To see the other types of publications on this topic, follow the link: Generalised Integrals.
Dissertations / Theses on the topic 'Generalised Integrals'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Generalised Integrals.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Feigin, Mikhail V. "Rings of quantum integrals for generalised Calogero-Moser problems." Thesis, Loughborough University, 2002. https://dspace.lboro.ac.uk/2134/35847.
Full textAbstract:
The rings of quantum integrals for generalised Calogero-Moser problems are studied in the special case when all the parameters are integers. The problem is reduced to the description of the rings of polynomials satisfying a certain quasi-invariance property (quasi-invariants). The quasi-invariants of dihedral groups are fully described. It is shown that they form a free module over invariants generated by m-harmonic polynomials. The m-harmonic polynomials for general Coxeter group are introduced and investigated. For the non-Coxeter generalisations of Calogero-Moser problems related to the systems An(m), Cn+1(m, l), the rings of quantum integrals are considered. The Poincare series for the quasi-invariants of two-dimensional deformations are computed. It is shown that the rings of quasi-invariants are Gorenstein like in the Coxeter case.
2
Bär, Christian. "Renormalized integrals and a path integral formula for the heat kernel on a manifold." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6005/.
Full textAbstract:
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.
3
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.
Full textAbstract:
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.
4
Taylor, C. James. "Generalised proportional-integral-plus control." Thesis, Lancaster University, 1996. http://eprints.lancs.ac.uk/49452/.
Full textAbstract:
This thesis is concerned with the True Digital Control (TDC) design philosophy and its practical embodiment in the non-minimal state space (NMSS) approach to control design, for systems described by discrete time transfer function models in the backward shift operator. This yields Proportional-Integral-Plus (PIP) controllers that are particularly easy to implement in practice, since the state variables are defined only in terms of the sampled input and output signals. The basic PIP algorithm is extended and enhanced in various ways to form a more sophisticated Generalised PIP controller. This includes an investigation into the importance of structure in PIP control design, the development of a command input anticipation technique and the introduction of two stochastic formulations of the problem, namely Kalman Filtering and risk sensitive optimal control. Finally, the thesis discusses the relationship between PIP and predictive control, in particular Generalised Predictive Control (GPC) and the Smith Predictor. The power of the approach is illustrated by the design of PIP controllers for a number of difficult applications also described in the thesis, including the control of a large horticultural greenhouse at Silsoe Research Institute; the control of carbon dioxide in crop growth experiments; the control of a Statistical Traffic Model simulation of interurban traffic networks; and, finally, the control of the multivariable Shell heavy oil fractionator simulation.
5
Katugampola, Don Udita Nalin. "ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/dissertations/387.
Full textAbstract:
In this paper we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin transforms of such generalized fractional operators which are important in solving fractional differential equations.
6
Delaney, Christopher. "Generalized Differential and Integral Categories." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37136.
Full textAbstract:
This paper provides two generalizations of differential and integral categories: Leibniz and generalized Rota-Baxter categories, which capture certain algebraic structures, and q-categories, which capture structures of quantum calculus. In the search for new examples of differential and integral categories, it was observed that many structures were not quite examples but satisfied certain properties and not others. This leads us to the definition of Leibniz, Rota-Baxter and proto-FTC categories. In generalizing Rota-Baxter categories further to an arbitrary weight, we show that we recapture Ribenboim's generalized power series as a monad on vector spaces with a generalized integral transformation. This also subsumes the renormalization operator on Laurent series, which has applications in the quantum realm. Finally, we define quantum differential and quantum integral categories, show that they recapture the usual notions of quantum calculus on polynomials, and construct a new example to indicate their potential usefulness outside of that specific setting
7
Tang, W. "A generalized approach for transforming domain integrals into boundary integrals in boundary element methods." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378981.
Full text
8
Dunn, Thomas Boyd. "Integral Closure and the Generalized Multiplicity Sequence." Diss., North Dakota State University, 2015. https://hdl.handle.net/10365/27935.
Full text
9
Wilson, Julia Carol. "Generalized Dedekind sums and their connection with Franel integrals." Thesis, University of York, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358339.
Full text
10
Wilson, Michael. "Integral modelling of jets of variable composition in generalised crossflows." Thesis, University of Bath, 1986. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382563.
Full text
11
PLAKOO, ADUAYI JUSTIN E. "Jacobiennes generalisees reelles et systemes integrables." Toulouse 3, 1998. http://www.theses.fr/1998TOU30102.
Full textAbstract:
Parmi les varietes algebriques qui entrent en jeu dans l'etude des systemes hamiltoniens algebriquement completement integrables, on trouve les varietes abeliennes dont les jacobiennes de courbes lisses et les varietes semi-abeliennes dont les jacobiennes generalisees de courbes singulieres. Contrairement aux jacobiennes usuelles des courbes lisses, les jacobiennes generalisees des courbes singulieres sont peu connues des specialistes de systemes integrables. Cette these a pour objet l'etude des differentes jacobiennes generalisees et des structures reelles dont elles peuvent etre munies. Nos resultats principaux sont de deux types : nous donnons d'abord une caracterisation des parties reelles des jacobiennes generalisees et nous appliquons ensuite ces resultats a l'etude de la topologie des systemes associes. Nous considerons dans ce travail les courbes singulieres ayant uniquement des points doubles ordinaires a tangentes distinctes et les courbes singulieres definies par une courbe lisse complete et irreductible et un module de degre superieur ou egal a deux. Nous prouvons que la jacobienne generalisee de la courbe singuliere a points doubles ordinaires est une extension de la jacobienne usuelle de sa normalisee par le groupe multiplicatif. Il s'agit d'une variete semi-abelienne. Il en est de meme pour la jacobienne generalisee d'une courbe singuliere definie par un module simple (dont tous les coefficients sont egaux a 1). A partir de nos resultats ainsi que des proprietes bien connues de la jacobienne usuelle, nous fournissons des outils pour denombrer les tores et les cylindres de liouville des systemes qui se linearisent sur une jacobienne. Nous donnons des resultats concrets dans le cas des systemes de jacobi-moser-mumford. Une illustration de cette methode est donnee par l'etude de la topologie complete du systeme de gelfand-dikii a deux degres de liberte ainsi que les bifurcations. Pour terminer, nous avons constitue un catalogue de systemes hamiltoniens qui se linearisent sur une jacobienne generalisee. Cette liste non exhaustive contient entre autre le systeme bien connu de la toupie de lagrange. Comme application des resultats sur les jacobiennes generalisees reelles, nous proposons une nouvelle methode donnant la topologie de ce systeme.
12
Conway, Mark. "The Generalized Riemann Integral in R2." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142.
Full text
13
McAnally, Morgan Ashley. "Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7423.
Full textAbstract:
We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable.
We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order to construct integrable couplings. An enlarged spectral problem is presented starting from a generalization of the D-Kaup-Newell spectral problem. Then the enlarged zero curvature equations are solved from a series of Lax pairs producing the desired integrable couplings. A reduction is made of the original enlarged spectral problem generating a second integrable coupling system. Next, we discuss how to compute bilinear forms that are symmetric, ad-invariant, and non-degenerate on the given non-semisimple matrix Lie algebra to employ the variational identity. The variational identity is applied to the original integrable couplings of a generalized D-Kaup-Newell soliton hierarchy to furnish its Hamiltonian structures. Then we apply the variational identity to the reduced integrable couplings. The reduced coupling system has a bi-Hamiltonian structure. Both integrable coupling systems retain the properties of infinitely many commuting high-order symmetries and conserved densities of their original subsystems and, again, are Liouville integrable.
In order to find solutions to a generalized D-Kaup-Newell integrable coupling system, a theory of Darboux transformations on integrable couplings is formulated. The theory pertains to a spectral problem where the spectral matrix is a polynomial in lambda of any order. An application to a generalized D-Kaup-Newell integrable couplings system is worked out, along with an explicit formula for the associated Bäcklund transformation. Precise one-soliton-like solutions are given for the m-th order generalized D-Kaup-Newell integrable coupling system.
