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Broersma, Heather Ann. "Gauss-Bonnet formula." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3044.
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From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.
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Tang, Tunan. "Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903.
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Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-051305-162036/unrestricted/simonis.pdf.
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Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Digital WPI, 2005. https://digitalcommons.wpi.edu/etd-dissertations/285.
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Newton-Picard methods are iterative methods that work well for computing roots of nonlinear equations within a continuation framework. This project presents one of these methods and includes the results of a computation involving the Brusselator problem performed by an implementation of the method. This work was done in collaboration with Andrew Salinger at Sandia National Laboratories.
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Botteghi, Stefano. "Il teorema di Gauss-Bonnet." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14674/.
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La tesi tratta del teorema di Gauss-Bonnet per superfici astratte.L'elaborato ha come finalità la dimostrazione di tale teorema, sia da un punto di vista locale, sia da un punto di vista globale. Il teorema di Gauss-Bonnet locale studia curve chiuse in un intorno coordinato di una superficie differenziabile orientata qualsiasi, mettendo in relazione la curvatura gaussiana della superficie, la curvatura geodetica della curva e la somma degli angoli nei punti di singolarità della curva. Globalmente invece il teorema esprime una relazione tra l'integrale della curvatura gaussiana rispetto all'elemento d'area della superficie e una costante topologica detta caratteristica di Eulero. Per raggiungere tali risultati affronteremo lo studio di concetti quali la connessione, il fibrato tangente e il fibrato vettoriale. Vedremo in particolare come introdurre una struttura di fibrato vettoriale in rette complesse sul fibrato tangente di una superficie
orientata, e useremo abbondantemente nella dimostrazione questo strumento.
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Fogli, Filippo. "Il Teorema di Gauss-Bonnet." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20917/.
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Il Teorema di Gauss-Bonnet è probabilmente uno dei teoremi più profondi della geometria differenziale delle superfici. Una prima versione di questo teorema è stata presentata da Gauss in un suo famoso saggio. L'estensione del teorema a una regione limitata da una curva semplice non geodetica è dovuta a O.Bonnet, e da qui il nome di Teorema di Gauss-Bonnet. Per generalizzarlo ulteriormente alle superfici compatte occorre parlare di triangolazioni e di caratteristica di Eulero-Poincaré di una superficie compatta. Questo teorema ha notevoli applicazioni allo studio delle geodetiche e dei campi di vettori sulla superficie.
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Wu, Wei. "Paving the Randomized Gauss-Seidel." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1074.
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The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix A and its column submatrices. The analysis demonstrates that RBGS improves RGS more when given appropriate column-paving of the matrix, a partition of the columns into well-conditioned blocks. The main result yields a RBGS method that is more e cient than the simple RGS method.
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Ragnoli, Alessia. "Il problema del cerchio di Gauss." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
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Il problema del cerchio di Gauss è uno dei più noti problemi di teoria dei numeri che fornisce una stima del numero di punti interi contenuti in un cerchio. Questo elaborato si pone come obiettivo lo studio, da un punto di vista analitico, di tale risultato a partire dalla prova del Teorema di Dirichlet e del Teorema di Gauss, che forniscono una stima, per n grande, della media aritmetica di due particolari funzioni: la funzione di Dirichlet d(n), che associa ad n il numero dei suoi divisori positivi e r(n), che indica il numero di modi di scrivere n come somma di due quadrati. La ricerca di risultati migliori porta, rispettivamente, al problema dei divisori di Dirichlet e al problema del cerchio di Gauss. Tra questi, soltanto il secondo verrà analizzato dettagliatamente nel resto del lavoro e tramite il Teorema di Hardy-Landau si otterrà la stima ritenuta la più precisa fino ad oggi.
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Wölk, Sabine [Verfasser]. "Factorization with Gauss sums / Sabine Wölk." München : Verlag Dr. Hut, 2011. http://d-nb.info/1015605028/34.
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Lindström, Eva-Karin. "Gauss – Matematiken för 200 år sedan." Thesis, Mittuniversitetet, Avdelningen för ämnesdidaktik och matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-24951.
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Det här arbetet behandlar en del av Carl Friedrich Gauss livsverk. En historisk bakgrund om vetenskap ges från Euklides Elementa och om vetenskap från 1500–1800-talet. En inblick i Gauss barndom och ungdom samt hans liv och skolning,och vidare hans universitetstid beskrivs där fokus läggs på en 17-sidors regelbunden månghörning Gauss konstruerade utifrån Euklides teorier i Elementa. Gauss doktorsavhandling om Algebrans fundamentalsats från 1799 och dess bevis gås igenom. Därefter följer en beskrivning om Gauss matematiska teorier inom komplex analysoch hans geometriska tolkning om det komplexa talplanet; Talteorin – verket Aritmetiska Undersökningar och dess sju kapitel diskuteras. Numerisk matematik och astronomiska beräkningar beskrivs som minsta kvadratmetoden och statistik. Vidare behandlas nåagra viktiga resultat Gauss kom fram till om differentialgeometri och därefter beskrivs den icke-euklidiska geometrin som uppstod på 1800-talet. Teorin om vektorfältanalys, divergenssatsen behandlas och tilläampas. Med fokus på matematik beskrivs Gauss arbete med tillämpningar och teorier inom fysik, astronomi ochgeodesi samt kristallografi.
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Costa, Icoracy Coutinho da. "Inteiros de Gauss: uma abordagem elementar." Universidade Federal do Amazonas, 2016. http://tede.ufam.edu.br/handle/tede/5074.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The purpose of this research is to help High school students to learn complex number sets. Will be shown one of its subsets that has a great importance in Algebra, the Gaussian integers. At first, the study will demonstrate that Gaussian integers are an Algebraic structure, a Euclidean domain to be more specific. The study will compare the addition, subtraction, multiplication, division and exponentiation in algebraic form. Then, we will analyze the prime number in the Gaussian integers sets and compare them to prime numbers in the integer sets to show the differences. At last, some Gaussian integers applications will be presented.
Este trabalho tem como objetivo contribuir para o aprimoramento dos alunos do Ensino Médio no estudo do Conjunto dos Números Complexos, apresentando-lhes um de seus subconjuntos que possuí uma grande importância no estudo da Álgebra. Este conjunto é denominado de Conjunto dos Inteiros de Gauss. Inicialmente demonstraremos que o Conjunto dos Inteiros de Gauss é uma estrutura algébrica, mais precisamente um Domínio Fatorial. Na abordagem será feita a comparação entre os esses dois conjuntos definindo as operações de adição, subtração, multiplicação, divisão e potenciação na forma algébrica. Será feita, ainda, um estudo sobre os números primos dentro do Conjunto dos Inteiros de Gauss que serão comparados com os números primos do Conjunto dos Números Inteiros que possibilitará a visualização das diferenças existentes. Por fim, concluiremos com a apresentação de algumas aplicações dos inteiros de Gauss.
