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Sadykov, Timour. "Hypergeometric functions in several complex variables." Doctoral thesis, Stockholm : Univ, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-198.
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Mernik, Luka. "Positivity Conditions in Several Complex Variables." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586522855649564.
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McKeown, Jesse. "Functional methods in analysis of several complex variables." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101622.
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Nedic, Mitja. "Integral representations of Herglotz-Nevanlinna functions." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-138962.
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In this thesis, we study integral representations of Herglotz-Nevanlinna functions, that is to say holomorphic functions defined on a product of several copies of the complex upper half-plane having non-negative imaginary part. The manuscript is divided into three parts, beginning with a general introduction followed by two papers. In the general introduction, we familiarize ourselves with the concept of a Herglotz-Nevanlinna function as well as providing a comprehensive introduction into the theory of integral representations for this particular class of functions. Paper I treats exclusively the two-variable case and presents an integral representation of Herglotz-Nevanlinna functions in two complex variables in terms of a real number, two non-negative numbers and a positive Borel measure satisfying two properties. Three properties that hold for the class of measures appearing in such integral representations are also proven. In Paper II, we provide an integral representation for the class of Herglotz-Nevanlinna functions in arbitrarily many complex variables in terms of a real number, a linear term and a positive Borel measure satisfying two properties. Properties of the class of measures appearing in this representation are then discussed in detail as well as alternative descriptions of said class. Finally, a symmetry formula satisfied by Herglotz-Nevanlinna functions is proved at the end.
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Braun, H. T. F. "Model theory of holomorphic functions." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401108.
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This thesis is concerned with a conjecture of Zilber: that the complex field expanded with the exponential function should be `quasi-minimal'; that is, all its definable subsets should be countable or have countable complement. Our purpose is to study the geometry of this structure and other expansions by holomorphic functions of the complex field without having first to settle any number-theoretic problems, by treating all countable sets on an equal footing. We present axioms, modelled on those for a Zariski geometry, defining a non-first-order class of ``quasi-Zariski'' structures endowed with a dimension theory and a topology in which all countable sets are of dimension zero. We derive a quantifier elimination theorem, implying that members of the class are quasi-minimal. We look for analytic structures in this class. To an expansion of the complex field by entire holomorphic functions $\mathcal{R}$ we associate a sheaf $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ of analytic germs which is closed under application of the implicit function theorem. We prove that $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ is also closed under partial differentiation and that it admits Weierstrass preparation. The sheaf defines a subclass of the analytic sets which we call $\mathcal{R}$-analytic. We develop analytic geometry for this class proving a Nullstellensatz and other classical properties. We isolate a condition on the asymptotes of the varieties of certain functions in $\mathcal{R}$. If this condition is satisfied then the $\mathcal{R}$-analytic sets induce a quasi-Zariski structure under countable union. In the motivating case of the complex exponential we prove a low-dimensional case of the condition, towards the original conjecture.
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Lan, Ma. "Abschätzungen von Lösungen der [delta bar]-Gleichung auf streng q-konvexen Mengen mit nicht glattem Rand." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20436892.html.
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Zhang, Yunxin, and 张云鑫. "On the admissible pairs of rational homogeneous manifolds of Picard number 1 and geometric structures defined by their varieties of minimal rational tangents." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206439.
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In a series of works, Jun-Muk Hwang and Ngaiming Mok have developed a geometric theory of uniruled projective manifolds, especially those of Picard Number 1, relying on the study of Varieties of Minimal Rational Tangents (VMRT) from both the algebro-geometric and the G-structure perspectives. Based on this theory, Ngaiming Mok and Jaehyun Hong studied the standard embedding between two Rational Homogeneous Spaces (RHS) associated to long simple roots which are of different dimensions. In this thesis, I consider admissible pairs of RHS (X0, X) of Picard number 1 and locally closed complex submanifolds S ⊂ X inheriting VMRT sub-structures modeled on X0 = G0/P0 ⊂ X = G/P de_ned by taking intersections of VMRT of X with tangent space of S. Moreover, if any such S modeled on (X0, X) is necessarily the image of a standard embedding i : X0 → X, (X0, X) is said to be rigid. In this thesis, it is proved that an admissible pair (X0, X) is rigid whenever X is associated to a long simple root and X0 is non-linear and de_ned by a marked Dynkin sub-diagram. In the case of the pair (S0, S) of compact Hermitian Symmetric Spaces (cHSS), all the admissible pairs (S0, S) are completely classified. Based on this classification, a sufficient condition for the pair (S0, S) to be non-rigid is established through explicitly constructing a submanifold S ⊂ S such that S can never be obtained from the image of any standard embedding i : S0 → S. Besides, the term special pair is coined for those (S0; S) sorted out through classification, and the algebraicity of submanifolds modeled on special pairs is confirmed by checking a modified form of the non-degeneracy condition defined by Hong and Mok is satisfied. However, the question as to whether these special pairs are rigid, as pointed out in this thesis, remains to be investigated. Finally, pairs of hyperquadrics (Q^n, Q^m) are studied separately. Since non-rigidity is trivial, in these cases it is interesting to establish a characterization of the standard embedding i : Q^n→Q^m under some stronger condition. In this thesis, the latter problem is solved in terms of the partial vanishing of second fundamental forms.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Ravisankar, Sivaguru. "Lipschitz Properties of Harmonic and Holomorphic Functions." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1308299030.
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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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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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Karlsson, Jesper. "The Oka-Weil Theorem." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-138760.
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We give a proof of the Oka-Weil theorem which states that on compact, polynomially convex subsets of Cn, holomorphic functions can be approximated uniformly by holomorphic polynomials.Vi ger ett bevis av Oka-Weil sats som säger att på kompakta och polynomkonvexa delmängder av Cn kan holomorfa funktioner approximeras likformigt med holomorfa polynom.
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Oliver, Vendrell Roc. "Hankel operators on vector-valued Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/471520.
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The main goal of this work is to study vector-valued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operator-valued holomorphic symbols. We also study the big Hankel operator acting on vector-valued Bergman spaces.
In Chapter 1 we collect all the previous results and notations needed to follow the rest of the manuscript. More concretely, some of the topics covered in this chapter are the Bochner integral, the integral for vector-valued functions appearing first in Bochner; the Bergman metric, results of the metric used in Bn; harmonic and subharmonic function; basic notions of differentiation, where the differential operators R(a, t) are presented which is important in the next chapters and in the final section we recall some topics on Banach spaces, as the Rademacher type and cotype of a Banach space and some other related results.