14
Kerr, Fiona Helen. "Fractional powers of integral transforms for classical and generalized functions." Thesis, University of Strathclyde, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303285.
Full text
15
Torgerson, Mark Dolan 1964. "A classification of the rational integrable generalized standard maps." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282501.
Full textAbstract:
This dissertation examines the integrability of certain planar maps. An integral of a planar map is a real-valued function that remains invariant under composition with the map. In particular we classify the generalized standard maps, maps of the form φ(x, y) = (f(x)-y, x), that have a polynomial integral and those that have a rational integral. Chapter 1 brings to light the pertinent definitions. Here we show numerical examples of integrability, non-integrability and questionable integrability. Chapter 1 concludes with a discourse on linear maps, giving a classification of those with a polynomial or rational integral. The meat of this work lies in Chapter 2, which contains the classification of the generalized standard maps. Here we give a short list of the maps that have a polynomial integral as well as an integral for each case. Finally we show that if a generalized standard map has a rational integral then it has a polynomial integral. Deciding if a planar map is integrable or deciding what family the integral lies in is one of the difficult tasks assumed by the field of dynamical systems. Here we have approached the integrability question from an algebraic viewpoint. Some attempt has been made to make the proofs simple yet complete, without using the heavy-duty analytical tools that can often be found in the analysis of a dynamical systems.
16
Sakamoto, Junichi. "Integrable deformations of string sigma models and generalized supergravity." Kyoto University, 2019. http://hdl.handle.net/2433/242599.
Full text
17
Sanja, Kostadinova. "Some classes of integral transforms on distribution spaces and generalized asymptotics." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2014. https://www.cris.uns.ac.rs/record.jsf?recordId=87772&source=NDLTD&language=en.
Full textAbstract:
In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space K1(ℝn) and the topological tensor product K1(ℝn) ⊗ U(ℂn), where U(ℂn) is the space of entirerapidly decreasing functions in any horizontal band of ℂn. We then use such continuity results to develop a framework for the STFT on K'1(ℝn). Also, we devote one section to the characterization of K’1(ℝn) and related spaces via modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.Part of the thesis is dedicated to the ridgelet and the Radon transform. We define and study the ridgelet transform of (Lizorkin) distributions and we show that the ridgelet transform and the ridgelet synthesis operator can be extended as continuous mappings Rψ : S’0(ℝn) → S’(Yn+1) and Rtψ: S’(Yn+1) → S’0(ℝn). We then use our results to develop a distributional framework for the ridgelet transform that is, we treat the ridgelet transform on S’0(ℝn) via a duality approach. Then, the continuity theorems for the ridgelet transform are applied to discuss the continuity of the Radon transform on these spaces and their duals. Finally, we deal with some Abelian and Tauberian theorems relating the quasiasymptotic behavior of distributions with the quasiasymptotics of the its Radon and ridgelet transform.The last chapter is dedicated to the MRA of M-exponential distributions. We study the convergence of multiresolution expansions in various test function and distribution spaces and we discuss the pointwise convergence of multiresolution expansions to the distributional point values of a distribution. We also provide a characterization of the quasiasymptotic behavior in terms of multiresolution expansions and give an MRA sufficient condition for the existence of α-density points of positive measures.U ovoj doktorskoj disertaciji razmotreno je nekoliko integralnih transformacija. Prva je short time Fourier transform (STFT). Date su i dokazane teoreme o neprekidnosti STFT i njena sinteza na prostoru test funkcije K1(ℝn) i na prostoru K1(ℝn) ⊗ U(ℂn), gde je U(ℂn) prostor od celih brzo opadajućih funkcija u proizvoljnom horizontalnom opsegu na ℂn. Onda, ovi rezultati neprekidnosti su iskorišteni za razvijanje teorije STFT na prostoru K’1(ℝn). Jedno poglavlje je posvećeno karakterizaciji K’1(ℝn) sa srodnih modulaciskih prostora. Dokazani su i različiti Tauberovi rezultata za STFT. Deo teze je posvećen na ridglet i Radon transformacije. Ridgelet transformacija je definisana na (Lizorkin) distribucije i pokazano je da ridgelet transformacija i njen operator sinteze mogu da se prošire kako neprekidna preslikava Rψ : S’0(ℝn) → S’(Yn+1) and RtΨ: S’(Yn+1) → S’0(ℝn). Ridgelet transformacija na S’0(ℝn) je data preko dualnog pristupa. Naše teoreme neprekidnosti ridgelet transformacije su primenjene u dokazivanju neprekidnosti Radonove transformacije na Lizorkin test prostorima i njihovim dualima. Na kraju, dajemo Abelovih i Tauberovih teorema koji daju veze izmedju kvaziasimptotike distribucija i kvaziasimptotike rigdelet i Radonovog transfomaciju.Zadnje poglavje je posveceno multirezolucijskog analizu M - eksponencijalnih distrubucije. Proucavamo konvergenciju multirezolucijkog razvoja u razlicitih prostori test funkcije i distribucije i razmotrena je tackasta konvergencija multirezolucijkog razvoju u tacku u distributivnog smislu. Obezbedjena je i karakterizacija kvaziasimptotike u pogled multirezolucijskog razvoju i dat dovoljni uslov za postojanje α-tacka gustine za pozitivne mere.
18
Bastian, Ryan. "An Introduction to the Generalized Riemann Integral and Its Role in Undergraduate Mathematics Education." Ashland University Honors Theses / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1482504144122774.
Full text
19
Gomes, Francisco Augusto Aparecido [UNESP]. "Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial." Universidade Estadual Paulista (UNESP), 2006. http://hdl.handle.net/11449/88887.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0
Previous issue date: 2006-04-24Bitstream added on 2014-06-13T19:50:37Z : No. of bitstreams: 1
gomes_faa_me_ilha.pdf: 1304340 bytes, checksum: 93a9b85b39e238ee85d2a3ae10503b07 (MD5)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O fenômeno da ablação é um processo que envolve o estudo de proteções térmicas, com muitas aplicações, principalmente na engenharia mecânica e aeroespacial. O processo envolve transferência de calor com movimento de fronteira, onde a posição é desconhecida a priori. As equações governantes do processo formam um sistema não-linear de equações diferenciais acoplado. A análise unidimensional do processo ablativo é realizada em um corpo de revolução, o qual está sobre intenso aquecimento. Esse problema é resolvido utilizando a Técnica da Transformada Integral Generalizada – TTIG, para solução do sistema de equações governantes. Como condição de contorno é considerada um fluxo de calor transiente no contorno, como por exemplo, o que ocorre com veículos na reentrada da atmosfera. A teoria do fluxo de calor de Tauber e de Van Driest é utilizada nessa análise. Os resultados de interesse são, a espessura e a taxa de material ablatado. Os resultados obtidos são comparados com resultados disponíveis de outras técnicas de solução em literaturas.
The phenomenon of ablation is a process of thermal protection with several applications, mainly, in mechanical and aerospace engineering. This process involves heat transfer with a moving boundary which position is unknown a priori. The governing equations of the process are a non-linear system of coupled partial differential equations. The onedimensional analysis of ablative process has been done in a revolution body, which is on intense heating. This problem is performed by using the generalized integral transform technique – GITT for solution of the system of governing equations. As boundary condition is considered a transient heat flux like ones that occur, for example, in re-entrance of aerospace vehicles in the atmosphere. The heat flux theory of Tauber and Van Driest were used in that analysis. The results of interest are the thickness and the rate of loss of the ablative material. The obtained results are compared with available results of other techniques of solution in the literature.
20
Marques, Rafael dos Santos. "Integral equations in the sense of Kurzweil integral and applications." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08112016-104931/.