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Oliveira, Flavio Henrique de. "Grafos e aplicações de Gauss estáveis." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01122016-114253/.
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O objetivo desta dissertação é estudar grafos com pesos nos vértices como um invariante global das aplicações de Gauss estáveis de superfícies compactas e orientadas. Apresentaremos também alguns invariantes locais que são importantes no estudo de aplicações estáveis. Abordaremos o problema de realização de grafos por aplicações de Gauss estáveis, considerando também um destes invariantes, o número de cúspides destas aplicações. Finalmente, usaremos matrizes para representar estes invariantes e definiremos classes de equivalências para estes representantes. Esta foi uma ideia que surgiu no final deste trabalho de mestrado.The propose of this work is to study graphs with weights at the vertices as a global invariant of stable Gauss applications on compact and oriented surfaces. We also present some local invariants that are important to the study of stable applications. We approach the problem of realization of graphs by stable Gauss applications, also emphasizing one of these invariants, the number of cusps of these applications. Finally, we use matrices to represent these invariants and define equivalence classes for these representatives. This idea appeared at the end of this master\'s thesis.
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Da, Conceicao Jean-Paul Costa. "Accelerating Gauss-Newton filters on FPGA's." Master's thesis, University of Cape Town, 2010. http://hdl.handle.net/11427/10329.
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Includes bibliographical references (leaves 123-128).Radar tracking filters are generally computationally expensive, involving the manipulation of large matrices and deeply nested loops. In addition, they must generally work in real-time to be of any use. The now-common Kalman Filter was developed in the 1960's specifically for the purposes of lowering its computational burden, so that it could be implemented using the limited computational resources of the time. However, with the exponential increases in computing power since then, it is now possible to reconsider more heavy-weight, robust algorithms such as the original nonrecursive Gauss-Newton filter on which the Kalman filter is based. This dissertation investigates the acceleration of such a filter using FPGA technology, making use of custom, reduced-precision number formats.
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Souza, Isaque Viza de. "Singularidades de Aplicações de Gauss Estáveis." Universidade Federal de Viçosa, 2012. http://locus.ufv.br/handle/123456789/4919.
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In this work, we study the graphs as invariants of stable Gauss maps from closed surfaces embedded in R3. We study the problem of realization of graphs by stable Gauss maps, emphasizing also cusp number of these maps.
Neste trabalho, estudamos os grafos como invariantes de aplicações de Gauss estáveis de superfícies fechadas mergulhadas em R3. Abordamos o problema de realização de grafos por aplicações de Gauss estáveis, enfatizando também o número de cúspides destas aplicações.
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Di, Marco Marco. "Superfici rigate con mappa di Gauss degenere." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20962/.
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Obiettivo di questa tesi è studiare la relazione tra le superfici rigate sviluppabili e la mappa di Gauss. Una superficie rigata è, in maniera euristica, una superficie ottenuta da una retta che si muove nello spazio. Alcune di queste superfici vengono dette sviluppabili: sono le superfici rigate che godono della proprietà di essere localmente isometriche ad un piano. Intuitivamente ciò vuol dire che possono essere localmente “srotolate” su un piano: ne sono un esempio i coni e i cilindri. Per mappa di Gauss in geometria differenziale classica si intende una mappa che (almeno localmente) a ogni punto della superficie assegna un versore normale alla superficie. Tuttavia per i nostri scopi sarà più utile considerare una generalizzazione di tale mappa: considereremo una mappa che a ogni punto di una superficie associa il suo piano tangente. Diremo poi che una mappa di Gauss è degenere per una superficie quando la dimensione dell'immagine della superficie ottenuta attraverso la mappa di Gauss è minore della dimensione della superficie. Vedremo sostanzialmente che una superficie rigata è sviluppabile se e solo se ha mappa di Gauss degenere e che questa condizione non vale solo in R^3 ma anche in P^3(C).
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Pou, Hio San. "The Gauss-Laguerre method for hypersingular integrals." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1942858.
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Benson, David 1978. "A Gauss pseudospectral transcription for optimal control." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/28919.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 237-243).
A pseudospectral method for solving nonlinear optimal control problems is proposed in this thesis. The method is a direct transcription that transcribes the continuous optimal control problem into a discrete nonlinear programming problem (NLP), which can be solved by well-developed algorithms. The method is based on using global polynomial approximations to the dynamic equations at a set of Gauss collocation points. The optimality conditions of the NLP have been found to be equivalent to the discretized optimality conditions of the continuous control problem, which is not true of other pseudospectral methods. This result indicates that the method can take advantage of the properties of both direct and indirect formulations, and allows for the costates to be estimated directly from the Lagrange multipliers of the NLP. The method has been shown empirically to have very fast convergence (exponential) in the states, controls, and costates, for problems with analytic solutions. This convergence rate of the proposed method is significantly faster than traditional finite difference methods, and has been demonstrated with many example problems. The initial costate estimate from the proposed method can be used to define an optimal feedback law for real time optimal control of nonlinear problems. The application and effectiveness of this approach has been demonstrated with the simulated trajectory optimization of a launch vehicle.
by David Benson.
Ph.D.
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Gül, Erdal. "An application for the Gauss-Bonnet theorem." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96180.
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The principal aim of this paper is to give an example of the Gauss-Bonnet Theorem together with its anew structure by using connection and curvature matrices with stereographic projection on the unit 2-sphere, S². We determine an orthonormal basis by applying stereographic projection on S² and we obtain the area of the unit 2 -sphere S² computing connection and curvature matrices.
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Guediri, Hedy. "Fonctions arithmétiques sur les entiers de Gauss." Amiens, 2007. http://www.theses.fr/2007AMIE0100.
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Caron, Christian Frédéric Roger Caron. "Harmonic generation in gases using Bessel-Gauss beams." Thesis, Durham University, 1998. http://etheses.dur.ac.uk/4668/.
