a template ear, head and torso shape from the shapes available in the SYMARE database. This part of the thesis explains a new procedure for developing the template ear shape. The template ear and head shapes were are verified by comparing the features in the template shapes to corresponding features in the CIPIC and SYMARE database population. The third section of the thesis examines the quality of the deformations from the template ear shape to target ears in SYMARE from both an acoustic and morphological standpoint. As a result of this investigation, it was identified that ear shapes can be studied more accurately by the use of two physical scales and that scales at which the ear shapes were studied were dependent on the parameters chosen when mapping ears in the LDDMM framework. Finally, this section concludes by noting how shape distances vary with the acoustic distances using the developed tools. In the final part of this thesis, the variations in the morphology of ears are examined using the Kernel Principle Component Analysis (KPCA) and the changes in the corresponding acoustics are studied using the standard principle component analysis (PCA). These examinations involved identifying the number of kernel principle components that are required in order to model ear shapes with an acceptable level of accuracy, both morphologically and acoustically.
37
Marx, Gregory. "Noncommutative Kernels." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/78353.
Full textAbstract:
Positive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative kernels in the setting of Hilbert C*-modules and Hilbert W*-modules. We prove an Arveson-type extension theorem for completely positive noncommutative kernels, and we show that a uniformly bounded noncommutative kernel can be decomposed into a linear combination of completely positive noncommutative kernels.Ph. D.
38
Tewodrose, David. "Some functional inequalities and spectral properties of metric measure spaces with curvature bounded below." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEE076.
Full textAbstract:
L’objectif de la thèse est de présenter de nouveaux résultats d’analyse sur les espaces métriques mesurés. Nous étendons d’abord à une certaine classe d’espaces avec doublement et Poincaré des inégalités de Sobolev pondérées introduites par V. Minerbe en 2009 dans le cadre des variétés riemanniennes à courbure de Ricci positives. Dans le contexte des espaces RCD(0,N), nous en déduisons une inégalité de Nash pondérée et un contrôle uniforme du noyau de la chaleur pondéré associé. Puis nous démontrons la loi de Weyl sur les espaces RCD(K,N) compactes à l’aide d’un théorème de convergence ponctuelle des noyaux de la chaleur associés à une suite mGH-convergente d’espaces RCD(K,N). Enfin nous abordons dans le contexte RCD(K,N) un théorème de Bérard, Besson et Gallot fournissant, à l’aide du noyau de la chaleur, une famille de plongements asymptotiquement isométriques d’une variété riemannienne fermée dans l’espace de ses fonctions de carré intégrable. Nous introduisons notamment les notions de métrique RCD, de métrique pull-back, et de convergence faible/forte de métriques RCD sur un espace RCD(K,N) compacte, et nous prouvons un résultat de convergence analogue à celui de Bérard, Besson et GallotThe aim of this thesis is to present new results in the analysis of metric measure spaces. We first extend to a certain class of spaces with doubling and Poincaré some weighted Sobolev inequalities introduced by V. Minerbe in 2009 in the context of Riemannian manifolds with non-negative Ricci curvature. In the context of RCD(0,N) spaces, we deduce a weighted Nash inequality and a uniform control of the associated weighted heat kernel. Then we prove Weyl’s law for compact RCD(K,N) spaces thanks to a pointwise convergence theorem for the heat kernels associated with a mGH-convergent sequence of RCD(K,N) spaces. Finally we address in the RCD(K,N) context a theorem from Bérard, Besson and Gallot which provides, by means of the heat kernel, an asymptotically isometric family of embeddings for a closed Riemannian manifold into its space of square integrable functions. We notably introduce the notions of RCD metrics, pull-back metrics, weak/strong convergence of RCD metrics, and we prove a convergence theorem analog to the one of Bérard, Besson and Gallot
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Abbott, Catherine Ann. "Operators on Continuous Function Spaces and Weak Precompactness." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331171/.
Full textAbstract:
If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property.
40
Esterhuizen, Stefanie-Marié. "An intervention programme to optimise the cognitive development of grade R-learners :|ba bounded pilot study / Stefani-Marié Esterhuizen." Thesis, North-West University, 2012. http://hdl.handle.net/10394/10431.