Full textAbstract:
Being part of a research group on functional differential equations (FDEs, for short), due to my formation in non-absolute integration theory and because certain kinds of FDEs can be expressed as integral equations, I was motivated to investigate the latter. The purpose of this work, therefore, is to develop the theory of integral equations, when the integrals involved are in the sense of Kurzweil- Henstock or Kurzweil-Henstock-Stieltjes, through the correspondence between solutions of integral equations and solutions of generalized ordinary differential equations (we write generalized ODEs, for short). In order to be able to obtain results for integral equations, we propose extensions of both the Kurzweil integral and the generalized ODEs (found in [36]). We develop the fundamental properties of this new generalized ODE, such as existence and uniqueness of solutions results, and we propose stability concepts for the solutions of our new class of equations. We, then, apply these results to a class of nonlinear Volterra integral equations of the second kind. Finally, we consider a model of population growth (found in [4]) that can be expressed as an integral equation that belongs to this class of nonlinear Volterra integral equations.Sendo parte de um grupo de pesquisa em equações diferenciais funcionais (escrevemos EDFs), por causa de minha formação em teoria de integração não absoluta e porque certos tipos de EDFs podem ser escritas como equações integrais, decidi estudar esse último tipo de equações. O objetivo desse trabalho, portanto, é desenvolver a teoria de equações integrais, quando as integrais envolvidas são no sentido de Kurzweil-Henstock ou Kurzweil-Henstock-Stieltjes, através da correspondência entre soluções de equações integrais e soluções de equações diferenciais ordinárias generalizadas (ou EDOs generalizadas). A fim de obter resultados para estas equações integrais, propomos extensões de ambas a integral de Kurzweil e as EDOs generalizadas (encontradas em [36]). Desenvolvemos propriedades fundamentais dessa nova EDO generalizada, como resultados de existência e unicidade de solução, e propomos conceitos de estabilidade para as soluções de nossa nova classe de equações. Nós, então, aplicamos esses resultados a uma classe de equações integrais de Volterra não lineares de segunda espécie. Finalmente, consideramos um modelo de crescimento de populações (encontrado em [4]) que pode ser escrito como uma equação integral pertencente a essa classe de equações integrais de Volterra não lineares.
21
Yeo, Stephen K. N. "Generalised periodic Green's function analysis of microstrip dipole arrays /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phy46.pdf.
Full text
22
Hanna, George T. "Cubature rules from a generalized Taylor perspective." full-text, 2009. http://eprints.vu.edu.au/1922/1/hanna.pdf.
Full textAbstract:
The accuracy and efficiency of computing multiple integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to build on past work and develop and analyze new numerical methods to evaluate double integrals efficiently. The fundamental aim is to develop and assess techniques for (numerically) evaluating double integrals with high accuracy. The general approach presented in this thesis involves the development of new multivariate approximations from a generalaised Taylor perspective in terms of Appell type polynomials and to study their use in multi-dimensional integration. The expectation is that the new methods will provide polynomial and polynomial-like approximations that can be used for application in a straight forward manner with better accuracy. That is, we aim to devise and investigate new multiple integration formulae and as well as provide information on a priori error bounds. A further major contribution of the work builds on the research conducted in the field of Grüss type inequalities and leads to a new approximation of the one and two dimensional finite Fourier transform. The approximations are in terms of the complex exponential mean and estimate of the error of approximation for different classes of functions of bounded variation defined on finite intervals. It is believed that this work will also have an impact in the area of numerical multidimensional integral evaluation for other integral operators.
23
Gory, Jeffrey J. "Marginally Interpretable Generalized Linear Mixed Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606.
Full text
24
Asaad, Magdy. "Pfaffian and Wronskian solutions to generalized integrable nonlinear partial differential equations." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/3956.
Full textAbstract:
The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.
The derivation and solutions of integrable nonlinear partial differential equations in two spatial dimensions have been the holy grail in the field of nonlinear science since the late 1960s. The prestigious Korteweg-de Vries (KdV) and nonlinear Schrödinger (NLS) equations, as well as the ,Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable nonlinear partial differential equations in (1+1) and (2+1) dimensions, respectively. Do there exist Pfaffian and soliton solutions to generalized integrable nonlinear partial differential equations in (3+1) dimensions? In this dissertation, I obtained a set of explicit exact Wronskian, Grammian, Pfaffian and N-soliton solutions to the (3+1)-dimensional generalized integrable nonlinear partial differential equations, including a generalized KP equation, a generalized B-type KP equation, a generalized modified B-type KP equation, soliton equations of Jimbo-Miwa type, the nonlinear Ma-Fan equation, and the Jimbo-Miwa equation. A set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters and continuous functions is generated to guarantee that the Wronskian determinant or the Pfaffian solves these generalized equations.
On the other hand, as part of this dissertation, bilinear Bäcklund transformations are formally derived for the (3+1)-dimensional generalized integrable nonlinear partial differential equations: a generalized B-type KP equation, the nonlinear Ma-Fan equation, and the Jimbo-Miwa equation. As an application of the obtained Bäcklund transformations, a few classes of traveling wave solutions, rational solutions and Pfaffian solutions to the corresponding equations are explicitly computed.
Also, as part of this dissertation, I would like to apply the Pfaffianization mechanism of Hirota and Ohta to extend the (3+1)-dimensional variable-coefficient soliton equation of Jimbo-Miwa type to coupled systems of nonlinear soliton equations, called Pfaffianized systems.
Examples of the Wronskian, Grammian, Pfaffian and soliton solutions are explicitly computed. The numerical simulations of the obtained solutions are illustrated and plotted for different parameters involved in the solutions.
25
Cvijanovic, Zoran. "A computer laboratory for generalized information theory (COLGIT)." Diss., Online access via UMI:, 2007.
Find full textAbstract:
Thesis (Ph. D.)--State University of New York at Binghamton, Department or Systems Science and Industrial Engineeering, Thomas J. Watson School of Engineering and Applied Science, 2007.Includes bibliographical references.
26
Mazzoni, Michele. "Generalized hydrodynamics of a (1+1)-dimensional integrable scattering theory with roaming trajectories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23209/.
Full textAbstract:
The emergence of hydrodynamic features in off-equilibrium (1 + 1)-dimensional integrable quantum systems has been the object of increasing attention in recent years. In
this Master Thesis, we combine Thermodynamic Bethe Ansatz (TBA) techniques for
finite-temperature quantum field theories with the Generalized Hydrodynamics (GHD)
picture to provide a theoretical and numerical analysis of Zamolodchikov’s staircase
model both at thermal equilibrium and in inhomogeneous generalized Gibbs ensembles.
The staircase model is a diagonal (1 + 1)-dimensional integrable scattering theory with
the remarkable property of roaming between infinitely many critical points when moving
along a renormalization group trajectory. Namely, the finite-temperature dimensionless
ground-state energy of the system approaches the central charges of all the minimal unitary conformal field theories (CFTs) M_p as the temperature varies. Within the GHD
framework we develop a detailed study of the staircase model’s hydrodynamics and compare its quite surprising features to those displayed by a class of non-diagonal massless
models flowing between adjacent points in the M_p series. Finally, employing both TBA
and GHD techniques, we generalize to higher-spin local and quasi-local conserved charges
the results obtained by B. Doyon and D. Bernard [1] for the steady-state energy current
in off-equilibrium conformal field theories.
27
Gomes, Francisco Augusto Aparecido. "Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial /." Ilha Solteira : [s.n.], 2006. http://hdl.handle.net/11449/88887.