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The generation and propagation of harmonics in an atomic gas are described for the case of an incident Bessel-Gauss beam. Theoretical expressions are derived for the far-field amplitude of the harmonic field by solving the propagation equation using an elaborate integral formalism. We establish simple rules which determine the optimum Bessel-Gauss beam with respect to phase-matching as a function of the medium properties, such as the dispersion and the gas density. Target depletion due to photoionization and refractive index variations originating from both free electrons and dressed linear atomic susceptibilities are taken into account. The intensity-dependent complex atomic dipole moment is calculated using nonpertur- bative methods. Numerical propagation calculations for hydrogen, xenon and argon are presented. For hydrogen we consider the third harmonic of a 355-nm, 15-ps pump beam up to 3 X 10(^13) W/cm(^2) intensity, similarly for xenon, but at lower intensities. For argon we consider the 17th and 19th harmonic of a 810-nm, 30-fs pump beam around 10(^14) W/cm(^2) intensity. We compare conversion efficiencies and both spatial and temporal far-field profiles for an optimized Bessel-Gauss beam with respect to a Gaussian beam of same power and/or peak focal intensity. For the case of hydrogen, we investigate the effect of an ac-Stark-shift induced atomic resonance. We find all results in good agreement with our theoretical predictions. We conclude from our studies that Bessel-Gauss beams can perform better in terms of conversion efficiency than a comparable Gaussian beam. We find this to originate essentially from the more flexible phase-matching conditions for Bessel-Gauss beams. Bessel-Gauss beams also allow for spatial separation of the harmonic and the incident field in the far-field region, owing to the conical shape of their spatial far-field profile. Both features make Bessel-Gauss beams an attractive alternative to Gaussian beams in a limited but substantial number of experimental conditions.
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Akarsu, Emek Demirci. "Rational points on horocycles and incomplete Gauss sums." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.652044.
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This thesis studies the connection between the limiting distributions of rational points on horocyle flows and the value distribution of incomplete Gauss sums. A key property of the horocycle flow on a finite-area hyperbolic surface is that long closed horocycles are uniformly distributed. In this thesis we embed rational points on such horocycles on the modular surface and investigate their equidistribution properties. We later extend this study to the metaplectic cover of the modular surface. On the other hand, it is well known that the classical Gauss sums can be evaluated in closed form depending on the residue class of the number of terms in the sum modulo 4. This is not the case for the incomplete Gauss sums, where we restrict the range of summation to a sub-interval (both long and short relative to the complete sums) and study their limiting behavior at random argument as the number of terms goes to infinity. The main ingredient in the proof is the equidistribution of rationals on metaplectic horocyles mentioned above. We also establish an analogue of the weak invariance principle for incomplete Gauss sums.
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Graça, Neto Almir Cunha da. "O campo de tensão da aplicação de GAUSS." Universidade Federal do Amazonas, 2007. http://tede.ufam.edu.br/handle/tede/3693.
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This dissertation is concerned with a detailed proof of a Ruh-Vilms theorem which characterize the isometric immersion of a Riemannian manifold into the Euclidean space whose the mean curvature vector is parallel as being that immersion whose the associated Gauss map is harmonic.
Este trabalho apresenta uma demonstração detalhada do teorema que caracteriza as imersões isométricas (fórmula matemática) de uma variedade Riemanniana n-dimensional no espaço Euclidiano (p + n)-dimensional com vetor curvatura média paralelo como sendo aquelas cuja aplicação de Gauss associada é harmônica. O resultado deve-se a E.A.Ruh e J. Vilms.
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Carlsson, Mattias. "The Gauss-Bonnet theorem and applications on pseudospheres." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-453006.
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Olofsson, Rikard. "Supersymmetric Quantum Mechanics and the Gauss-Bonnet Theorem." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355985.
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We introduce the formalism of supersymmetric quantum mechanics, including super-symmetry charges,Z2-graded Hilbert spaces, the chirality operator and the Wittenindex. We show that there is a one to one correspondence of fermions and bosons forenergies different than zero, which implies that the Witten index measures the dif-ference of fermions and bosons at the ground state. We argue that the Witten indexis the index of an elliptic operator. Quantization of the supersymmetric non-linearsigma model shows that the Witten index equals the Euler characteristic of the un-derlying Riemannian manifold over which the theory is defined. Finally, the pathintegral representation of the Witten index is applied to derive the Gauss-Bonnettheorem. Apart from this we introduce elementary mathematical background in thesubjects of topological invariance, Riemannian manifolds and index theoryVi introducucerar formalismen f ̈or supersymmetrisk kvantmekanik, d ̈aribland super-symmetryladdningar,Z2-graderade Hilbertrum, kiralitetsoperatorn och Wittenin-dexet. Vi visar att det r ̊ader en till en-korrespondens mellan fermioner och bosonervid energiniv ̊aer skillda fr ̊an noll, vilket medf ̈or att Wittenindexet m ̈ater skillnadeni antal fermioner och bosoner vid nolltillst ̊andet. Vi argumenterar f ̈or att Wittenin-dexet ̈ar indexet p ̊a en elliptisk operator. Kvantisering av den supersymmetriskaicke-linj ̈ara sigmamodellen visar att Wittenindexet ̈ar Eulerkarakteristiken f ̈or denunderliggande Riemannska m ̊angfald ̈over vilken teorin ̈ar definierad. Slutligenapplicerar vi v ̈agintegralrepresentationen av Wittenindexet f ̈or att h ̈arleda Gauss-Bonnets sats. Ut ̈over detta introduceras ocks ̊a grundl ̈aggande matematisk bakrundi ämnena topologisk invarians, Riemmanska m ̊angfalder och indexteori.
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Alqahtani, Hessah Faihan. "GAUSS-TYPE QUADRATURE RULES, WITH APPLICATIONSIN LINEAR ALGEBRA." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1521760018029109.
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Liang, Yunxu. "Improved Gauss-Seidel iterative method on power networks." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008140.
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Vasconcelos, de Araújo Kalasas. "A Álgebra de Gauss de uma Álgebra Monomial." Universidade Federal de Pernambuco, 2007. https://repositorio.ufpe.br/handle/123456789/7075.
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Previous issue date: 2007Universidade Federal de Sergipe
A álgebra de Gauss associada à k-subálgebra de um anel polinomial k[t0; : : : ; td] gerado por um número finito de formas de mesmo grau corresponde ao anel de coordenadas homogêneo da imagem de Gauss de uma variedade projetiva uniracional sobre k. Focaremos o caso onde os geradores são monômios. Por caracterizar os menores da matriz jacobiana de um conjunto de monômios como certos n-produtos tornaremos mais concreta a natureza da álgebra de Gauss associada à subálgebra monomial correspondente. A versão reticulada destes n-produtos permite uma abordagem combinatória ao tema. Neste caminho, provaremos resultados já obtidos e estudaremos em detalhes a álgebra de Gauss associada ao conjunto dos monômios livre de quadrados de grau dois
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Cabrera, Gutiérrez Naty Citlali. "Modes de Laguerre-Gauss et canalisation d’atomes froids." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112360/document.