Having all that in mind, in Chapter 2, the vector-valued Bergman spaces are presented. The vector-valued Bloch type spaces play a similar role and therefore we dedícate one full chapter to these spaces. Chapter 3 is devoted to present and characterize the vector-valued Bloch type spaces. Since we mention Hankel operators, in Chapter 4 we prove the characterization of the boundedness of the small Hankel operator with analytic operator-valued symbols between vector-valued Bergman spaces (of different type). We explain what
this means in the following.
Another very important consequence of the boundedness of the small Hankel operator between vector-valued Bergman spaces is shown in Chapter 5. We establish the weak factorization of the vector-valued Bergman spaces. Factorization of analytic functions is a very big topic and many people worked on it during many years and it is known to have many applications.
Therefore, in Chapter 6 we fully characterize the boundedness of the big Hankel operator on vector-valued Bergman spaces in terms of its operator-valued holomorphic symbol for all cases of p > 1 and q > 1, and so we solve and generalize the previous problem.
Finally, in Chapter 7 we discuss some open problems we have not been able to solve, as well as some other interesting problems in the same line as this work in order to look on the future.
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AlBalushi, Rima Said Ali. "Model theory of generic functions of several variables." Thesis, University of East Anglia, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580564.
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Ahmad, Khan Mumtaz, and K. S. Nisar. "On a Generalizations of Lauricella’s Functions of Several Variables." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97061.
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The present paper introduces 10 Appell’s type generalized functions Ni, i = 1, 2, ...... 10 by considering the product of n − 3F2 functions. The paper contains Fractional derivative representations, Integral representations and symbolic forms similar to those obtained by J. L. Burchnall and T. W.Chaundy for the four Appell’s functions, have been obtained for these newly defined functions N1, N2.......N10. The results obtained are believed to be new.El presente artículo introduce 10 tipo de funciones generalizadas tipo Appell Ni, 1 ≤ i ≤ 10, considerando el producto de n funciones 3F2. El artículo contiene representaciones por derivadas fraccionales, representaciones integrales y formas simbólicas similares a aquellas obtenidas por J. L. Burchnall y T. W. Chaundy para las cuatro funciones de Appell, han sido obtenidas para estas nuevas funciones N1, N2.......N10. Los resultados parecen ser nuevos.
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Önskog, Thomas. "Invariant Pseudodistances and Pseudometrics in Complex Analysis in Several Variables." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-51362.
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At present time invariant pseudodistances and pseudometrics pose an important tool in complex analysis in several variables. This thesis is mainly devoted to giving a thorough definition of these objects and in particular to Schwarz-Pick systems such as the Carathéodory and Kobayashi pseudodistances. Most basic properties, such as continuity and boundary behaviour, of the Carathéodory and Kobayashi pseudo-distances and pseudometrics are investigated. As an application of the theory, the thesis is concluded with a proof of the biholomorphic inequivalence between the unit ball and unit polydisc in Cn.
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Gubkin, Steven A. "L2 Mergelyan Theorems in Several Complex Variables." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320.
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Bianchi, Fabrizio. "Motions of Julia sets and dynamical stability in several complex variables." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30099/document.
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Dans cette thèse, on s'intéresse aux systèmes dynamiques holomorphes dépendants de paramètres. Notre objectif est de contribuer à une théorie de la stabilité et des bifurcations en plusieurs variables complexes, généralisant celle des applications rationnelles fondées sur les travaux de Mané, Sad, Sullivan et Lyubich. Pour une famille d'applications d'allure polynomiale, on prouve l'équivalence de plusieurs notions de stabilité, entre autres une version asymptotique du mouvement holomorphe des cycles répulsifs et d'un sous-ensemble de l'ensemble de Julia de mesure pleine. Cela peut etre considéré comme une généralisation mesurable à plusieurs variables du célèbre lambda-lemme et nous permet de dégager un concept cohérent de stabilité dans ce cadre. Après avoir compris les bifurcations holomorphes, on s'intéresse à la continuité Hausdorff des ensembles de Julia. Nous relions cette propriété à l'existence de disques de Siegel dans l'ensemble de Julia, et donnons un exemple de ce phénomène. Finalement, on étudie la continuité du point de vue de l'implosion parabolique. Nous établissons un théorème de Lavaurs deux-dimensionel, ce qui nous permet d'étudier des phénomènes de discontinuité pour des perturbations d'applications tangentes à l'identitéIn this thesis we study holomorphic dynamical systems depending on parameters. Our main goal is to contribute to the establishment of a theory of stability and bifurcation in several complex variables, generalizing the one for rational maps based on the seminal works of Mané, Sad, Sullivan and Lyubich. For a family of polynomial like maps, we prove the equivalence of several notions of stability, among the others an asymptotic version of the holomorphic motion of the repelling cycles and of a full-measure subset of the Julia set. This can be seen as a measurable several variables generalization of the celebrated lambda-lemma and allows us to give a coherent definition of stability in this setting. Once holomorphic bifurcations are understood, we turn our attention to the Hausdorff continuity of Julia sets. We relate this property to the existence of Siegel discs in the Julia set, and give an example of such phenomenon. Finally, we approach the continuity from the point of view of parabolic implosion and we prove a two-dimensional Lavaurs Theorem, which allows us to study discontinuities for perturbations of maps tangent to the identity
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LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.
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The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators developed by E. Stein and A. Nagel, D.H. Phong and E. Stein. Next, in the second part, we will introduce a new method to investigate the Cauchy-Riemann equations δu = φ. The solutions are constructed via the integral representation method. Moreover, we will show that the new method here is also applied well to the complex Monge-Ampère operator (ddc)n inCn. The main point is that our method can pass some well-known results from the case of finite type to infinite type.Lo scopo di questa tesi è quello di presentare l'influenza di notazioni di " tipo'' su equazioni differenziali alle derivate parziali in più variabili complesse. Le notazioni di "tipo" qui includono il finito e il tipo di infinito, nel senso di Hormander, e D'Angelo. In particolare, nella prima parte, a condizione tipo finito, prenderemo in considerazione l'esistenza e l'unicità delle soluzioni per il problema del valore iniziale associato ai operatore calore δs+□b su varietà CR. Il tipo finito m è la condizione fondamentale per fornire stime puntuali del nucleo del calore attraverso la teoria degli operatori integrali singolari sviluppate da E. Stein e A. Nagel, D.H. Phong e E. Stein. Prossimo, nella seconda parte, introdurremo un nuovo metodo per indagare la equazioni Cauchy-Riemann δu = φ. Le soluzioni sono costruite con via metodo rappresentazione integrale. Inoltre, mostreremo che il nuovo metodo qui viene applicato anche ben al complesso operatore Monge-Ampère (ddc)n inCn. Il punto principale è che il nostro metodo può passare alcuni risultati noti dal caso di tipo finito al tipo di infinito.