Full textAbstract:
Resumo: O fenômeno da ablação é um processo que envolve o estudo de proteções térmicas, com muitas aplicações, principalmente na engenharia mecânica e aeroespacial. O processo envolve transferência de calor com movimento de fronteira, onde a posição é desconhecida a priori. As equações governantes do processo formam um sistema não-linear de equações diferenciais acoplado. A análise unidimensional do processo ablativo é realizada em um corpo de revolução, o qual está sobre intenso aquecimento. Esse problema é resolvido utilizando a Técnica da Transformada Integral Generalizada - TTIG, para solução do sistema de equações governantes. Como condição de contorno é considerada um fluxo de calor transiente no contorno, como por exemplo, o que ocorre com veículos na reentrada da atmosfera. A teoria do fluxo de calor de Tauber e de Van Driest é utilizada nessa análise. Os resultados de interesse são, a espessura e a taxa de material ablatado. Os resultados obtidos são comparados com resultados disponíveis de outras técnicas de solução em literaturas.Abstract: The phenomenon of ablation is a process of thermal protection with several applications, mainly, in mechanical and aerospace engineering. This process involves heat transfer with a moving boundary which position is unknown a priori. The governing equations of the process are a non-linear system of coupled partial differential equations. The onedimensional analysis of ablative process has been done in a revolution body, which is on intense heating. This problem is performed by using the generalized integral transform technique - GITT for solution of the system of governing equations. As boundary condition is considered a transient heat flux like ones that occur, for example, in re-entrance of aerospace vehicles in the atmosphere. The heat flux theory of Tauber and Van Driest were used in that analysis. The results of interest are the thickness and the rate of loss of the ablative material. The obtained results are compared with available results of other techniques of solution in the literature.
Orientador: João Batista Campos Silva
Coorientador: Antonio João Diniz
Banca: Cássio Roberto Macedo Maia
Banca: Paulo Gilberto de Paula Toro
Mestre
28
Osten, David [Verfasser], and Dieter [Akademischer Betreuer] Lüst. "Current algebra, generalised geometry and integrable models in string theory / David Osten ; Betreuer: Dieter Lüst." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1218466855/34.
Full text
29
Su, Ting. "The generalized dressing method and algebra curves method and their applications to integrable equations /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082687f.pdf.
Full textAbstract:
Thesis (Ph.D.)--City University of Hong Kong, 2009."Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 157-176)
30
Acuña, Rogelio Grau. "On qualitative properties of generalized ODEs." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-26102016-090644/.
Full textAbstract:
In this work, our goal is to prove results on prolongation of solutions, uniform boundedness of solutions, uniform stability as well uniform asymptotic stability (in the classical sense of Lyapunov) for measure differential equations and for dynamic equations on time scales. In order to get our results, we employ the theory of generalized ODEs, since these equations encompass measure differential equations and dynamic equations on time scales. Therefore, to get our results, we start by proving the expected result for abstract generalized ODEs. Then, using the correspondence between the solutions of these equations and the solutions of measure differential equations (see [38]), we extend all the results to these the latter. After that, using the correspondence between the solutions of measure differential equations and the solutions of dynamic equations on time scales (see [21]), we extend all the results to these last equations. Finally, we investigate autonomous generalized ODEs and show that these equations do not enlarge the class of classical autonomous ODEs, even when we consider a more general class of functions as right-hand sides. All the new results presented in this work are contained in papers [16, 17, 18, 19].Neste trabalho, nosso objetivo e provar resultados sobre prolongamento de soluções, limitação uniforme de soluções, estabilidade uniforme e estabilidade uniforme assintótica (no sentido clássico de Lyapunov) para equações diferenciais em medida e para equações dinâmicas em escalas temporais. A fim de obter os nossos resultados, empregamos a teoria de EDOs generalizadas, uma vez que estas equações abrangem equações diferenciais em medida e equações dinâmicas em escalas temporais. Portanto, para obter nossos resultados, vamos começar por provar, os resultados que queremos para EDOs generalizadas abstratas. Em seguida, usando a correspondência entre as soluções de EDOs generalizadas e soluções de equações diferenciais em medida (ver [38]), estenderemos os resultados para estas ultimas equações. Depois disso, usando a correspondência entre as soluções de equações diferenciais em medida e as soluções de equações dinâmicas em escalas temporais (ver [21]), estenderemos todos os resultados para estas ultimas equações. Finalmente, investigamos EDOs generalizadas autônomas e mostramos que estas equações não aumentam a classe de EDOs autônomas clássicas, mesmo quando consideramos uma classe mais geral de funções nos lados direitos das equações. Os novos resultados encontrados estão contidos em [16, 17, 18, 19].
31
Oliveira, Heron Silva. "Introdução ao cálculo de ordem arbitrária." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307000.
Full textAbstract:
Orientador: Edmundo Capelas de OliveiraDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-16T18:34:10Z (GMT). No. of bitstreams: 1 Oliveira_HeronSilva_M.pdf: 1078106 bytes, checksum: 9eb6e7bdc70150b5e616010bdfc9ab58 (MD5) Previous issue date: 2010
Resumo: Efetuamos um levantamento histórico concernente ao cálculo integral e diferencial de ordem arbitrária, também conhecido como cálculo de ordem fracionária ou ainda cálculo fracionário, com o intuito de justificar sua importância, nos dias de hoje, a partir de uma audaciosa e profética frase proferida por Leibniz. A partir das várias definições para derivada de ordem arbitrária, em particular, as definições de Riemann, Liouville, Riemann-Liouville, Grünwald-Letnikov, Weyl e Caputo, elucidamos e justificamos a importância de cada uma delas, nas aplicações, quando associadas ao estudo de uma equação diferencial parcial de ordem arbitrária. Justificamos que, para problemas modelados pelas assim chamadas equações diferenciais de ordem arbitrária, o enfoque conforme proposto por Caputo parece ser o mais conveniente
Abstract: We propose a hystorical review associated with the integral and differential calculus of arbitrary order, known as calculus of fractional order or also fractional calculus with the objective to justify its importance nowadays as of an audacious and profetic phrasis said by Leibniz. By means of several definitions associated with the derivative of fractional order, specifically, the definitions of Riemann, Liouville, Riemann-Liouville, Grünwald-Letnikov,Weyl and Caputo, we discuss and justify the importance of each one, in the applications, when associated with the study to the so-called differential equations of arbitrary order. We also justify that the derivative as proposed by Caputo is the most convenient in problems modelled by a fractional differential equation
Mestrado
Mestre em Matemática
32
Karabin, Svyatoslav. "Generalized hydrodynamics of a class of integrable quantum field theories with non-diagonal scattering." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18009/.
Full textAbstract:
In questo lavoro di tesi abbiamo analizzato alcuni modelli conformi con perturbazioni integrabili, in particolare il modello di Ising tri-critico e i successivi modelli minimali. Abbiamo costruito un protocollo che realizza questi modelli in un regime fuori dall'equilibrio termodinamico. Questo sistema è stato ottenuto connettendo due sistemi semi-infiniti termalizzati a due diverse temperature. In tempi e spazi grandi ci si aspetta che questo sistema evolva verso uno stato stazionario indipendente dal tempo. Le quantità fisiche di nostro interesse sono le correnti stazionarie generate in tale situazione. Per studiare questo sistema abbiamo utilizzato strumenti di integrabilità come il Bethe ansatz termodinamico, concetti di idrodinamica generalizzata e l'insieme di Gibbs generalizzato. Finora questo schema è stato formulato per le teorie di campo con un'interazione tra le particelle data da una matrice S diagonale, ovvero per i modelli con lo spettro di quasi-particelle prive di gradi di libertà interni. In questa tesi abbiamo proposto un'estensione di questo metodo a un modello dotato di uno spettro contenente quasi-particelle organizzate in multipletti di simmetrie e quindi dotate di gradi di libertà interni detti magnoni con processi d'urto descritti da matrici S non diagonali. Abbiamo quindi risolto numericamente le equazioni differenziali che descrivono il sistema di non equilibrio e abbiamo discusso questi risultati.
33
Shu, Chang. "Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation." Thesis, University of Glasgow, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361006.
Full text
34
David, Manolis. "The Henstock–Kurzweil Integral." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-166430.