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Les modes de Laguerre-Gauss sont une des solutions de l’équation de propagation de la lumière dans l’approximation paraxiale en coordonnées cylindriques. Ces modes sont caractérisés par deux indices (azimutal et radial) et présentent des propriétés particulières : une structure en forme d’anneau et une phase en hélice. Ces propriétés ont été mises au profit pour plusieurs applications allant de la microscopie à l’astronomie. Cette thèse a été dédiée à l’étude de ces modes et à leur application dans le domaine des atomes froids. Dans un premier temps, la pureté des modes fabriqués par la méthode d’holographie numérique a été étudiée, ainsi que le rôle que la pureté joue dans leur propagation. Ces modes ont été ensuite utilisés pour l’obtention une source d’atomes froids brillante. Depuis plus de 20 ans, des efforts considérables ont été faits pour obtenir des sources d’atomes froids les plus brillantes et les plus compactes possibles. Un piège magnéto-optique à deux dimensions (2D-MOT) est couramment utilisé pour obtenir une source continue d’atomes froids avec un flux important de l’ordre de 1010 atomes/s. Toutefois, le jet atomique ainsi obtenu présente une divergence d’environ 40 mrad ce qui contraint l’utilisateur à travailler près de la sortie mais avec un accès optique limité ou bien loin où il a un bon accès optique mais au prix d’une densité atomique plus faible. Une alternative est présentée, dans laquelle un mode de Laguerre-Gauss est utilisé pour canaliser les atomes à la sortie d’un 2D-MOT. Le mode de Laguerre-Gauss réalise un piégeage dipolaire qui confine les atomes sont le centre noir du mode, ce qui présente l’intérêt de limiter le chauffage dû à l’absorption/émission de la lumière. Ainsi, puisque les modes de Laguerre-Gauss gardent leur forme au cours de leur propagation, les atomes sont canalisés sur une distance de plusieurs décimètres. Nous avons étudié le fonctionnement de ce système pour différents ordres du mode de Laguerre-Gauss et différentes fréquences, et nous avons montré que ce système est efficace et permet d’atteindre un gain en densité d’un facteur 200 par rapport au cas d’un 2D-MOT conventionnel. Un cas particulier est aussi présenté, dans lequel la fréquence du mode de Laguerre-Gauss est choisie pour effectuer non seulement la canalisation des atomes mais aussi leur repompage, ce qui conduit à une simplification importante du système. D’un autre côté, les modes de Laguerre-Gauss sont d’un grand intérêt dans le domaine de l’information et la cryptographie quantique car ils peuvent être utilisés pour encoder et enregistrer l’information. Pour cela, il est indispensable de pouvoir les détecter de façon non-équivoque. Dans ce contexte, nous nous sommes intéressés à la détermination de ces modes. Jusqu’à maintenant, les techniques de détection ont permis de mesurer l’indice azimutal mais peu d’entre elles mesurent l’indice radial. Si on est capable de mesurer aussi l’indice radial, il peut être utilisé comme une nouvelle variable pour le codage et l’enregistrement de l’information. Sous cette motivation, une technique basée sur la transformation du mode de Laguerre-Gauss par un système astigmatique a été mise au point pour déterminer les deux indices qui le caractérisent. Nous avons montré que cette technique peut aussi être utilisée pour optimiser expérimentalement la fabrication des modes de Laguerre-Gauss d’ordre élevé les plus purs possiblesLaguerre-Gaussian modes of light are one of the solutions to the propagation equation of light in the paraxial approximation in cylindrical coordinates. These modes are characterized by two indices (azimuthal and radial) and present particular properties: ring-shaped structure and a helical phase. These properties have been put to use in several applications going from microscopy to astronomy. This work has been devoted to the study of these modes and their application in the cold atom domain. Initially, the purity of such modes generated by numerical holography was studied, as well as the role played by the purity in their propagation. These modes were then used to obtain a bright source of cold atoms. For more than 20 years, considerable efforts have been made to create sources of cold atoms as bright and compact as possible. A two dimensional magneto-optical trap (2D-MOT) is currently used to obtain a continuous source of cold atoms with high flux of the order of 1010 atomes/s. Nevertheless, the source of cold atoms thereby achieved show a divergence of about 40 mrad which constrains the user to work by output but with a limited optical access or far from the output but at the cost of lower density. An alternative is presented, in which a Laguerre-Gaussian mode of light is used to channel the atoms at the output of a 2D-MOT. The Laguerre-Gaussian mode of light carries out a dipole trapping that confines the atoms in the black center of the mode, which has the advantage of limiting the heating due to absorption/emission of light. Thus, since the Laguerre-Gaussian modes of light keep their ring-shape along their propagation, the atoms are channeled over a distance of several decimeters. We studied the functioning of this system for different orders of the Laguerre-Gaussian mode and at different frequencies, and we showed that this system is efficient and allows to achieve a density gain of a factor 200 compared to a conventional 2D-MOT. A particular case is also presented, in which the frequency of the Laguerre-Gaussian mode of light is chosen to carry out not only the channeling of the atoms, but also their repumping, which leads to an important simplification of the system. Laguerre-Gaussian modes of light are also of great interest in the domain of quantum information and quantum cryptography because they can be used to encode and store information. In order to do that, it is crucial to be able to detect them in an unequivocal way. In this context, we are interested in the determination of these modes. Until now, different detection techniques have measured the azimuthal index, but few of them have been able to measure the radial index. If we are able to measure the radial index, it can be used as a new variable to encode and store information. Under this motivation, a technique based on the transformation of a Laguerre-Gaussian mode of light by an astigmatic system has been extended to determine the two indices characterizing them. We showed that this technique can also be used to experimentally optimize the generation of the purest possible Laguerre-Gaussian modes of high order
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Baltrušaitytė, Šukutienė Diana. "Didelių masyvų matavimų rezultatų aproksimavimas Kvazi-Gauso funkcijomis." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2008. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20080929_101443-15357.