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Clos, Timothy George. "Compactness of Hankel Operators with Continuous Symbols on Domains in ℂ2." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1492445282323501.
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Castillo, Andrew Z. "L^p and weighted L^2 estimates for barred derivatives in several complex variables." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004.
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Mercer, Nathan T. "Quasiconformal mappings in the complex plane." Virtual Press, 2006. http://liblink.bsu.edu/uhtbin/catkey/1348866.
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It is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quasiconformal maps are nice homeomorphisms, they might only be differentiable in the real sense almost everywhere and, surprisingly, complex differentiable nowhere. We shall rely on the work of Lehto and Virtanen as well as Shishikura in exploring these interesting complex valued functions.Department of Mathematical Sciences
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Tsang, Chiu-yin, and 曾超賢. "Fatou-Shishikura inequality." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40887777.
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Tsang, Chiu-yin. "Fatou-Shishikura inequality." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40887777.
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Guo, Yunbo. "Multi-population genetic algorithm for the mapping of landscape of complex function /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202009%20GUO.
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Persson, Håkan. "On Stein Neighborhood Bases and the Nebenhülle." Thesis, Umeå University, Mathematics and Mathematical Statistics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-31704.
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This thesis consists of three parts. The first part is a introduction to the theory of domains of holomorphy through holomorphic convexity. The second part gives a introduction to Stein neighborhood bases in Cn and presents some minor results on the Nebenhülle of a compact set in Cn. The third and final part reviews some results on the existence of Stein neighborhood bases.
Denna uppsats består av tre delar. Den första delen introducerar holomorfiområden genom teorin för konvexitet med avseende på holomorfa funktioner. Den andra delen är en introduktion till Steinomgivningsbaser i Cn och presenterar några smärre resultat rörande Nebenhüllet till en kompakt mängd i Cn. Den tredje och sista delen ger en överblick över en del resultat om existensen av Steinomgivningsbaser.
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Yang, Ronghua. "Studies on value distribution of solutions of complex linear differential equations /." Joensuu : Joensuun yliopistopaino, 2006. http://www.loc.gov/catdir/toc/fy0706/2006421381.html.
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Mayboroda, Svitlana. "The poisson problem on Lipschitz domains." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4133.
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Thesis (Ph.D.)--University of Missouri-Columbia, 2005.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (January 25, 2007) Vita. Includes bibliographical references.
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Gilder, Kye M. "Extensions and application of the modified large-sample approach for constructing confidence intervals on functions of variance components /." View online ; access limited to URI, 2003. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3115629.
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Garner, William Howard. "Iteration of the power operation." Virtual Press, 1995. http://liblink.bsu.edu/uhtbin/catkey/941367.
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This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting.Department of Mathematical Sciences
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Xiao, Jian. "Positivité en géométrie kählérienne." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM027/document.
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L’objectif de cette thèse est d’étudier divers concepts de positivité en géométrie kählerienne. En particulier,pour une variété kählerienne compacte de dimension n, nous étudions la positivité des classes transcendantes de type (1,1) et (n-1, n-1) - ces classes comprennent donc en particulier les classesde diviseurs et les classes de courbesThe goal of this thesis is to study various positivity concepts in Kähler geometry. In particular, for a compact Kähler manifold of dimension n, we study the positivity of transcendental (1,1) and (n-1, n-1) classes. These objects include the divisor classes and curve classes over smooth complex projective varieties
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Schürmann, Jörg. "Topology of singular spaces and constructible sheaves /." Basel [u.a.] : Birkhäuser, 2003. http://www.loc.gov/catdir/toc/fy0803/2003062963.html.
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Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.
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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.
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Huynh, Huy. "Estimating the maximum probability of categorical classes with applications to biological diversity measurements." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44868.
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The study of biological diversity has seen a tremendous growth over the past few decades. Among the commonly used indices capturing both the richness and evenness of a community, the Berger-Parker index, which relates to the maximum proportion of all species, is particularly effective. However, when the number of individuals and species grows without bound this index changes, and it is important to develop statistical tools to measure this change. In this thesis, we introduce two estimators for this maximum: the multinomial maximum and the length of the longest increasing subsequence. In both cases, the limiting distribution of the estimators, as the number of individuals and species simultaneously grows without bound, is obtained. Then, constructing the 95% confidence intervals for the maximum proportion helps improve the comparison of the Berger-Parker index among communities. Finally, we compare the two approaches by examining their associated bias corrected estimators and apply our results to environmental data.
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Silva, Marcos Afonso da. "Análise complexa e aplicações /." Rio Claro, 2018. http://hdl.handle.net/11449/153862.
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Orientador: Suzete Maria Silva AfonsoBanca: Eliris Cristina Rizziolli
Banca: Luciane Parron Gimenes Arantes
Resumo: O objetivo principal deste trabalho é desenvolver um estudo introdutório, porém detalhado, sobre Análise Complexa e algumas de suas aplicações. Apresentamos o corpo dos números complexos, exploramos as funções complexas de uma variável complexa, exibimos parte da teoria das funções analíticas e parte da teoria de integração complexa. Provamos importantes resultados, tais como o Teorema de Cauchy, o Teorema de Taylor, o Teorema dos Resíduos, entre outros igualmente relevantes. Como aplicação da teoria, destacamos a utilização do Teorema dos Resíduos para determinar a transformada inversa de Laplace de uma função F(s)
Abstract: The main objective of this work is to develop an introductory but detailed study on Complex Analysis and some of its applications. We present the field of the complex numbers, explore the complex functions of a complex variable, exhibit part of the theory of analytic functions, and part of the complex integration theory. We prove important results, such as Cauchy's Theorem, Taylor's Theorem, Residue Theorem, among others equally relevant. As an application of the theory, we highlight the use of the Residue Theorem to determine the inverse Laplace transform of a function F(s)
Mestre
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Ranorovelonalohotsy, Marie Brilland Yann. "Riemann hypothesis for the zeta function of a function field over a finite field." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85713.