Full textAbstract:
Since the introduction of the Riemann integral in the middle of the nineteenth century, integration theory has been subject to significant breakthroughs on a relatively frequent basis. We have now reached a point where integration theory has been thoroughly researched to a point where one has to delve quite deep into a particular subject in order to encounter open conjectures. In education the Riemann integral has for quite some time been the standard integral in elementary analysis courses and as the complexity of these courses incrementally increase the more general Lebesgue integral eventually becomes the standard integral. Unfortunately, in the transition from the Riemann integral to the Lebesgue integral there are certain topics of pure theoretical interest which to a certain extent are neglected. This is particularly the case for topics regarding the inverse relationship between differential and integral calculus and the integration of exceedingly complicated functions which for example might be of a highly oscillatory nature. From an applied mathematician's point of view, the partial neglection of these topics in the case of highly problematic functions might be justified in the sense that this theory is unnecessary for modeling most problems that appear in nature. From a theoretician's point of view however this negligence is unacceptable. Consequently, there are alternative integrals which give rise to theories which one can use in an attempt to study these aforementioned topics. An example of such an integral is the Henstock–Kurzweil integral, which can be developed in a rather similar manner to that of the Riemann integral. In this thesis we will develop the Henstock–Kurzweil integral in order to answer some of the questions which to a certain extent are beyond the scope of the Lebesgue integral while using rather basic proof techniques from complex analysis and measure theory. In addition to that we extended various properties of the Lebesgue integral to the Henstock–Kurzweil integral, in particular when it comes to Lebesgue's fundamental theorem of calculus and the basic convergence theorems of the Lebesgue integral.
35
Monteiro, Giselle Antunes. "Generalized linear differential equations in a Banach space: continuous dependence on parameters and applications." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30032012-105214/.
Full textAbstract:
The purpose of this work is to investigate continuous dependence on parameters for generalized linear differential equations in a Banach space- valued setting. More precisely, we establish a theorem inspired by the clas- sical continuous dependence result due to Z. Opial. In addition, our second outcome extends, to Banach spaces, the result proved by M. Ashordia in the framework of finite dimensional generalized linear differential equations. Roughly speaking, the continuous dependence derives from assumptions of uniform convergence of the functions in the right-hand side of the equations, together with the uniform boundedness of variation of the linear terms. Fur- thermore, applications of these results to dynamic equations on time scales and also to functional differential equations are proposed. Besides these results on continuous dependence, we complete the theory of abstract Kurzweil-Stieltjes integration so that it is well applicable for our purposes in generalized linear differential equations. In view of this, our contributions are related not only to differential equations but also to the abstract Kurzweil-Stieltjes integration theory itself. The new results presented in this work are contained in the papers [26] and [27], both accepted for publicationO objetivo deste trabalho é investigar a dependência contínua de soluções em relação a parâmetros para equações diferenciais lineares generalizadas no contexto de espaços de Banach. Mais precisamente, apresentamos um teo- rema inspirado no resultado clássico de dependência contínua obtido por Z. Opial. Nosso segundo resultado estende, para espaços de Banach, o provado por M. Ashordia no contexto de equações diferenciais lineares gen- eralizadas em dimensão finita. Em linhas gerais, a dependência contínua decorre da convergência uniforme das funções à direita das equações, junta- mente com a limitação uniforme da variação dos termos lineares. No mais, são propostas aplicações desses resultados em equações dinâmicas em escalas temporais e também em equações diferenciais funcionais. Além dos resultados em dependência contínua, completamos à teoria de integração abstrata de Kurzweil-Stieltjes de modo que esta se adeque aos nossos propósitos em equações diferenciais lineares generalizadas. Assim, nossas contribuições dizem respeito não apenas a equações diferenciais, mas também a teoria de integração abstrata de Kurzweil-Stieltjes em si. Os resultados originais apresentados neste trabalho estão contidos nos artigos [26] e [27], ambos aceitos para publicação
36
Wang, Zipeng. "Generalized Dirichlet to Neumann map for linear evolution equations on half-line, and, Singular integrals of non-convolution type on product spaces." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709335.
Full text
37
Khajehnasiri, Amirreza. "A Generalized 2-D Multiport Model for Planar Circuits with Slots in Ground Plane." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/777.
Full textAbstract:
With increasing complexity of microwave integrated circuits and tendency towards building integrated modules, real estate in printed circuit boards becomes more at premium. On the other hand, building MIC's on a single semiconductor substrate such as GaAs has other drawbacks as substrate requirements for different components are sometimes contradictory. This has motivated researchers to consider multi-layer and stacked designs. Multi-layer planar circuits offer advantages that cannot be equaled by traditional single layer designs. In this respect, a new class of planar structures, based upon a multi-layered stack of dual-mode stripline or microstrip patches is becoming increasingly popular. In the new stacked design coupling between planar circuits separated by a ground plane is accomplished through coupling apertures in the common ground plane. This thesis is about developing a new approximate multiport network model for fast analysis of multi-layered planar structures with ground plane slots. To extend applicability of multiport network model (MNM) to the class of planar structures containing ground plane slots, a generalized network formulation for aperture problems is combined with traditional MNM to account for the presence of the slot. To this end, the slot is replaced by an unknown equivalent surface magnetic current. Slot ports are defined in terms of electric and magnetic fields over the slot in accordance with the generalized network formulation for aperture problems. While traditional MNM for planar circuits is based on generalized impedance matrices, we adopt a hybrid matrix approach for multi-layer structures. The hybrid matrix consists of four sub-matrices that relate terminal voltages and currents of edge and slot ports. The same generalized impedance matrix in the absence of the slot can be used to relate terminal voltages and currents of edge ports when the slot ports are short-circuited. Open circuit voltage at edge ports due to terminal voltages at slot ports and terminal currents at slot ports due to input currents at edge ports are represented by two transfer matrices. Both these transfer matrices can be calculated from 2D analysis which only considers TMz modes.
Interaction among slot ports, represented by a generalized admittance matrix, however, requires considering both TMz and TEz modes. This generalized admittance matrix is obtained from tangential component of the magnetic field over the slot due to the equivalent surface magnetic current and relates terminal voltages and currents of slot ports. Full modal expansion consisting of both TMz and TEz modes is used to compute the generalized admittance matrix of a slot in a regularly shaped planar cavity. For irregularly shaped patches, modal expansion is not available. Instead, a new contour integral equation for magnetic field, derived for the first time in this thesis, is combined with complex images method for calculation of generalized admittance matrix of a slot radiating in a planar cavity of arbitrary shape.
Once the hybrid matrix representation of a planar circuit on a ground plane containing a slot is derived, it can be connected to the hybrid matrix of any other planar circuit on the other side of the ground plane. This can be done by enforcing network equivalent of continuity of tangential fields across the slot. This leads to a generalized impedance matrix for the multi-layer structure relating terminal voltages and currents of edge ports of both planar circuits.
To show the accuracy of the proposed method of analysis, several proof-of-concept structures have been analyzed by both this method and ANSOFT HFSS full-wave simulator as a reference. In most cases excellent agreement is achieved in predicting the return loss and radiation patterns of these multi-layer structures which proves the validity of the proposed approach for fast analysis and design of multi-layer planar structures.
38
Maeda, Kazuki. "Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188859.
Full text
39
Sulkosky, Vincent Anthony. "The spin structure of helium-3 and the neutron at low momentum transfer: A measurement of the generalized GDH integrand." W&M ScholarWorks, 2007. https://scholarworks.wm.edu/etd/1539623521.