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Sudaryta ir išbandyta Matchad‘o programiniu paketu Gauso funkcijų splino programa glodinanti didelio matavimo skaičiaus eksperimentinį masyvą. Glodinimo funkciją sudaro polinomų ir Gauso funkcijų sandaugos suma. Glodinimo procedūra suvedama į algebrinių lygčių sistemą neapibrėžtiems koeficientams Cn,l rasti. Sudaryta Matchad‘o programa, kuri panaudojus suglodintą funkciją apruoksimuoja ją tik teigiamų Gauso funkcijų suma.Šis uždavinys realizuotas programa, kuri remiasi didžiausio nuolydžio metodu. Glodinimo ir aproksimavimo rezultatai tenkina eksperimentatorių reikalavimus.Formed and, used MathCad software, tested Gauss function spline program, which smoothes big measure number experimental array. Smoothing function contains polynomial and Gauss functions multiplication sum. Smoothing procedure is reduced to algebraic equation system to find indeterminate coefficients Cn,l. Created MathCad program, which, by using smoothed function, approximates it to positive Gauss functions sum. This task was solved with program, which refers to biggest pitch method. Smoothing and approximation results fit experimenters’ requirements.
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Rossi, Cecilia. "Il carteggio fra Sophie Germain e Carl Friedrich Gauss." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13640/.
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Lo scopo di questo lavoro è analizzare la corrispondenza fra Sophie Germain e Carl Friedrich Gauss ed alcuni manoscritti di Sophie Germain. La tesi è suddivisa in tre capitoli, il primo è incentrato sulla vita di Sophie Germain, il suo ambiente socio-culturale ed i principali oggetti di studio. Nel secondo e nel terzo capitolo l'analisi si sposta sulla corrispondenza, in particolare sullo studio della prima e della nona lettera che ruotano attorno alla risoluzione dell'ultimo Teorema di Fermat per alcune categorie di numeri che oggi vengono chiamati "Numeri primi di Sophie Germain". Proprio a tal fine nel terzo capitolo, oltre alla nona lettera, si esaminano altri tre manoscritti conservati alla Bibliothèque Nationale de France a Parigi.
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Gauss, S. [Verfasser]. "Eigenschaften von Nb₃Sn-Supraleiterdraehten mit Pulverkompositkernen / S. Gauss." Karlsruhe : KIT-Bibliothek, 2016. http://d-nb.info/1196632197/34.
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Vartak, Aniket Arun. "GAUSS-NEWTON BASED LEARNING FOR FULLY RECURRENT NEURAL NETWORKS." Master's thesis, University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4429.
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The thesis discusses a novel off-line and on-line learning approach for Fully Recurrent Neural Networks (FRNNs). The most popular algorithm for training FRNNs, the Real Time Recurrent Learning (RTRL) algorithm, employs the gradient descent technique for finding the optimum weight vectors in the recurrent neural network. Within the framework of the research presented, a new off-line and on-line variation of RTRL is presented, that is based on the Gauss-Newton method. The method itself is an approximate Newton's method tailored to the specific optimization problem, (non-linear least squares), which aims to speed up the process of FRNN training. The new approach stands as a robust and effective compromise between the original gradient-based RTRL (low computational complexity, slow convergence) and Newton-based variants of RTRL (high computational complexity, fast convergence). By gathering information over time in order to form Gauss-Newton search vectors, the new learning algorithm, GN-RTRL, is capable of converging faster to a better quality solution than the original algorithm. Experimental results reflect these qualities of GN-RTRL, as well as the fact that GN-RTRL may have in practice lower computational cost in comparison, again, to the original RTRL.M.S.
Department of Electrical and Computer Engineering
Engineering and Computer Science
Electrical and Computer Engineering
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Nordström, Marcus. "A Gauss-Newton Based Approach to Automatic Beam Commissioning." Thesis, KTH, Numerisk analys, NA, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-181962.
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In computer assisted planning of radiation treatment and more specifically the software RayStation developed by RaySearch, certain kinds of model calibration problems arise. The process of solving these problems is called beam commissioning. Today beam commissioning is handled by optimizing subsets of the underlying parameters using a quasi-Newton algorithm. In this thesis we investigate the beam commissioning problem space for all of the parameters. We find that the variables are rather well behaved and therefor propose a method based on linearizing dose before scoring. This reduces the number of expensive function calls drastically and allows us to optimize with regard to all of the underlying parameters simultaneously. When using a least squares score function, the method coincides with the Gauss-Newton method, a well-known nonlinear least squares method with fast convergence properties if good starting points are available. We use this method applied to a weighted least squares approximation of our score function for two different machine models using two different dose engines. For all of our simulation experiments, the models are improved. We conclude that a method like this may be used for beam commissioning processes and that our method probably has room for improvement.I datorassisterad strålbehandling och mer specifikt i mjukvaran RayStation utvecklad av RaySearch, uppkommer vissa typer av kalibreringsproblem. Processen att lösa dessa kallas maskinkommissionering. Idag hanteras problemet genom att optimera subset av de underliggande modelparametrarna med en quasi- Newton algoritm. I den här uppsatsen undersöker vi hela problemrymden associerad med maskinkommissionerings problemet. Vi finner att parametrarna beter sig ganska enkelt och föreslår på grund av detta att dosen kan linjäriseras i en punkt och poängsättas i en region omkring den punkten. Detta reducerar antalet dyra funktionsanrop kraftigt och tillåter oss att samoptimera alla modelparametrar samtidigt. Om kvadratiska straff används sammanfaller metoden med Gauss-Newton metoden, en välkänd metod med snabb konvergens om bra startvärden finns tillgängliga. Vi använder den här metoden applicerad på en viktad minstakvadratapproximation av vår poängsättningsfunktion för två maskinmodeller och två dosmotorer. För samtliga experiment är modellerna förbättrade. Vi drar slutsatsen att metoder som denna kan användas i maskinkommissionerings processenen och att det antagligen är möjligt att förbättra vår metod ytterligare.