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Pauley, Blaga Slavcheva. "Constructible circles on the unit sphere." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1675.
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In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.
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Guimar?es, Bruce Franca. "Um estudo sobre fun??es de v?rias vari?veis." UFVJM, 2017. http://acervo.ufvjm.edu.br/jspui/handle/1/1639.
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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES)
O foco do presente trabalho ? apresentar um estudo sobre fun??es reais de v?rias vari?veis reais, bem como, estudar as principais t?cnicas envolvendo esse tipo de fun??o. Conv?m destacar os conceitos de limites, derivadas parciais, m?ximos e m?nimos multiplicadores de Lagrange. Na parte final da disserta??o, apresentamos uma aplica??o na Engenharia.
Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o Matem?tica, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017.
The focus of the present work is to present a study on the real functions of several real variables, as well as to study the main techniques involving this type of function. It is worth mentioning the concepts of limits, partial derivatives, maximum and minimum and Lagrange multipliers. In the final part of the dissertation, we present an application in Engineering.
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Foo, Wei Guo. "Explicit Calculations of Siu’s Effective Termination of Kohn’s Algorithm and the Hachtroudi-Chern-Moser Tensors in CR Geometry." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS041/document.
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La première partie présente des calculs explicites de terminaison effective de l'algorithme de Kohn proposée par Siu. Dans la deuxième partie, nous étudions la géométrie des hypersurfaces réelles dans Cⁿ, et nous calculons des invariants explicites avec la méthode d'équivalences de Cartan pour déterminer les lieux CR-ombilicsThe first part of the thesis consists of calculations around Siu's effective termination of Kohn's algorithm. The second part of the thesis studies the CR real hypersurfaces in complex spaces and calculates various explicit invariants using Cartan's equivalence method to study CR-umbilical points
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Piasson, Diego. "Otimização de colunas de destilação : uma abordagem aplicada dos multiplicadores de Lagrange." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306533.
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Orientador: Sandra Augusta SantosDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho aborda a otimizacao de um processo de destilacao de uma mistura binaria em uma coluna de pratos, motivado pela destilacao do metanol no processo de produção do biodiesel. Mais especificamente, considera a minimização de uma função custo energetico envolvendo o calor do refervedor e a temperatura fornecida a carga de alimentação sujeita a restrições de equilibrio e canalizações. Esse problema foi formulado baseado no artigo de More A collection of Nonlinear Model Problems. Para a solução foi utilizada a metodologia dos multiplicadores de Lagrange delineada no Teorema de Karush-Kuhn-Tucker para otimização de problemas com restrições mistas. Os softwares Maxima e MatLab foram utilizados para a investigação numerica da solução do problema. Uma explanação do funcionamento da coluna tambem e feita, bem como a apresentação dos principais resultados envolvendo otimização, desde problemas irrestritos ate problemas com varias restrições mistas
Abstract: This work tackles the optimization of a distillation process of a binary mixture in a column with plates, which came from the methanol distillation in the production process of the biodiesel. More specifically, it considers the minimization of a cost objective function that encompass the heat rate supplied to the reboiler and the feed temperature, subject to equilibrium constraints and simple bounds. This problem was formulated based on Mor'e¿s article A collection of Nonlinear Model Problems. The Lagrange multiplier methodology was used for solve it, outlined in the Karush-Kuhn-Tucker Theorem for optimization problems with mixed constraints. The softwares Maxima and MatLab were employed for the numerical investigation of the problem solution. An explanation about the operation of the column is also included, together with the presentation of the main results encompassing optimization, from unconstrained to mixed constrained problems
Mestrado
Otimização
Mestre em Matemática
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Padua, Suzan Grazielle Benetti de. "Multiplicadores de Lagrange : aspectos geometricos e algebricos e uma aplicação em engenharia quimica na destilação do metanol." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306532.
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Orientador: Sandra Augusta SantosDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho se inicia com um breve resgate histórico da abordagem de Fermat para encontrar máximos e mínimos sem o uso de derivadas. Em termos teóricos, trás uma discussão sobre máximos e mínimos de funções em Rn, com um estudo detalhado sobre a otimizacao sem restrições, destacando a regra de Fermat e a classificacao dos pontos críticos. Trata também da otimização com restrições, por meio dos Teoremas dos Mul-tiplicadores de Lagrange para restrições de igualdade e desigualdade, e para restrições mistas, o Teorema de Karush-Kuhn-Tucker (KKT). Do ponto de vista prático, apresenta uma aplicacao envolvendo uma coluna de destilacao do metanol vinculada 'a produção do biodiesel, com a otimização da proporção de metanol destilado
Abstract: This work begins with a brief historical overview of Fermat¿s method to find maxima and minima without derivatives. In theoretical terms, the elements concerning maximum and minimum of functions of n variables are discussed, together with a detailed study of unconstrained optimization, focusing on the Fermat¿s rule and the classification of critical points. Constrained optimization is also analyzed, by means of the Lagrange Multilplier Theorem for equality constrained problems, and the Karush-Kuhn-Tucker (KKT) Theorem for mixed constrained optimization. In practical terms, an application concerning a distillation column of methanol associated to the biodiesel production is presented, with the optimization of the proportion of methanol in the amount of material that is removed from the top of the column
Mestrado
Otimização
Mestre em Matemática
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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.
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Casseli, Irène. "Eléments sur la transformée de Berezin et sur les opérateurs de Toeplitz dans des espaces de fonctions polyanalytiques." Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0578.