Full textAbstract:
Since the 1980's, the study of nucleon (proton or neutron) spin structure has been an active field both experimentally and theoretically. One of the primary goals of this work is to test our understanding of Quantum Chromodynamics (QCD), the fundamental theory of the strong interaction. In the high energy region of asymptotically free quarks, QCD has been verified. However, verifiable predictions in the low energy region are harder to obtain due to the complex interactions between the nucleon's constituents: quarks and gluons. In the non-pertubative regime, low-energy effective field theories such as chiral perturbation theory provide predictions for the spin structure functions in the form of sum rules.;Spin-dependent sum rules such as the Gerasimov-Drell-Hearn (GDH) sum rule are important tools available to study nucleon spin structure. Originally derived for real photon absorption, the Gerasimov-Drell-Hearn (GDH) sum rule was first extended for virtual photon absorption in 1989. The extension of the sum rule provides a unique relation, valid at any momentum transfer ( Q2), that can be used to study the nucleon spin structure and make comparisons between theoretical predictions and experimental data.;Experiment E97-110 was performed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) to examine the spin structure of the neutron and 3He. The Jefferson Lab longitudinally-polarized electron beam with incident energies between 1.1 and 4.4 GeV was scattered from a longitudinally or transversely polarized 3He gas target in the Hall A end station. Asymmetries and polarized cross-section differences were measured in the quasielastic and resonance regions to extract the spin structure functions g1(x, Q2) and g2(x, Q2) at low momentum transfers (0.02 < Q2 < 0.3 GeV2). The goal of the experiment was to perform a precise measurement of the Q2 dependence of the extended GDH integral and of the moments of the neutron and 3He spin structure functions at low Q2. This Q 2 range allows us to test predictions of chiral perturbation theory and check the GDH sum rule by extrapolating the integral to the real photon point. This thesis will discuss preliminary results from the E97-110 data analysis.
40
RAMIL, BOUABID. "Methode de galerkin avec elements finis et algorithmes rapides de type gradient conjugue generalise appliques a la resolution de l'equation integrale de la radiosite." Université Louis Pasteur (Strasbourg) (1971-2008), 2000. http://www.theses.fr/2000STR13040.
Full textAbstract:
La resolution de l'equation de la radiosite obtenue avec la methode galerkin est traditionnellement effectuee par l'algorithme de gauss - seidel, qui n'est pas proportionnelle par suite de son caractere recursif. Afin de depasser ces limitations pratiques, nous avons monte comment il est possible de resoudre l'equation de la radiosite a l'aide des algorithmes du type gradient conjugue generalise, qui sont non parametriques et robustes. Afin de simuler l'eclairement a l'interieur des batiments, nous avons propose une approche algorithmique originale qui resout localement cette equation. Il est desormais possible de resoudre cette equation de radiosite par la simulation de l'eclairement.
41
Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.
Full textAbstract:
Mestrado em Mathematical FinanceO objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de soluções. O resultado, original desta dissertação, é aplicado a um modelo Vasicek fraccionário de taxas de juro.
This dissertation aims to generalize a result on the exponential stability of trivial solutions of stochastic differential equations driven by the fractional Brownian motion by Garrido-Atienza et al. to non-trivial solutions in the scalar case. Notions on fractional calculus are presented, as well as the definition and main properties of the fractional Brownian motion. Subsequently the framework for SDEs driven by fractional Brownian motion with a pathwise approach is characterized along with some existence and uniqueness results. The result on stability is then applied to the fractional Vasicek model for interest rates.
info:eu-repo/semantics/publishedVersion
42
Silva, Marcos de Souza e. "Análise dos efeitos razão de aspecto e inclinação na convecção natural em cavidades via transformação integral." Universidade Federal de Uberlândia, 2002. https://repositorio.ufu.br/handle/123456789/15028.
Full textAbstract:
In this work, the effects of the aspect radio and inclination angle in the convection heat transfer
inside a square cavity are analyzed through integral transformation. The numerical simulations
were made in square and plane cavity in a fluid with constant and variable properties and identifying
the effect of the temperature variations. Varying the geometry of the cavity and its inclination it was
identified the most sensitive properties at the temperature variations, as well as the geometric
combinations which optimize the convection heat transfer. The Generalized Integral Transform
Technique (JLWW) was capable to simulate the physical phenomenon successfully, capturing
recirculations in critical convective cases numerically. The correlations were established between
the rate of convection heat transfer and the aspect radio and the inclination angle of the cavity.Neste trabalho, serão analisados os efeitos da razão de aspecto e ângulo de inclinação na transferência de calor por convecção via transformação integral, através de simulações em uma cavidade quadrada e plana com um fluido de propriedades constantes e variáveis, identificando a influência à variações de temperatura, bem como as combinações geométricas que otimizam a troca de calor por convecção. A Técnica da Transformada Integral Generalizada (Generalized Integral Transform Technique - JLWW) foi capaz de obter sucesso na simulação do fenômeno físico, sendo capaz de capturar recirculações em casos convectivos críticos do ponto de vista numérico. Foram estabelecidas correlações entre a taxa de transferência de calor por convecção e a razão de aspecto e o ângulo de inclinação da cavidade.
Mestre em Engenharia Mecânica
43
Santos, Fábio Lima. "Dicotomias em equações diferenciais ordinárias generalizadas e aplicações." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-24032017-102955/.
Full textAbstract:
Neste trabalho, estabelecemos a teoria de dicotomias para equações diferenciais ordinárias generalizadas, introduzindo os conceitos de dicotomias para essas equações generalizadas, estudando as suas propriedades e propondo resultados novos. Investigamos condições para a existência de soluções limitadas e condições para a existência de dicotomia exponencial. Utilizando teoremas de correspondência entre equações diferenciais ordinárias generalizadas e outras equações, traduzimos os resultados obtidos para os casos particulares de dicotomias para equações diferenciais em medida e para equações diferenciais com impulsos. O fato de trabalharmos no ambiente das equações diferenciais ordinárias generalizadas faz com que os resultados obtidos para os casos particulares possam envolver funções com muitas descontinuidades e de variação ilimitada.In this work we establish the theory of dichotomies for generalized ordinary dierential equations, introducing the concepts of dichotomies for these equations, studying their properties and proposing new results. We investigate conditions of existence of exponential dichotomies and bounded solutions. Using correspondence theorems between generalized ordinary dierential equations and other equations, we translate the obtained results to the particular cases of dichotomies for measure dierential equations and for impulsive dierential equations. The fact that we work in the framework of generalized ordinary dierential equations allows us to obtain results for the particular cases where the functions involved can have many discontinuities and be of unbounded variation.
44
Vu, Dinh-Long. "A diagrammatic approach towards the thermodynamics of integrable systems." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASS143.
Full textAbstract:
Dans cette thèse, nous cherchons à remplacer la dérivation traditionnelle de l'Ansatz de Bethe Thermodynamique (TBA) par une nouvelle méthode basée sur une sommation directe. L'idée centrale est d'utiliser le théorème de matrice-arbre pour écrire le déterminant de Gaudin qui apparaît dans l'expansion de cluster comme une somme sur des graphs. Pour les théories quantiques des champs intégrables avec une matrice de diffusion diagonale, nous obtenons avec cette nouvelle approche diverses quantités, notamment l'équation de TBA, la formule de Leclair-Mussardo pour la fonction à un point d'un opérateur local, l'énergie des états excités en volume fini et l'entropie du bord ou la fonction g, le tout d'une façon uniforme. Elle peut également être utilisée pour trouver les équations d'état dans l'Hydrodynamique Généralisée - un cadre récemment proposé pour décrire les propriétés de transport de systèmes intégrables hors d'équilibre. D'un autre côté, les théories avec une matrice de diffusion non diagonale posent plusieurs problèmes à cette méthode. Une théorie candidate a été considérée et une procédure pour trouver la fonction g dans ce cas a été proposéeIn this thesis, we seek to replace the traditional derivation of the Thermodynamic Bethe Ansatz (TBA) by a new method of direct summation. The key idea is to use the matrix-tree theorem to write the Gaudin determinant appearing in the cluster expansion as a sum over graphs. For integrable quantum field theories with diagonal scattering matrix, we find that this new approach can recover various quantities including the TBA equation, the Leclair-Mussardo formula for the one point function of a local operator, the excited state energies in finite volume and the boundary entropy or g-function, all in a uniform fashion. It can also be used to find the equations of state in Generalized Hydrodynamics- a recently proposed framework to describe transport properties of integrable systems out of equilibrium. On the other hand, this method faces several problems when applied to theories with non-diagonal scattering matrix and case-dependent analysis is required. A candidate theory has been considered and a procedure to find the g-function of such theory has been proposed
45
Silva, Fernanda Andrade da. "Controlabilidade e observabilidade em equações diferenciais ordinárias generalizadas e aplicações." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08022018-100936/.