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Vasconcellos, Luiz Fernando Nascimento. "Utilização do método de Gauss-Jordan no ensino médio." Universidade Federal de Juiz de Fora, 2014. https://repositorio.ufjf.br/jspui/handle/ufjf/817.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Este trabalho é voltado para professores e alunos do Ensino Médio. Tem como objetivo mostrar a utilização do Método da Eliminação de Gauss-Jordan para a resolução de sistemas de equações lineares, cálculo de matrizes inversas e cálculo de determinantes. A motivação para a escolha desse tema é que, cada vez mais, o estudo das matrizes, dos determinantes e, consequentemente, dos sistemas de equações lineares vem sendo deixado de lado no Ensino Médio. Inicialmente, é feito um pequeno apanhado sobre o que são matrizes equivalentes e operações elementares, além de se falar sobre cofator de um elemento de uma matriz e sobre matriz adjunta, necessária para o cálculo da inversa utilizando-se determinantes. Apresenta-se um pouco da história de Gauss e de Jordan e, logo em seguida, o método propriamente dito. Também é visto o que acontece com o método quando as matrizes não são invertíveis, os sistemas são possíveis e indeterminados ou os sistemas são impossíveis. Quanto aos determinantes, são apresentadas suas propriedades e mostrada a eficácia do método para determinantes de ordem n 3 e, além disso, é mostrada a aplicação dos determinantes no cálculo de inversas e na resolução de sistemas de equações pela Regra de Cramer. Finalmente, são apresentadas sugestões de exercícios com uma breve resolução.
This work is oriented to teachers and students in the high school. It aims to show the usage of Gauss-Jordan’s Elimination Method to solve systems of linear equations, calculation of inverse matrices and determinants. The motivation behind the selection of this topic is that, more and more, the study of matrices, determinants, and consequently, systems of linear equations has been ignored in the high school. Firstly, an abridgement is done on what equivalent matrices and elementary operations are. Secondly, it explains about the cofactor of an element of a matrix and about adjoint matrices, needed for the calculation of the inverse matrix using determinants. A little introduction of Gauss and Jordan’s histories is made, and then, the method itself. It is also shown what happens with the method when the matrices are not invertible, the systems are possible but undetermined, or, the systems are not possible. Concerning determinants, their properties are presented and the method’s efficacy for determinants of order n 3 is shown and furthermore, it is shown the application of the determinants in the calculation of inverse matrices and resolutions of systems using Cramer’s Rule. Finally, some suggestions for exercises are presented with brief resolutions.
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Waara, Einar. "Gauss and Jacobi Sums and the Congruence Zeta Function." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354760.
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Nadjiasngar, Roaldje. "On improving the performance of the Gauss-Newton filter." Doctoral thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/5142.
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Includes abstract.Includes bibliographical references.
The Gauss-Newton filter is a tracking filter developed by Norman Morrison around the same time as the celebrated Kalman filter. It received little attention, primarily due to the computation requirements at the time. Today computers have vast processing capacity and computation is no-longer an issue. The filter finite memory length is identified as the key element in the Gauss-Newton filter adaptability and robustness. This thesis focuses on improving the performance of the Gauss-Newton. We incorporate the process noise statistics into the filter algorithm to obtain a filter which explains the error covariance inconsistency of the Kalaman filter. In addition, a biased version of the linear Gauss-Newton filter, with lower mean squared error than the unbiased filter, is proposed. Furthermore the Gauss-Newton filter is adapted using the Levenberg Marquardt method for improved convergence. In order to improve the computation requirements, a recursive version of the filter is obtained.
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LIMA, Emerson Alexandre de Oliveira. "Código de Gauss não 2-face coloráveis em RP2." Universidade Federal de Pernambuco, 2003. https://repositorio.ufpe.br/handle/123456789/7246.
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Previous issue date: 2003Um código de Gauss é uma seqüência cíclica de n símbolos na qual cada símbolo ocorre exatamente duas vezes. Um lacet em uma variedade bidimensional S é um mergulho nesta variedade de uma curva fechada com auto-intercessões de tal forma que cada intercessão se apresente como um vértice 4-valente e que o complemento da curva na variedade seja homeomorfo a uma coleção de discos abertos. Diremos que o lacet é ou não 2-colorável conforme esta coleção de discos forma um mapa 2-colorável. Um lacet l em uma variedade bidimensional S realiza um código de Gauss g quando existir uma rotulação das auto-intercessões de l de tal forma que ao percorrer o lacet a seqüência cíclica dos rótulos dos vértices encontrados seja g. Quando existir em uma variedade bidimensional S um lacet realizando um código de Gauss g, diremos que g é realizável em S. O problema em aberto da caracterização do conjunto dos códigos de Gauss realizáveis no Plano Projetivo RP2 por lacets não 2-coloráveis é o nosso objeto de estudo. Investigamos tal conjunto generalizando os resultados anteriormente obtidos por Lins para o conjunto dos códigos de Gauss realizáveis em RP2 por um lacets 2-coloráveis fornecendo uma completa caracterização dos códigos não 2-coloráveis no plano projetivo e completando, portanto, a caracterização de todos os códigos de Gauss realizáveis em RP2. As técnicas desenvolvidas neste trabalho também podem ser aplicadas na tentativa de resolver os problemas em aberto de caracterização do conjunto dos códigos de Gauss realizáveis por lacets não 2-coloráveis em outras superfícies tais como o Toro e a Garrafa de Klein
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Pozza, Stefano. "GAUSS QUADRATURE FOR LINEAR FUNCTIONALS AND NEW SEQUENCE TRANSFORMATIONS." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424192.
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This thesis is divided into two parts. In the first one we present an extension of the Gauss quadrature formula for the approximation of the quasi definite linear functionals. This extension is obtained using the orthogonal polynomials theory and, in particular, using the relation between sequences of these polynomials and some matrices called Jacobi matrices. We call this proposed formula n-weight Gauss quadrature and we show that it satisfies all the main properties of the “classical” formula, which we call n-node Gauss quadrature. Furthermore, we show that the proposed quadrature can be computed by the non-Hermitian Lanczos algorithm, in the same way in which the n-node Gauss quadrature can be computed by the Hermitian Lanczos algorithm. In the last chapter of the first part we present some preliminary results about possible applications. We approximate the centrality indexes of a complex network. These are indexes that measure the importance of a node in terms of communicability in a graph.