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Les fonctions polyanalytiques entières généralisent les fonctions entières dans la mesure où elles sont les solutions sur le plan complexe \mathbb{C} de l'équation de Cauchy-Riemann à l'ordre n, de la forme { partial} nf / \partial \overline{z} n = 0. Un espace de Fock polyanalytique F2 {\alpha,n} est, par analogie avec le cas classique, le sous-espace fermé de l'espace de Hilbert L^2 (\mathbb{C},d\mu \alpha), où \mu \alpha est une mesure de probabilité gaussienne sur \mathbb{C} de paramètre alpha>0, formé des fonctions polyanalytiques entières d'ordre n. L'objet de cette thèses est l'étude d'éléments classiques de la théorie des opérateurs tels que la transformée de Berezin et les opérateurs de Toeplitz dans le cadre particulier des espaces de Fock polyanalytiques. Dans ce manuscrit, il est montré en particulier que les points fixes de la transformée de Berezin qui appartiennent aux espaces de Lebesgue sont les fonctions nulles ou éventuellement constantes. Concernant les opérateurs de Toeplitz, le problème de Sarason est étudié. Etant donné une fonction f, l'opérateur de Toeplitz de symbole f est formellement défini par T {alpha,n} f(h)=P {alpha,n}(f h), où P {alpha,n} est la projection orthogonale de L^2(\mathbb{C},d\mu {alpha}) sur F^2 {alpha,n}. Le problème de Sarason consiste à donner une condition nécessaire et suffisante sur f et g pour que le produit d'opérateurs de symboles f et bar g soit continuEntire polyanalytic functions generalize entire functions in that they are solutions of "Cauchy-Riemann equations of order n, of the form {\partial}^n f / \partial \overline{z}^n = 0, over the whole complex plane \mathbb{C}. Polyanalytic Fock space F^2_{\alpha,n} is, by analogy with the classical case, the closed subspace of the Hilbert space L^2(\mathbb{C},d\mu_\alpha), where \mu_\alpha is a Gaussian probability measure over \mathbb{C} with weight \alpha>0, of polyentire functions of order n. The aim of this PhD thesis is the study of classical objects of operator theory such that the Berezin transform and Toeplitz operators in the particular case of polyanalytic Fock spaces. In this written, it is shown among other results, that the L^p fixed points of the Berezin transform are constant functions. Concerning Toeplitz operators, the Sarason problem is studied. Given a function f, the Toeplitz operator with symbol f is formally defined by T^n_f(h)=P_{F^2_n}(f h), where P_{F^2_n} is the orthogonal projection from L^2(\mathbb{C},d\mu) on to F^2_n. The so-called Sarason's problem consists in finding necessary and sufficient conditions on the symbols f and g for the Toeplitz product with symbols f and \bar g to be bounded in the Fock space
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Orsoni, Marcu-Antone. "Espaces de fonctions holomorphes et espace atteignable de l'équation de la chaleur." Thesis, Bordeaux, 2021. http://www.theses.fr/2021BORD0011.
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Cette thèse est consacrée à la description de l'espace atteignable de l'équation de la chaleur à l'aide de méthodes de l'analyse complexe moderne. Ce problème central de la théorie du contrôle est vieux de 50 ans et a captivé de nombreuses recherches depuis les travaux pionniers de Fattorini et Russel en 1971. Dans ce travail, on s'intéresse à l'équation de la chaleur 1-D sur un segment avec contrôle de Dirichlet au bord.Dans une première partie, on démontre à l'aide d'un théorème de type Paley-Wiener que l'espace atteignable est égal à la somme de deux espaces de Bergman, puis qu'il contient un espace de Smirnov-Zygmund en étudiant la régularité de la transformée de Cauchy.Dans une deuxième partie, en utilisant des méthodes de noyaux reproduisants et de d-bar, on résout le problème de séparation de singularités (problème de type Cousin) pour l'espace de Bergman dans plusieurs configurations. On en déduit ainsi une caractérisation définitive de l'espace atteignable comme espace de Bergman sur un carré.Enfin, la dernière partie est consacrée à l'équation de chaleur avec un potentiel quadratique et à son espace atteignableThis thesis is devoted to the description of the reachable space of the heat equation using methods of modern complex analysis. This central problem in control theory is about 50 years old and has captivated a lot of research efforts since the pioneering work of Fattorini and Russell in 1971. In this work, we are interested in the 1-D heat equation on a segment with Dirichlet boundary control.In the first part, using a Paley-Wiener theorem we prove that the reachable space is the sum of two Bergman spaces, then that it contains a Smirnov-Zygmund space by studying the regularity of the Cauchy transform.In a second part, using reproducing kernels and d-bar methods, we solve the problem of separation of singularities (Cousin-type problem) for the Bergman space in several configurations. This enables us to deduce a definitive characterization of the reachable space as the Bergman space on a square.Finally, the last part is devoted to the heat equation with a quadratic potential and its reachable space
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Célariès, Benjamin. "Opérateurs et semi-groupes d’opérateurs sur des espaces de fonctions holomorphes : Applications à la théorie de l’universalité." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1077/document.
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Les travaux de cette thèse relèvent du domaine de la théorie des opérateurs, et se situent à l'interface de l'analyse complexe, de la théorie des semi-groupes et de la théorie de l'universalité. Le premier résultat principal de cette thèse relève de l'étude des opérateurs de composition sur des espaces de fonctions holomorphes : nous déterminons le spectre d'un opérateur de composition par un symbole de Koenigs sur l'espace des fonctions holomorphes sur le disque unité, et en déduisons des informations sur la forme générale du spectre des opérateurs de composition par un symbole de Koenigs sur des espaces de Banach de fonctions holomorphes. L'outil principal que nous développons pour notre étude est une description des projections spectrales associées à ces opérateurs. Le second résultat principal de cette thèse relève de la théorie de l'universalité : nous étendons aux semi-groupes d'opérateurs la notion d'opérateur universel, et établissons l'existence d'un semi-groupe universel pour les semi-groupes quasi-contractifs en exhibant un semi-groupe sur un espace de fonctions holomorphes. Nous élargissons ensuite ce résultats aux semi-groupes d'opérateurs concavesThe works in this thesis address topics from operator theory and involves ideas and notions arising from complex analysis, the theory of operator semigroups and the theory of universality. The first main result of this thesis relates to the study of composition operators on spaces of holomorphic functions: we compute the spectrum of an operator of composition by a Koenigs's symbol acting on the space of holomorphic functions on the open unit disk, and derive from it the general description of the spectrum of composition operators on Banach spaces of holomorphic functions. The key tool we develop in this study is a description of spectral projections associated with such operators.The second main result of this thesis relates to the thoery of universality: we extend to operator semigroups the notion of universality. Then, we prove the existence of a universal semigroup for quasi-contractive operators semigroups. We then show a similar result for concave semigroups
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Betah, Mohamed Haye. "Un théorème de Gallagher pour la fonction de Möbius." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0461/document.