Full textAbstract:
Neste trabalho, introduzimos os conceitos de controlabilidade e de observabilidade para equações diferenciais ordinárias generalizadas, apresentamos resultados inéditos sobre condições suficientes e necessárias para controlabilidade e para observabilidade para estas equações e também apresentaremos uma aplicação. Utilizando teoremas de correspondência entre equações diferenciais ordinárias generalizadas e outras equações diferenciais, traduzimos os resultados obtidos para os casos particulares de controlabilidade e observabilidade para equações diferenciais em medida e equações diferencias com impulsos. O fato de trabalharmos no ambiente das equações diferenciais ordinárias generalizadas permitiu que os resultados obtidos pudessem envolver funções com muitas descontinuidades e muito oscilantes, ou seja, de variação ilimitada. Os resultados novos apresentados aqui estão contidos no artigo [21] que se encontra em fase final de redação e será submetido à publicação em breve.In this work, we introduce concepts of controllability and observability for generalized ordinary differential equations, we present new results on necessary and sufficient conditions for controllability and observability for these equations and we also present an application. Using theorems of correspondence between generalized ordinary differential equations and other differential equations, we translate the results obtained for the particular cases of controllability and observability for measure differential equations and differential equations with impulses. The fact that we work in the framework of generalized ordinary differential equations allows us to obtain results where the functions involved can have many discontinuities and be highly oscillating, that is, of unbounded variation. The new results presented here are contained in the preprint [21] which is under final revision and will soon be submitted for publication.
46
Andrade, Adson Íkaro Silva Leite de. "Estudos analíticos e em Pspice de Transferência de calor em corpos cilíndricos." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/8969.
Full textAbstract:
Submitted by Maike Costa (maiksebas@gmail.com) on 2017-05-29T13:55:12Z
No. of bitstreams: 1
arquivototal.pdf: 5619701 bytes, checksum: 3d5e3403144a3249722499b4dea043e9 (MD5)Made available in DSpace on 2017-05-29T13:55:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 5619701 bytes, checksum: 3d5e3403144a3249722499b4dea043e9 (MD5) Previous issue date: 2016-08-31
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
It is presented in this thesis, a proposal for solution of engineering problems in heat transfer area using the network simulation method (NSM - Network Simulation Method), which is to solve these problems by analogy between the thermal circuits and electrical circuits. It will be presented to validate the two-dimensional problem of heat conduction in a cylinder in which the solutions obtained by simulation with the solution analytically obtained via Technical Generalized Integral Transform will face (GITT). In the simulations makes up the body discretization study with the aim of establishing a correlation between the amount of cells (the mesh refinement) and the relationship between the radius of the size and length of the cylinder so that the problem solution of heat transfer in the body can be considered one-dimensional. A comparison will be made between the analytical response and obtained by simulation, varying the number of divisions and different relationships between beam dimensions and length of the cylinder. From the solution validated the proposed method, applying the work presented as a generic fabric prepared by the NSM and implementation PSPICE, which serves for solving many problems of heat conduction in a cylindrical geometry.
É apresentada neste trabalho de tese, uma proposta para solução de problemas de engenharia na área de transferência de calor utilizando o método de simulação de rede (NSM – Network Simulation Method), que consiste na resolução destes problemas pela analogia existente entre os circuitos térmicos e os circuitos elétricos. Nele será apresentada a validação do problema bidimensional de condução de calor em um cilindro, no qual, serão confrontadas as soluções obtidas por simulação com a solução obtida analiticamente via Técnica da Transformada Integral Generalizada (GITT). Nas simulações realizadas fazse a discretização do corpo em estudo, com o objetivo de se estabelecer uma correlação entre a quantidade de células (refinamento da malha) e a relação entre o tamanho do raio e comprimento do cilindro para que a solução do problema de transferência de calor no corpo possa ser considerada unidimensional. A comparação se dará entre a resposta analítica e a obtida por simulação, variando o número de divisões e as diferentes relações entre as dimensões raio e comprimento do cilindro. A partir da solução validada pela metodologia proposta, o trabalho apresenta como aplicação, uma malha genérica elaborada através do NSM e implementação no PSPICE, a qual serve para resolução de diversos problemas de condução de calor em geometria cilíndrica.
47
Frachon, Didier. "Développement de bancs de mesure magnétique pour ondulateurs et wigglers." Grenoble 1, 1992. http://www.theses.fr/1992GRE10040.
Full textAbstract:
Les nouvelles sources de rayonnement synchrotron telles que l'esrf, permettent de generer des faisceaux de rayons x a tres haute brillance grace a l'utilisation des elements d'insertion: ondulateurs et wigglers. Contrairement aux elements magnetiques classiques utilises dans les accelerateurs (dipoles, quadripoles,. . . ), les elements d'insertion ne doivent pas affecter la dynamique du faisceau de particules. L'emploi tres courant d'aimants permanents pour leur realisation ne permet pas d'atteindre directement les qualites magnetiques requises. Dans le but de mettre au point des methodes de compensation magnetique, des outils de diagnostic ont du etre developpes et caracterises (bancs de mesure d'integrale de champ, de mesures locales)
48
Zhang, Xingyou. "Dynamics and numerics of generalised Euler equations : a thesis submitted to Massey University in partial fulfillment of the requirements for the degree of Ph.D in Mathematics." Massey University, 2008. http://hdl.handle.net/10179/980.
Full textAbstract:
This thesis is concerned with the well-posedness, dynamical properties and numerical treatment of the generalised Euler equations on the Bott-Virasoro group with respect to the general Hk metric , k 2. The term “generalised Euler equations” is used to describe geodesic equations on Lie groups, which unifies many differential equations and has found many applications in such as hydrodynamics, medical imaging in the computational anatomy, and many other fields. The generalised Euler equations on the Bott-Virasoro group for k = 0, 1 are well-known and intensively studied— the Korteweg-de Vries equation for k = 0 and the Camassa-Holm equation for k = 1. Unlike these, the equations for k 2, which we call the modified Camassa-Holm (mCH) equation, is not known to be integrable. This distinction motivates the study of the mCH equation. In this thesis, we derive the mCH equation and establish the short time existence of solutions, the well-posedness of the mCH equation, long time existence, the existence of the weak solutions, both on the circle S and R, and three conservation laws, show some quite interesting properties, for example, they do not lead to the blowup in finite time, unlike the Camassa-Holm equation. We then consider two numerical methods for the modified Camassa-Holm equation: the particle method and the box scheme. We prove the convergence result of the particle method. The numerical simulations indicate another interesting phenomenon: although mCH does not admit blowup in finite time, it admits solutions that blow up (which means their maximum value becomes infinity) at infinite time, which we call weak blowup. We study this novel phenomenon using the method of matched asymptotic expansion. A whole family of self-consistent blowup profiles is obtained. We propose a mechanism by which the actual profile is selected that is consistent with the simulations, but the mechanism is only partly supported by the analysis. We study the four particle systems for the mCH equation finding numerical evidence both for the non-integrability of the mCH equations and for the existence of the fourth integral. We also study the higher dimensional case and obtain the short time existence and well-posedness for the generalised Euler equation in the two dimension case.
49
Canziani, Tatiana de Medeiros. "Análise da perspectiva integrada do currículo flexibilizado na licenciatura em ciências da Universidade Federal do Paraná - setor litoral." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-09032016-151119/.