Full textAbstract:
It is imperative to prepare South African learners to participate and function confidently within the context of a rapidly changing world. The curriculum of the South African Education System emphasises the significance of optimising learners‟ cognitive development as early as pre-school age to enable them to become creative and critical citizens who lead purposeful lives in a safe and prejudice-free environment. Despite continuous efforts by educators to optimise cognitive development, recently executed research studies indicate that cognitive development has not been adequately optimised in South African schools. This study was undertaken to establish the cognitive development level (cognitive and meta-cognitive skills and strategies, cognitive functions and non-intellective factors) of Grade R-learners and to determine the effect of an intervention programme, the Cognitive Enhancement Programme for Pre-schoolers (CEPP), on their cognitive development. By means of a literature study, I investigated whether, to what extent the cognitive development of Grade R-learners was taking place, and established which cognitive and meta-cognitive thinking skills and strategies, cognitive functions and non-intellective factors are required for effective cognitive development among Grade R-learners. In addition to this, the role of mediation for optimising cognitive development was investigated. A concurrent embedded mixed methods design was conducted in the implementation of the research. Intervention research within a quasi-experimental research design was applied. The data collection by means of a quantitative strategy (quasi-experimental research) and qualitative strategy (observation study) was executed simultaneously. By means of convenient sampling, one Grade R-class with twenty learners was subjected to a pre-test to establish their cognitive developmental level. The test results as well as the observations conducted during the pre-test revealed that the learners experienced problems related to their cognitive development. Ten of the twenty learners were then divided purposively based on their test performance into two experimental groups, Experimental Group A and Experimental Group B consisting of five participants each. Experimental group A and Experimental Group B took part in the CEPP intervention based on the principles of mediation on a rotational basis over a period of twelve weeks, during which intentional attempts were made to optimise their cognitive development. Both groups completed a post-test and delayed post-test (retention) to determine the effect of the CEPP intervention on their cognitive development. In addition to the test results, observations in the form of structured running and anecdotal records and reflective notes were utilised to understand the nature and quality of the cognitive development of the learners better. Furthermore, the effect of the intervention on their cognitive development was established. The cognitive development of Grade R-learners who participated in this study was optimised, which is a clear indication that cognitive capacity can be optimised when instruction is based on the principles of mediationPhD, Teaching and Learning, North-West University, Vaal Triangle Campus, 2012
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Soneji, Parth. "Lower semicontinuity and relaxation in BV of integrals with superlinear growth." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:c7174516-588e-46ae-93dc-56d4a95f1e6f.
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Manca, Luigi. "Kolmogorov operators in spaces of continuous functions and equations for measures." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85697.
Full textAbstract:
La thèse est consacrée à étudier les relations entre les Équations aux Derivées Partielles Stochastiques et l'operateur de Kolmogorov associé dans des espaces de fonctions continues.Dans la première partie, la théorie de la convergence faibles des fonctions est mis au point afin de donner des résultats généraux sur les semi-groupes des Markov et leur générateur.
Dans la deuxième partie, des modèles de semi-groups de Markov associés à des équations aux dérivées partielles stochastiques sont étudiés. En particulier, Ornstein-Uhlenbeck, réaction-diffusion et équations de Burgers ont été envisagées. Pour chaque cas, le semi-groupe de transition et son générateur infinitésimal ont été étudiées dans un espace de fonctions continues.
Les résultats principaux montrent que l'ensemble des fonctions exponentielles fournit un Core pour l'opérateur de Kolmogorov. En conséquence, on prouve l'unicité de l'équation de Kolmogorov de mesures (autrement dit de Fokker-Planck).
43
Piffet, Loïc. "Décomposition d’image par modèles variationnels : débruitage et extraction de texture." Thesis, Orléans, 2010. http://www.theses.fr/2010ORLE2053/document.