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La fonction de Möbius est définie par$$\mu(n)= \begin{cases} 1 & \textit{si $n=1$},\\ (-1)^k& \textit{si n est le produit de k nombres premiers distincts,}\\ 0 & \textit{si n contient un facteur carré. } \end{cases}$$Nous avons démontré que pour $x \ge \exp( 10^9) $ et $h=x^{1-\frac{1}{16000}}$, il existe dans chaque intervalle $[x-h,x]$ des entiers $n_1$ avec $\mu(n_1)=1$ et des entiers $n_2$ avec $\mu(n_2)=-1$.\\Ce résultat est une conséquence d'un résultat plus général.\\Pour $x \ge \exp(4\times 10^6)$, $\frac{1}{\sqrt{\log x}} \le \theta \le \frac{1}{2000}$, $h=x^{1-\theta}$ et $Q=(x/h)^{\frac{1}{20}}$, nous avons \\$$\sum_{q \leq Q} \log(Q/q)\sum_{\chi mod q}^*\left| \sum_{x.-h\le n \le x} \mu(n) \chi(n) \right| \leq 10^{20} h \theta \log(x) \exp( \frac{-1}{300 \theta}); $$la somme $\sum^*$ portant sur les caractères primitifs sauf l'éventuel caractère exceptionnel.\\Et en particulier pour $x \ge \exp( 10^9)$,$$ \left | \sum_{x.-x^{1-\frac{1}{16000}}\le n \le x} \mu(n) \right | \le \frac{1}{100} x^{1-\frac{1}{16000}}.\\$$The Möbius function is defined by$$\mu(n)= \begin{cases} 1 & \textit{if $n=1$},\\ (-1)^k& \textit{if n is a product of k distinct prime numbers,}\\ 0 & \textit{if n contains a square factor. } \end{cases}$$We demonstrate that for $x \ge \exp( 10^9) $ and $h=x^{1-\frac{1}{16000}}$, it exists in each interval $[x-h,x]$ integers $n_1$ with $\mu(n_1)=1$ and integers $n_2$ with $\mu(n_2)=-1$.\\This result is a consequence of a more general result. \\For $x \ge \exp(4\times 10^6)$, $\frac{1}{\sqrt{\log x}} \le \theta \le \frac{1}{2000}$, $h=x^{1-\theta}$ et $Q=(x/h)^{\frac{1}{20}}$, we have \\ $$\sum_{q \leq Q} \log(Q/q)\sum_{\chi mod q}^*\left| \sum_{x-h \le n \le x} \mu(n) \chi(n) \right| \leq 10^{20} h \theta \log(x) \exp( \frac{-1}{300 \theta}); $$the sum $\sum^*$ relating to primitive characters except for possible exceptional character.\\And in particular for $x \ge \exp( 10^9)$,$$\left | \sum_{x-.x^{1-\frac{1}{16000}}\le n \le x} \mu(n) \right | \le \frac{1}{100} x^{1-\frac{1}{16000}}.$$
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Chaabi, Slah. "Analyse complexe et problèmes de Dirichlet dans le plan : équation de Weinstein et autres conductivités non-bornées." Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00916049.
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L'équation de Weinstein á coefficients complexes est une équation régissant les Potentiels á Symétrie Axiale (PSA) qui s'écrit $L_m[u]=\Delta u+\left(m/x\right)\d_x u =0$, oú $m\in\C$. Cette équation intervient notamment pour la modélisation du bord du plasma dans un Tokamak pour $m=-1$, ou encore elle est, lorsque $m=1$, appelée équation de Ernst linéarisée (équation permettant de donner explicitement des solutions aux équations d'Einstein). Ici, on généralise des résultats connus pour $m\in \R$ au cas $m\in\C$ (on donne des expressions explicites de solutions fondamentales aux opérateurs de Weinstein et leurs estimations au voisinage des singularités, puis on démontre une formule de Green pour les PSA dans le demi-plan droit $\H^+$ pour Re $m< 1$). On prouve un nouveau théoréme de décomposition des PSA dans des domaines annulaires quelconques pour $m\in\C$ et dans une géométrie annulaire particuliére faisant intervenir les coordonnées bipolaires, on prouve toujours pour $m\in\C$ qu'une famille de solutions des PSA en termes de fonctions de Legendre Associées de premiére et seconde espéce forme une famille compléte (par une méthode de quasi-séparabilité des variables et par une analyse de Fourier) permettant d'exprimer les PSA sous forme de série et lorsque $m\in \R$, on montre que cette famille est même une base de Riesz dans certains anneaux á bord circulaire non concentrique. Dans une deuxiéme partie, par une méthode qui est due á A. S. Fokas, on donne, sous forme intégrale explicite, des formules des PSA dans un domaine circulaire du demi-plan droit $\H^+$, dans le cas oú le paramétre $m$ est un entier relatif. Ces représentations sont obtenues par la résolution d'un probléme de Riemann-Hilbert sur le plan complexe ou sur une surface de Riemann á deux feuillets selon la parité du coefficient $m$. Ces formules font intervenir de façon explicites les données Dirichlet et Neumann des PSA. On montre aussi que cette méthode s'applique á tous les domaines simlement connexe de $\H^+$ á bord régulier. Dans la derniére partie, on étudie une classe de fonctions qui englobe les PSA, ce sont les fonctions pseudo-holomorphes, {\it i. e.} les solutions de l'équation $\bar\d w=\alpha\overline{w}$. avec $\alpha\in L^r$, $2\leq r<\infty$. Un résultat qui semble être le tout premier de son genre a été obtenu, c'est une extension de la régularité du principe de similarité (décomposition des fonction pseudo-holomorphe sous la forme $e^s F$ sous certaines hypothéses de régularités et oú $F$ est une fonction holomorphe) et une réciproque de ce principe qui conduit á un paramétrage analytique de cette classe de fonctions dans le cas critique $r=2$. Puis en utilisant la connexion entre les fonctions pseudo-holomorphes et les solutions de l'équation de Beltrami conjuguée, on résoud un probléme de Dirichlet á données $L^p$ pondérées sur des domaines lisses pour des équations du type conductivité á coefficient dont le log appartient á l'espace de Sobolev $W^{1,2}$.
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Cruz, Carla Maria. "Numerical and combinatorial applications of generalized Appell polynomials." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13962.