Full textAbstract:
Essa tese verifica, a partir de uma análise da representação de estudantes e professores do curso de Licenciatura em Ciências da Universidade Federal do Paraná Setor Litoral, como se estabelece a perspectiva integrada dos conteúdos curriculares específicos de Física, Química e Biologia e com os conteúdos pedagógicos na formação de professores generalistas. Esse encaminhamento implica, do ponto de vista legal e pedagógico, na análise dos pressupostos que regem a implementação de um currículo por áreas do saber e cuja formação pedagógica não é realizada na Faculdade de Educação. A discussão sobre o tema é relevante e pertinente ao cenário brasileiro atual uma vez que é legitimada pelas Diretrizes Curriculares Nacionais de Ensino Médio (DCNEM), de 2012, e pelo Projeto de Lei no. 6.840/2013, que propõe a alteração do disposto no Artigo no.36 da LDB, Lei no. 9.394/96, ao estabelecer o currículo do Ensino Médio por áreas de conhecimento. Com o intuito de repensar esse panorama, examina os motivos que levaram à retomada da oferta no país de cursos de licenciatura de cunho generalista como é o caso da licenciatura em Ciências, em comparação com os cursos polivantes de formação docente, de curta duração, da década de 60. O estudo demonstra que há uma mudança de perspectiva, de maneira lenta e incipiente, no panorama da educação brasileira que propõe o estabelecimento de currículos em uma perspectiva integrada e que supõe a necessidade de reorganização dos saberes de modo menos fragmentado e por meio de áreas de conhecimento. A partir dos pressupostos apresentados, essa tese assume a hipótese central de que, o modelo de formação de professores por áreas do conhecimento, construído a partir de uma perspectiva curricular integrada entre os conteúdos específicos e os conteúdos pedagógicos, constitui-se como um modelo inovador de curso de licenciatura. Essa hipótese se vale do princípio de que se rompe com o tradicional modelo de formação docente em que o conteúdo específico é mais importante do que a formação pedagógica, o que implica em um maior compromisso com a formação do professor e o papel social atribuído às universidades. É um estudo de caso, de cunho qualitativo, sobre o referido curso voltado à formação docente em Ciências Naturais para atuar no 6o a 9o ano, do Ensino Fundamental II, mas em processo de transformação para lecionar também no Ensino Médio. A pesquisa se realizou por meio de triangulação de dados captados por meio de levantamento bibliográfico, análise documental e pesquisa de campo desenvolvida através de observação de aulas e entrevistas. A partir da análise dos dados, essa tese verifica as contribuições e os problemas desse modelo de formação inicial de professores por áreas do conhecimento, em uma perspectiva integrada de conteúdos, que se apresenta como pioneiro na formação de professores generalistas, em licenciatura plena.This thesis verifies, from an analysis of the representation of students and teachers of the Licentiate Degree Course in Sciences of the Universidade Federal do Paraná - Setor Litoral, how it establishes an integrated perspective of the specific curriculum contents of Physics, Chemistry and Biology and teaching contents of generalist teachers training. This referral implies, from a legal and a pedagogical point of view, on the analysis of conditions governing the implementation of a curriculum for areas of knowledge and which pedagogical training is not performed at the Faculty of Education. The discussion on the topic is relevant and pertinent to the current Brazilian scenario since it is legitimized by the Diretrizes Curriculares Nacionais de Ensino Médio (DCNEM), from 2012, and by the Projeto de Lei nº. 6.840/2013, that proposes an alteration on the Artigo nº.36 disposed on LDB, Lei no. 9.394/96, that establishes the Ensino Médio curriculum by areas of knowledge. In order to rethink this situation, examines the reasons that led to the resumption of supply in the country of generalist degree courses such as in Science, compared to polivant courses of teacher training, of short duration, in the 60s. The study shows that there is a change of perspective, slow and incipient, in the panorama of Brazilian education that proposes the establishment of curriculum in an integrated perspective and assuming the need for reorganization of knowledge in a less fragmented way and through areas knowledge. From the presented assumptions, this thesis takes the central hypothesis that the model of teacher training by areas of knowledge, built from an integrated curriculum perspective between specific content and pedagogical content, establishes an innovative model of licentiate degree course. This hypothesis relies on the principle that breaks with the traditional teacher training model where specific content is more important than pedagogical training, which implies a greater commitment to the teacher formation and the social role assigned to universities. This is a case study of qualitative character on the refered course aimed at teacher training in Natural Sciences to work in the 6º to 9º year of Ensino Fundamental II, but in the process of transformation to also teach in Ensino Médio. The survey was conducted by means of triangulation of data obtained through a literature review, document analysis and field research developed through classroom observation and interviews. From the data analysis, this thesis verifies the contributions and the problems of this initial training model for teachers by areas of knowledge, in an integrated content perspective, which presents itself as a pioneer in the training of generalist teachers, in full licentiate degree.
50
Ruas, Patrícia Haueisen Dias. "Análise teórica do escoamento bifásico e/ou dois-fluidos imiscíveis anular ascendente via GITT." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/8965.
Full textAbstract:
Submitted by Maike Costa (maiksebas@gmail.com) on 2017-05-24T14:26:07Z
No. of bitstreams: 1
arquivototal.pdf: 2237346 bytes, checksum: 088238fab84060042b385a40d43c4c3b (MD5)Made available in DSpace on 2017-05-24T14:26:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2237346 bytes, checksum: 088238fab84060042b385a40d43c4c3b (MD5) Previous issue date: 2016-02-04
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The present paper makes an analysis of multiphase flow up (oil-gas) in laminar regime, with hidrodynamically developed profiles and interacting heat. The fluids analyzed are considered immiscible, developing into separated speed and temperature fields. The energy equations are applied to obtain of heat fields in the thermal entry region of the fluids flowing in the same direction. Although the results of parameters of practical interest has been obtained by purely numerical procedures, the system governing equations involving partial differential and have not been resolved successfully analytically yet. Thus, the use of Generalizes Integral Transform Technique, as powerful mathematical tool, is proposed to solve the energy equations associated with the flow and to producing hybrid results, analytical-numerical, more extension e analysis flexibility to a large number of parameter used in oil and gas engineering. Auxiliary problems with the greatest possible number of original problem information are presented in an attempt of improving the numerical convergence. Lastly, a computational routine is developed in FORTRAN to obtain the numerical solution. The numerical results obtained for the fields are presented in tables and graphs for then be compared with the maximum care to the parameters of special cases available in the literature.
O presente trabalho realiza uma análise do escoamento multifásico (óleo-gás) ascendente em regime laminar, com perfis hidrodinamicamente desenvolvidos e interagindo termicamente. Os fluidos em análise são considerados imiscíveis, desenvolvendo-se em campos separados de velocidade e temperatura. A equação da energia é aplicada para a obtenção dos campos térmicos em desenvolvimento na região de entrada térmica dos fluidos escoando na mesma direção. Embora resultados de parâmetros de interesse prático já tenham sido obtidos através de procedimentos puramente numéricos, o sistema de equações que regem esse tipo de escoamento envolve diferenciais parciais e ainda não foram solucionadas analiticamente com sucesso. Dessa forma, o uso da Técnica de Transformada Integral Generalizada, como ferramenta matemática, é proposto para resolver as equações de energia associada ao escoamento produzindo resultados híbridos, analítico-numérico, com maior flexibilidade de análise e extensão para um grande número de parâmetros utilizados na engenharia de petróleo e gás. Problemas auxiliares com o maior número possível de informações do problema original são apresentados na busca da melhoria da convergência numérica. Por fim, uma rotina computacional é elaborada em FORTRAN para a obtenção da solução numérica. Os resultados numéricos obtidos para os campos são apresentados na forma de tabelas e gráficos para em seguida serem comparados com o máximo de esmero aos parâmetros de casos especiais disponíveis na literatura especializada.