In the second part we propose some sequence transformations. Using sequence transformations we can use the elements of a sequence to obtain another sequence which converges faster to the same limit of the original one. Indeed, in numerical analysis and applied mathematics we often consider sequences arising, for example, from iterative methods that converge so slowly that they become useless. It has been proved that there cannot exist a transformation able to accelerate every sequence. Moreover, usually better results are given by transformations which are built to accelerate little classes of sequences. For this reason in the second chapter of this part we define three new transformations able to accelerate a class of sequences which extends the class of the well-known Aitken's process. We then consider the best of the three transformations and give some necessary conditions under which it accelerates the convergence of a given sequence. Finally, this transformation is compared with some of the most used transformations (Aitken's process, ε-algorithm, θ-algorithm, Levin type transformation) obtaining competitive results.Questa tesi si compone di due parti. Nella prima parte viene presentata un'estensione della formula di quadratura di Gauss per l'approssimazione dei funzionali lineari quasi-definiti. Tale estensione viene costruita partendo dalla teoria dei polinomi ortogonali e in particolare dalla relazione tra le successioni di tali polinomi e alcune matrici dette matrici di Jacobi. La formula qui proposta, detta quadratura di Gauss a n pesi, soddisfa tutte le principali proprietà delle formula “classica” che definiremo quadratura di Gauss a n nodi. Inoltre, la tesi mostra come tale estensione possa essere calcolata tramite l'algoritmo di Lanczos non Hermitiano, al pari della formula a n nodi che può essere ottenuta tramite l'algoritmo di Lanczos Hermitiano. Al termine della prima parte sono presentati alcuni risultati preliminari relativi a una delle possibili applicazioni. Si tratta dell'approssimazione di indici di centralità di reti complesse, ovvero indici che stabiliscono quale nodo in un grafo è considerato più importante in termini di facilità di trasmissione di informazioni con altri nodi. Nella seconda parte sono proposte alcune trasformazioni di successioni. Tali trasformazioni sono utilizzate al fine di ottenere, a partire da alcuni elementi di una successione data, un'altra successione che converge allo stesso limite ma a velocità maggiore. Infatti, spesso in analisi numerica e nella matematica applicata vi sono esempi di successioni, ottenute per esempio dai metodi iterativi, che convergono talmente lentamente da risultare inutili. È ben nota l’impossibilità di definire una trasformazione in grado di accelerare la convergenza di qualunque successione. Inoltre, usualmente le trasformazioni costruite per accelerare piccole classi di successione danno risultati migliori. Per questa ragione nel secondo capitolo di questa parte sono definite tre nuove trasformazioni in grado di accelerare una classe di successioni che estende quella relativa al noto processo di Aitken. Nella tesi vengono poi date condizioni necessarie affinché si abbia accelerazione della convergenza per la migliore delle tre trasformazioni proposte. Infine, tale trasformazione viene confrontata con altre trasformazioni. Da tale confronto si sono ottenuti risultati competitivi con alcuni dei più noti metodi di accelerazione (processo di Aitken, algoritmo ε, algoritmo θ, trasformazione di Levin).
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Fehringer, Franz. "Kodierung von Gaussmassen." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962880116.
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Dereich, Steffen. "High resolution coding of stochastic processes and small ball probabilities." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968920284.
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Batista, Ricardo Alexandre [UNESP]. "Tópicos de geometria diferencial." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/94373.
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batista_ra_me_rcla.pdf: 818880 bytes, checksum: 6293c2c753e3d0bd5a6900cfc890944f (MD5)O principal objetivo deste trabalho é confeccionar um texto para alunos de gradua ção na área de Ciências Exatas e da Terra concernente ao estudo da Curvatura Gaussiana e Aplicação de Gauss, Superfícies Mínimas, Teorema Egregium de Gauss e o Teorema de Gauss- Bonnet para curvas simples fechadas
The main objective from this work is to make a text for students of graduation in the area of exact sciences and of the land concerning to the study of the Gaussian Curvature and the Gauss Map, Minimal Surfaces, Gauss's Theorem Egregium and the Gauss-Bonnet Theorem for Simple Closed Curves
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Beliaeva, Tatiana. "Unités semi-locales modulo sommes de Gauss en théorie d'Iwasawa." Besançon, 2004. http://www.theses.fr/2004BESA2042.
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Morellini, Umberto. "Il teorema di Gauss-Bonnet e il teorema di Morse." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16393/.
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Le finalità di questa trattazione sono la presentazione e la dimostrazione del Teorema di Gauss-Bonnet e, conseguentemente, del Teorema di Morse. Si tratta di risultati fondamentali di geometria differenziale che evidenziano vincoli di rigidità per campi vettoriali e funzioni differenziabili definiti su varietà, dovuti alla natura topologica di quest'ultima. L'impostazione di questo elaborato prevede preliminarmente la presentazione del metodo dei "moving frames" di Cartan, il quale, avvalendosi di strumenti quali le forme differenziali, permette lo studio della geometria locale di una varietà e, in seguito, consente di ricavare quei risultati di geometria differenziale citati in precedenza e che danno il titolo alla tesi stessa.
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Noel, Filho Antonio [UNESP]. "A relação cartográfica e geometria diferencial de Mercator a Gauss." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102109.
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noelfilho_a_dr_rcla.pdf: 5554552 bytes, checksum: d7ac8c9e804b77fa358a56a9655da58b (MD5)Este trabalho é resultado de uma pesquisa que vislumbra encontrar relações entre a Cartografia e a Geometria Diferencial. Toma como ponto de partida os problemas adjacentes à Projeção de Mercator e explicita sua influencia na história do Cálculo e da Geometria Diferencial nas análises das obras de Pedro Nunes, Edward Wright e Gauss. A falta do trabalho original impediu a análise do verdadeiro método usado por Mercator na construção de sua projeção. Nos tratados, Sobre Certas Dúvidas da Navegação e em Defensam da Carta de Marear, são encontrados vestígios da contribuição da obra de Pedro Nunes na construção da Projeção de Mercator e em Certaine Errors in Navegation, Edward Wright apresenta uma justificativa matemática para o problema. O estudo da obra General Investigations of Curved Surfaces revela que o tratamento cartográfico dado aos resultados obtidos por Gauss no levantamento geodésico da cidade de Hannover serviu como base para muitos dos seus trabalhos. Os conhecimentos de Cartografia e de Astronomia adquiridos na experiência de campo, podem ter levado Gauss à formalização da teoria geral das superfícies curvas e com esta foi possível traduzir a lei da projeção de Mercator em linguagem moderna
This work is a result of research that envisions finding relations between Cartography and Differential Geometry. It takes as its starting point the problems surrounding the Mercator Projection and explains their influence in the history of calculus and differential geometry in the analysis of works of Pedro Nunes, Edward Wright and Gauss. The lack of labor prevented the original analysis of the true method used by Mercator in the construction of its projection. In the treaties, on Certain Questions of Navigation and the Letter of Defensam Marear traces of the contribution of the work of Pedro Nunes are found in the construction of the Mercator Projection and Certaine Errors in Navegation, Edward Wright presents a mathematical justification for the problem. The study of the book General Investigations of Curved Surfaces reveals that the treatment given to the mapping results obtained by the Gauss geodesic survey of Hannover city was the basis for many of his works. The knowledge of Cartography and Astronomy acquired in the field experience, may have taken Gauss to the formalization of the general theory of the surfaces curves and with this it was possible to translate the law of the projection of Mercator in modern language
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Tanzer, Christian. "Im Vergessen das Gedächtnis sein der Essayist Karl-Markus Gauss." Stuttgart Heinz, 2003. http://d-nb.info/98800612X/04.