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Cette thèse est consacrée dans un premier temps à l’élaboration d’un modèle variationnel dedébruitage d’ordre deux, faisant intervenir l’espace BV 2 des fonctions à hessien borné. Nous nous inspirons ici directement du célèbre modèle de Rudin, Osher et Fatemi (ROF), remplaçant la minimisation de la variation totale de la fonction par la minimisation de la variation totale seconde, c’est à dire la variation totale de ses dérivées. Le but est ici d’obtenir un modèle aussi performant que le modèle ROF, permettant de plus de résoudre le problème de l’effet staircasing que celui-ci engendre. Le modèle que nous étudions ici semble efficace, entraînant toutefois l’apparition d’un léger effet de flou. C’est afin de réduire cet effet que nous introduisons finalement un modèle mixte, permettant d’obtenir des solutions à la fois non constantes par morceaux et sans effet de flou au niveau des détails. Dans une seconde partie, nous nous intéressons au problème d’extraction de texture. Un modèle reconnu comme étant l’un des plus performants est le modèle T V -L1, qui consiste simplement à remplacer dans le modèle ROF la norme L2 du terme d’attache aux données par la norme L1. Nous proposons ici une méthode originale permettant de résoudre ce problème utilisant des méthodes de Lagrangien augmenté. Pour les mêmes raisons que dans le cas du débruitage, nous introduisons également le modèle T V 2-L1, consistant encore une fois à remplacer la variation totale par la variation totale seconde. Un modèle d’extraction de texture mixte est enfin très brièvement introduit. Ce manuscrit est ponctué d’un vaste chapitre dédié aux tests numériquesThis thesis is devoted in a first part to the elaboration of a second order variational modelfor image denoising, using the BV 2 space of bounded hessian functions. We here take a leaf out of the well known Rudin, Osher and Fatemi (ROF) model, where we replace the minimization of the total variation of the function with the minimization of the second order total variation of the function, that is to say the total variation of its partial derivatives. The goal is to get a competitive model with no staircasing effect that generates the ROF model anymore. The model we study seems to be efficient, but generates a blurry effect. In order to deal with it, we introduce a mixed model that permits to get solutions with no staircasing and without blurry effect on details. In a second part, we take an interset to the texture extraction problem. A model known as one of the most efficient is the T V -L1 model. It just consits in replacing the L2 norm of the fitting data term with the L1 norm.We propose here an original way to solve this problem by the use of augmented Lagrangian methods. For the same reason than for the denoising case, we also take an interest to the T V 2-L1 model, replacing again the total variation of the function by the second order total variation. A mixed model for texture extraction is finally briefly introduced. This manuscript ends with a huge chapter of numerical tests
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Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.
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Dissertation for the Degree of Doctor of Philosophy in MathematicsFundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA
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Spinnler, Florian. "Star-exponential of normal j-groups and adapted Fourier transform." Doctoral thesis, Universite Libre de Bruxelles, 2015. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209089.
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This thesis provides the explicit expression of the star-exponential for the action of normal j-groups on their coadjoint orbits, and of the so-called modified star-exponential defined by Gayral et al. Using this modified star-exponential as the kernel of a functional transform between the group and its coadjoint orbits yields an adapted Fourier transform which is also detailed here. The normal j-groups arise in the work of Pytatetskii-Shapiro, who established the one-to-one correspondence with homogeneous bounded domains of the complex space; these groups are also the central element of the deformation formula recently developed by Bieliavsky & Gayral (a non abelian analog of the strict deformation quantization theory of Rieffel). Since these groups are exponential, the results given in this text illustrate the general work of Arnal & Cortet on the star-representations of exponential groups.As this work is meant to be as self-contained as possible, the first chapter reproduces many definitions introduced by Bieliavsky & Gayral, in order to obtain the expression of the symplectic symmetric space structure on normal j-groups, and of their unitary irreducible representations. The Weyl-type quantizer associated to this symmetric structure is then computed, thus yielding the Weyl quantization map for which the composition of symbols is precisely the deformed product defined by Bieliavsky-Gayral on normal j-groups. A detailed proof of the structure theorem of normal j-groups is also provided.
The second chapter focuses on the expression and properties of the star-exponential itself, and exhibits a useful tool for the computation, namely the resolution of the identity associated to square integrable unitary irreducible representations of the groups. The result thus obtained satisfies the usual integro-differential equation defining the star-exponential. A criterion for the existence of a tempered pair underlying a given tempered structure on Lie groups is proven; the star-exponential functions are also shown to belong to the multiplier algebra of the Schwartz space associated to the tempered structure. Before that, it is shown that all Schwartz spaces that appear in this work are isomorphic as topological vector spaces.