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Doutoramento em MatemáticaThis thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the construction of new bases for the space of homogeneous holomorphic polynomials whose elements are all isomorphic to the integer powers of the complex variable. For this reason, such polynomials are called pseudo-complex powers (PCP). Different variants of them are subject of a detailed investigation. Special attention is paid to the numerical aspects of PCP. An efficient algorithm based on complex arithmetic is proposed for their implementation. In this context a brief survey on numerical methods for inverting Vandermonde matrices is presented and a modified algorithm is proposed which illustrates advantages of a special type of PCP. Finally, combinatorial applications of generalized Appell polynomials are emphasized. The explicit expression of the coefficients of a particular type of Appell polynomials and their relation to a Pascal simplex with hypercomplex entries are derived. The comparison of two types of 3D Appell polynomials leads to the detection of new trigonometric summation formulas and combinatorial identities of Riordan-Sofo type characterized by their expression in terms of central binomial coefficients.
Esta tese estuda propriedades e aplicações de diferentes polinómios de Appell generalizados no contexto da análise de Clifford. Exemplificando uma transformação realizada por polinómios de Appell generalizados, é introduzida uma transformação análoga à transformação de Joukowski complexa de ordem dois. A análise de um n- simplex de Pascal com entradas hipercomplexas permite sublinhar a relevância combinatória de polinómios hipercomplexos de Appell. O conceito de variáveis totalmente regulares e a sua relação com polinómios de Appell generalizados conduz à construção de novas bases para o espaço dos polinómios homogéneos holomorfos cujos elementos são todos isomorfos às potências inteiras da variável complexa. Por este motivo, tais polinómios são chamados de potências pseudo-complexas (PCP). Diferentes variantes de PCP são objeto de uma investigação detalhada. É dada especial atenção aos aspectos numéricos de PCP. Um algoritmo eficiente baseado em aritmética complexa é proposto para a sua implementação. Neste contexto, é apresentado um breve resumo de métodos numéricos para inverter matrizes de Vandermonde e é proposto um algoritmo modificado para ilustrar as vantagens de um tipo especial de PCP. Finalmente, são enfatizadas aplicações combinatórias de polinómios de Appell generalizados. A expressão explícita dos coeficientes de um tipo particular de polinómios de Appell e a sua relação com um simplex de Pascal com entradas hipercomplexas são obtidas. A comparação de dois tipos de polinómios de Appell tridimensionais leva à deteção de novas fórmulas envolvendo somas trigonométricas e de identidades combinatórias do tipo de Riordan – Sofo, caracterizadas pela sua expressão em termos de coeficientes binomiais centrais.
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Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.
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Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.
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Tavares, Lucas Alves. "O envolvimento da proteína adaptadora 1 (AP-1) no mecanismo de regulação negativa do receptor CD4 por Nef de HIV-1." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/17/17136/tde-06012017-113215/.
Full textAbstract:
O Vírus da Imunodeficiência Humana (HIV) é o agente etiológico da Síndrome da Imunodeficiência Adquirida (AIDS). A AIDS é uma doença de distribuição mundial, e estima-se que existam atualmente pelo menos 36,9 milhões de pessoas infectadas com o vírus. Durante o seu ciclo replicativo, o HIV promove diversas alterações na fisiologia da célula hospedeira a fim de promover sua sobrevivência e potencializar a replicação. A rápida progressão da infecção pelo HIV-1 em humanos e em modelos animais está intimamente ligada à função da proteína acessória Nef. Dentre as diversas ações de Nef está a regulação negativa de proteínas importantes na resposta imunológica, como o receptor CD4. Sabe-se que esta ação resulta da indução da degradação de CD4 em lisossomos, mas os mecanismos moleculares envolvidos ainda são totalmente elucidados. Nef forma um complexo tripartite com a cauda citosólica de CD4 e a proteína adaptadora 2 (AP-2), em vesículas revestidas por clatrina nascentes, induzindo a internalização e degradação lisossomal de CD4. Pesquisas anteriores demonstraram que o direcionamento de CD4 aos lisossomos por Nef envolve a entrada do receptor na via dos corpos multivesiculares (MVBs), por um mecanismo atípico, pois, embora não necessite da ubiquitinação de carga, depende da ação de proteínas que compõem os ESCRTs (Endosomal Sorting Complexes Required for Transport) e da ação de Alix, uma proteína acessória da maquinaria ESCRT. Já foi reportado que Nef interage com subunidades dos complexos AP-1, AP-2, AP-3 e Nef não parece interagir com subunidades de AP-4 e AP-5. Entretanto, o papel da interação de Nef com AP-1 e AP-3 na regulação negativa de CD4 ainda não está totalmente elucidado. Ademais, AP-1, AP-2 e AP-3 são potencialmente heterogêneos devido à existência de isoformas múltiplas das subunidades codificadas por diferentes genes. Todavia, existem poucos estudos para demonstrar se as diferentes combinações de isoformas dos APs são formadas e se possuem propriedades funcionais distintas. O presente trabalho procurou identificar e caracterizar fatores celulares envolvidos na regulação do tráfego intracelular de proteínas no processo de regulação negativa de CD4 induzido por Nef. Mais especificamente, este estudo buscou caracterizar a participação do complexo AP-1 na modulação negativa de CD4 por Nef de HIV-1, através do estudo funcional das duas isoformas de ?-adaptina, subunidades de AP-1. Utilizando a técnica de Pull-down demonstramos que Nef é capaz de interagir com ?2. Além disso, nossos dados de Imunoblot indicaram que a proteína ?2-adaptina, e não ?1-adaptina, é necessária no processo de degradação lisossomal de CD4 por Nef e que esta participação é conservada para degradação de CD4 por Nef de diferentes cepas virais. Ademais, por citometria de fluxo, o silenciamento de ?2, e não de ?1, compromete a diminuição dos níveis de CD4 por Nef da membrana plasmática. A análise por imunofluorêsncia indireta também revelou que a diminuição dos níveis de ?2 impede a redistribuição de CD4 por Nef para regiões perinucleares, acarretando no acúmulo de CD4, retirados por Nef da membrana plasmática, em endossomos primários. A depleção de ?1A, outra subunidade de AP-1, acarretou na diminuição dos níveis celulares de ?2 e ?1, bem como, no comprometimento da eficiente degradação de CD4 por Nef. Além disso, foi possível observar que, ao perturbar a maquinaria ESCRT via super-expressão de HRS (uma subunidade do complexo ESCRT-0), ocorreu um acumulo de ?2 em endossomos dilatados contendo HRS-GFP, nos quais também detectou-se CD4 que foi internalizado por Nef. Em conjunto, os resultados indicam que ?2-adaptina é uma importante molécula para o direcionamento de CD4 por Nef para a via ESCRT/MVB, mostrando ser uma proteína relevante no sistema endo-lisossomal. Ademais, os resultados indicaram que as isoformas ?