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Brown, Richard A. "Brane world cosmology with Gauss-Bonnet and induced gravity terms." Thesis, University of Portsmouth, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.439185.
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Alenazi, Mohammed J. F., and Cenk Sahin. "Design Improvement and Implementation of 3D Gauss-Markov Mobility Model." International Foundation for Telemetering, 2012. http://hdl.handle.net/10150/581657.
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ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, CaliforniaThe current ns-3 implementation of the 3D Gauss-Markov mobility model (3D-GMMM) allows mobile nodes to reach and bounce off the simulation boundaries. This causes sudden and unnatural movement of the nodes in the vicinity of the simulation boundaries. In this paper, we present a modification to the current ns-3 implementation of the 3D-GMMM. We follow an approach in which mobile nodes are directed toward the center of the simulation region at a random angle if they are within a certain distance from the simulation boundaries. As the simulation results show, the improved ns-3 implementation of 3D-GMMM prevents mobile nodes from reaching the simulation boundaries while resulting in smooth movement.
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Assis, Carmencita Ferreira Silva. "Sistemas lineares: métodos de eliminação de Gauss e fatoração LU." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4490.
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Made available in DSpace on 2015-05-07T13:40:12Z (GMT). No. of bitstreams: 2 Dissertação - Carmencita Ferreira Silva Assis - 2014.pdf: 1032992 bytes, checksum: dcfbc22b53a2352c6e65a7615ffb72b5 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-03-20
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work aims to present te hniques for solving systems of linear equations, in its traditional formulation, where it sought to explore the referen es ommonly used in ourses in linear algebra and numeri al omputation, fo using on the dire t methods of Gauss elimination and LU fa torization. Troubleshooters established in the literature are ondu ted, in order to illustrate the operation and appli ation of su h methods to real problems, thus highlighting the possibility of inserting them in high s hool. The ontents were treated and exposed so that exemplify the diversity of areas in luding linear systems, su h as engineering, e onomi s and biology, showing the gains that an be a hieved by students if they have onta t with the methods as soon as possible. At the end we suggest the use of omputational resour es in math lasses, sin e the redu tion of time spent in algebrai manipulation will allow the tea her to deepen the on epts and to address larger systems, to enhan e the resolution perspe tive, and motivate the student in the learning pro ess.
Este trabalho tem por objetivo apresentar té ni as de resolução de sistemas de equações lineares, em sua formulação tradi ional, onde se bus ou explorar as referên ias usualmente utilizadas em ursos de álgebra linear e ál ulo numéri o, enfo ando os métodos diretos de Eliminação de Gauss e Fatoração LU. Resoluções de problemas onsolidados na literatura são realizadas, om a nalidade de ilustrar o fun ionamento e apli ação de tais métodos em problemas reais, desta ando assim a possibilidade de inserção dos mesmos no Ensino Médio. Os onteúdos foram tratados e expostos de modo que exempli quem a diversidade de áreas que abrangem os sistemas lineares, tais omo engenharia, e onomia e biologia, mostrando os ganhos que podem ser al ançados pelos alunos, se tiverem ontato om os métodos o quanto antes. Ao nal sugere- se a utilização de re ursos omputa ionais nas aulas de matemáti a, uma vez que a redução do tempo empregado na manipulação algébri a permitirá que o professor possa aprofundar os on eitos e abordar sistemas de maior porte, que ampliem a perspe tiva de resolução, além de motivar o aluno no pro esso de aprendizagem.
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Sampaio, Josà Edson. "A aplicaÃÃo de Gauss de superfÃcies no espaÃo de Heisenberg." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8627.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoFundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico
Nesta dissertaÃÃao, estudamos as superfÃcies mÃnimas do grupo de Heisenberg tridimensional, bem como a aplicaÃÃo de Gauss destas superfÃcies. Inicialmente à feito uma breve exposiÃÃo sobre a geometria do grupo de Heisenberg. EntÃo, mostramos que, em tal espaÃo: as Ãnicas superfÃcies com aplicaÃÃo de Gauss constante sÃo os planos verticais; nÃo existem superfÃcies totalmente umbÃlicas nem superfÃcies mÃnimas compactas; toda superfÃcie mÃnima Ã, necessariamente, estÃvel. Mostramos, ainda, que as Ãnicas superfÃcies mÃnimas verticais sÃo os planos verticais. Por fim, apresentamos uma classificaÃÃo das superfÃcies com aplicaÃÃo de Gauss de posto constante, igual a zero ou um.
In this report, we study minimal surfaces of the tridimensional Heisenberg group, as well as their Gauss maps. We begin with a short presentation of the geometry of the Heisenberg group. Then, we show that, in this space: the only surfaces with constant Gauss map are the vertical planes; there are no totally umbilical surfaces nor compact minimal surfaces; every minimal surface is, necessarily, stable. We also show that the only vertical minimal surfaces are vertical planes. Finally, we present a classification of the surfaces with Gauss map of constant rank, equal to zero or one.
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Zapata, Juan Fernando Zapata. "Hipersuperficies completas com curvatura de Gauss-Kronecker nula em esferas." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-07112013-142031/.
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Neste trabalho mostramos que hipersuperfícies completas da esfera Euclidiana S^4, com curvatura média constante e curvatura de Gauss-Kronecker nula são mínimas, sempre que o quadrado da norma da segunda forma fundamental for limitado superiormente. Além disso apresentamos uma descrisão local das hipersuperfícies mínimas e completas em S^5 com curvatura de Gauss- Kronecker nula e algumas hipóteses adicionais sobre as funções simétricas das curvaturas principais.In this work we show that a complete hipersurface of the unitary sphere S^4, with constant mean curvature and zero Gauss-Kronecker curvature must be minimal, if the squared norm of the second fundamental form is bounded from above. Also, we present a local description for complete minimal hipersurfaces in S^5 with zero Gauss-Kronecker curvature, and some restrictions for the symmetric functions of the principal curvatures.