The modified version of this star-exponential is computed in chapter three, first for elementary normal j-groups and then for normal j-groups. It is then used to define an adapted Fourier transform between the group and the dual of its Lie algebra. This transform generalizes (to all normal j-groups) a Fourier transform that was already studied in the “ax+b” case by Gayral et al. (2008), as well as by Ali et al. (2003) in the context of wavelet transforms.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Massarczyk, Ralph. "The effect of neutron excess and nuclear deformation on dipole strength functions below the neutron separation energy - nuclear resonance fluorescence experiments on 124,128,132,134 Xe at ELBE and HI gamma S." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-154377.
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Within this thesis, nuclear resonance fluorescence experiments were analyzed which have been performed at the gamma ELBE facility of the Helmholtz-Zentrum Dresden-Rossendorf and the HI gamma S facility of the Triangle Universities Nuclear Laboratory. The dipole strength up to the neutron separation energy, its distribution as well as its split into electric and magnetic strength were determined. The influence of crucial nuclear parameters, like deformation and neutron excess, on the data was investigated.
For the first time a whole set of enriched gaseous targets was measured in the energy region close to the neutron separation threshold. At ELBE the scattering of photons on four different isotopes 124, 128, 132, 134 Xe was investigated by irradiating containers with enriched target material with a broad bremsstrahlung distribution. The endpoint energies were chosen to be 12MeV. This ensures excitations up to the neutron separation threshold. The two isotopes 128, 134 Xe were measured in an additional campaign at HI gamma S facility. The region below the threshold was explored in detail in these experiments. A second, more model-independent determination of the cross section was possible.
The work shows, how the measured spectra taken with high-purity germanium detectors, have to be corrected for several, partly overlapping effects in order to determine the complete excitation strength.
The calculation of different backgrounds, detector response functions and the influence of inelastic scattering constitute the main part of the presented work. With the help of GEANT4 simulations the amount of not-nuclear scattered photons was estimated. GEANT4 was also used to test the influence of the extended targets on the detection efficiency and response. The code gamma DEX, which calculates deexcitation schemes based on statistical assumptions, was updated and finally used for the unfolding of the spectrum.
The measured data is compared to different strength function models and a theoretical prediction based on a QRPA calculation. The summed strength is also set into comparison to other experimental data sets and a global trend for low-lying strength was found. This shows, that the nuclear deformation which has a large influence on the dipole strength above the threshold is only of minor impact for the strength at lower energies.
Instead of this, the neutron excess seems to be the dominating factor for the strength in the investigated energy region.
This work was supported by the German Research Foundation (DFG), Project No. SCHW883/1-1.
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Hernandez, Michelle Fernanda Pierri. "Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/.
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Este trabalho está voltado para o estudo de uma classe de funções contínuas e limitadas f : [0; \'INFINITO\') \'SETA\' X para as quais existe \'omega\' \'> OU =\' 0 tal que \'lim IND. t\' \'SETA\' \'INFINITO\' (f(t + \'omega\') - f(t)) = 0. No decorrer do trabalho, chamaremos estas funções de S-assintoticamente \'omega\'-periódicas. Nós discutiremos propriedades qualitativas para estas funções e algumas relações entre este tipo de funções e a classe de funções assintoticamente \'omega\'-periódicas. Também estudaremos a existência de soluções fracas S-assintoticamente \'omega\'-periódicas para uma classe de primeira ordem de um problema de Cauchy abstrato bem como para algumas classes de equações diferenciais funcionais parciais neutras com retardo não limitado. Algumas aplicações para equações diferenciais parciais serão consideradasThis work is devoted to the study of the class of continuous and bounded functions f : [0 \'INFINIT\') \'ARROW\' X for which there exists \'omega\' > 0 such that \'limt IND.t \'ARROW\' \'INFINIT\'(f(t + \'omega\'!) - f(t)) = 0 (in the sequel called S-asymptotically !-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically \'omega\'-periodic functions. We also study the existence of S-asymptotically \'omega\'-periodic mild solutions for a first-order abstract Cauchy problem in Banach spaces and for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given
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Persson, Håkan. "Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables." Doctoral thesis, Uppsala universitet, Analys och sannolikhetsteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-251325.