-adaptinas não só possuem funções distintas, mas também parecem compor complexos AP-1 com diferentes funções celulares, já que apenas a variante AP-1 contendo ?2, mas não ?1, participa da regulação negativa de CD4 por Nef. Estes estudos contribuem para o melhor entendimento dos mecanismos moleculares envolvidos na atividade de Nef, que poderão também ajudar na melhor compreensão da patogênese do HIV e da síndrome relacionada. Em adição, este trabalho contribui para o entendimento de processos fundamentais da regulação do tráfego de proteínas transmembrana no sistema endo-lisossomal.The Human Immunodeficiency Virus (HIV) is the etiologic agent of Acquired Immunodeficiency Syndrome (AIDS). AIDS is a disease which has a global distribution, and it is estimated that there are currently at least 36.9 million people infected with the virus. During the replication cycle, HIV promotes several changes in the physiology of the host cell to promote their survival and enhance replication. The fast progression of HIV-1 in humans and animal models is closely linked to the function of an accessory protein Nef. Among several actions of Nef, one is the most important is the down-regulation of proteins from the immune response, such as the CD4 receptor. It is known that this action causes CD4 degradation in lysosome, but the molecular mechanisms are still incompletely understood. Nef forms a tripartite complex with the cytosolic tail of the CD4 and adapter protein 2 (AP-2) in clathrin-coated vesicles, inducing CD4 internalization and lysosome degradation. Previous research has demonstrated that CD4 target to lysosomes by Nef involves targeting of this receptor to multivesicular bodies (MVBs) pathway by an atypical mechanism because, although not need charging ubiquitination, depends on the proteins from ESCRTs (Endosomal Sorting Complexes Required for Transport) machinery and the action of Alix, an accessory protein ESCRT machinery. It has been reported that Nef interacts with subunits of AP- 1, AP-2, AP-3 complexes and Nef does not appear to interact with AP-4 and AP-5 subunits. However, the role of Nef interaction with AP-1 or AP-3 in CD4 down-regulation is poorly understood. Furthermore, AP-1, AP-2 and AP-3 are potentially heterogeneous due to the existence of multiple subunits isoforms encoded by different genes. However, there are few studies to demonstrate if the different combinations of APs isoforms are form and if they have distinct functional properties. This study aim to identify and characterize cellular factors involved on CD4 down-modulation induced by Nef from HIV-1. More specifically, this study aimed to characterize the involvement of AP-1 complex in the down-regulation of CD4 by Nef HIV-1 through the functional study of the two isoforms of ?-adaptins, AP-1 subunits. By pull-down technique, we showed that Nef is able to interact with ?2. In addition, our data from immunoblots indicated that ?2- adaptin, not ?1-adaptin, is required in Nef-mediated targeting of CD4 to lysosomes and the ?2 participation in this process is conserved by Nef from different viral strains. Furthermore, by flow cytometry assay, ?2 depletion, but not ?1 depletion, compromises the reduction of surface CD4 levels induced by Nef. Immunofluorescence microscopy analysis also revealed that ?2 depletion impairs the redistribution of CD4 by Nef to juxtanuclear region, resulting in CD4 accumulation in primary endosomes. Knockdown of ?1A, another subunit of AP-1, resulted in decreased cellular levels of ?1 and ?2 and, compromising the efficient CD4 degradation by Nef. Moreover, upon artificially stabilizing ESCRT-I in early endosomes, via overexpression of HRS, internalized CD4 accumulates in enlarged HRS-GFP positive endosomes, where co-localize with ?2. Together, the results indicate that ?2-adaptin is a molecule that is essential for CD4 targeting by Nef to ESCRT/MVB pathway, being an important protein in the endo-lysosomal system. Furthermore, the results indicate that ?-adaptins isoforms not only have different functions, but also seem to compose AP-1 complex with distinct cell functions, and only the AP-1 variant comprising ?2, but not ?1, acts in the CD4 down-regulation induced by Nef. These studies contribute to a better understanding on the molecular mechanisms involved in Nef activities, which may also help to improve the understanding of the HIV pathogenesis and the related syndrome. In addition, this work contributes with the understanding of primordial process regulation on intracellular trafficking of transmembrane proteins.
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Biswas, Chandan. "Analytic Continuation In Several Complex Variables." Thesis, 2012. https://etd.iisc.ac.in/handle/2005/2331.
Full textAbstract:
We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study is radically different from that of domains in C by discussing some examples of special types of domains in Cn , n ≥2, such that every function holomorphic on them extends to strictly larger domains. Given a domain in Cn , n ≥ 2, we wish to construct the maximal domain of existence for the holomorphic functions defined on the given domain. This leads to Thullen’s construction of a domain (not necessarily in Cn)spread overCn, the so-called envelope of holomorphy, which fulfills our criteria. Unfortunately this turns out to beavery abstract space, far from giving us sense in general howa domain sitting in Cn can be constructed which is strictly larger than the given domain and such that all the holomorphic functions defined on the given domain extend to it. But with the help of this abstract approach we can give a characterization of the domains of holomorphyin Cn , n ≥ 2.
The aforementioned characterization is as follows: adomain in Cn is a domain of holomorphy if and only if it is holomorphically convex. However, holomorphic convexity is a very difficult property to check. This calls for other (equivalent) criteria for a domain in Cn , n ≥ 2, to be a domain of holomorphy. We survey these criteria. The proof of the equivalence of several of these criteria are very technical – requiring methods coming from partial differential equations. We provide those proofs that rely on the first part of our survey: namely, on analytic continuation theorems.
If a domain Ω Cn , n ≥ 2, is not a domain of holomorphy, we would still like to explicitly describe a domain strictly larger than Ω to which all functions holomorphic on Ω continue analytically. Aspects of Thullen’s approach are also useful in the quest to construct an explicit strictly larger domain in Cn with the property stated above. The tool used most often in such constructions s called “Kontinuitatssatz”. It has been invoked, without a clear statement, in many works on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We provide a precise statement of this folk Kontinuitatssatz and give a proof of it.