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This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0<α<1, is hyperconvex. Global estimates of the exhaustion function are given. In Paper IV, it is shown that on the closure of a domain whose boundary locally is the graph of a continuous function, all plurisubharmonic functions with continuous boundary values can be uniformly approximated by smooth plurisubharmonic functions defined in neighbourhoods of the closure of the domain. Paper V studies Poletsky’s notion of plurisubharmonicity on compact sets. It is shown that a function is plurisubharmonic on a given compact set if, and only if, it can be pointwise approximated by a decreasing sequence of smooth plurisubharmonic functions defined in neighbourhoods of the set. Paper VI introduces the notion of a P-hyperconvex domain. It is shown that in such a domain, both the Dirichlet problem with respect to functions plurisubharmonic on the closure of the domain, and the problem of approximation by smooth plurisubharmoinc functions in neighbourhoods of the closure of the domain have satisfactory answers in terms of plurisubharmonicity on the boundary.
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Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.
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In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases.
The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales
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Larsson, David. "Generalized Riemann Integration : Killing Two Birds with One Stone?" Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-96661.
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Since the time of Cauchy, integration theory has in the main been an attempt to regain the Eden of Newton. In that idyllic time [. . . ] derivatives and integrals were [. . . ] different aspects of the same thing. -Peter Bullen, as quoted in [24] The theory of integration has gone through many changes in the past centuries and, in particular, there has been a tension between the Riemann and the Lebesgue approach to integration. Riemann's definition is often the first integral to be introduced in undergraduate studies, while Lebesgue's integral is more powerful but also more complicated and its methods are often postponed until graduate or advanced undergraduate studies. The integral presented in this paper is due to the work of Ralph Henstock and Jaroslav Kurzweil. By a simple exchange of the criterion for integrability in Riemann's definition a powerful integral with many properties of the Lebesgue integral was found. Further, the generalized Riemann integral expands the class of integrable functions with respect to Lebesgue integrals, while there is a characterization of the Lebesgue integral in terms of absolute integrability. As this definition expands the class of functions beyond absolutely integrable functions, some theorems become more cumbersome to prove in contrast to elegant results in Lebesgue's theory and some important properties in composition are lost. Further, it is not as easily abstracted as the Lebesgue integral. Therefore, the generalized Riemann integral should be thought of as a complement to Lebesgue's definition and not as a replacement.Ända sedan Cauchys tid har integrationsteori i huvudsak varit ett försök att åter finna Newtons Eden. Under den idylliska perioden [. . . ] var derivator och integraler [. . . ] olika sidor av samma mynt.-Peter Bullen, citerad i [24] Under de senaste århundradena har integrationsteori genomgått många förändringar och framförallt har det funnits en spänning mellan Riemanns och Lebesgues respektive angreppssätt till integration. Riemanns definition är ofta den första integral som möter en student pa grundutbildningen, medan Lebesgues integral är kraftfullare. Eftersom Lebesgues definition är mer komplicerad introduceras den först i forskarutbildnings- eller avancerade grundutbildningskurser. Integralen som framställs i det här examensarbetet utvecklades av Ralph Henstock och Jaroslav Kurzweil. Genom att på ett enkelt sätt ändra kriteriet for integrerbarhet i Riemanns definition finner vi en kraftfull integral med många av Lebesgueintegralens egenskaper. Vidare utvidgar den generaliserade Riemannintegralen klassen av integrerbara funktioner i jämförelse med Lebesgueintegralen, medan vi samtidigt erhåller en karaktärisering av Lebesgueintegralen i termer av absolutintegrerbarhet. Eftersom klassen av generaliserat Riemannintegrerbara funktioner är större än de absolutintegrerbara funktionerna blir vissa satser mer omständiga att bevisa i jämforelse med eleganta resultat i Lebesgues teori. Därtill förloras vissa viktiga egenskaper vid sammansättning av funktioner och även möjligheten till abstraktion försvåras. Integralen ska alltså ses som ett komplement till Lebesgues definition och inte en ersättning.