Relevant bibliographies by topics / Geometric and numerical sequences

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Geometric and numerical sequences'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Geometric and numerical sequences"

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Vorontsov, Oleg, Larissa Tulupova, and Iryna Vorontsova. "Discrete modeling of building structures geometric images." International Journal of Engineering & Technology 7, no. 3.2 (June 20, 2018): 727. http://dx.doi.org/10.14419/ijet.v7i3.2.15467.

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For discrete modeling of geometric images, it is possible to use the numerical method of finite differences, the static-geometric method, the mathematical apparatus of numerical sequences. Each of them has certain advantages and disadvantages, which depend on the solution of specific practical problems.This article proposes to use the geometric apparatus of superpositions together with the above-mentioned methods. It allows significantly to improve the efficiency and expanding capacities of the process of geometric images discrete modeling. In particular, it makes it possible to investigate an opportunity of interpolating as parabolic functions as well as other elementary functional dependencies.The purpose of this article is to expand capacities of the classical finite difference method and static-geometric method by using the geometric apparatus of superpositions. It allows using hyperbolic functions as interpolators for the geometric images discrete modeling.The result of this study is the obtained interpolating and extrapolating templates, which allow modeling geometric images of architectural and building constructions in a form of chain lines discrete frames.
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Ali Suliman, Bandar. "Modeling Three-Dimensional Geometric Shapes from Nucleic Acid Sequences Using a Computerized Numerical Control." International Journal of Clinical and Experimental Medical Sciences 5, no. 3 (2019): 49. http://dx.doi.org/10.11648/j.ijcems.20190503.12.

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Guillaume, Tristan. "Computation of the Survival Probability of Brownian Motion with Drift When the Absorbing Boundary is a Piecewise Affine or Piecewise Exponential Function of Time." International Journal of Statistics and Probability 5, no. 4 (June 27, 2016): 119. http://dx.doi.org/10.5539/ijsp.v5n4p119.

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A closed form formula is provided for the probability, in a closed time interval, that an arithmetic Brownian motion remains under or above a sequence of three affine, one-sided boundaries (equivalently, for the probability that a geometric Brownian motion remains under or above a sequence of three exponential, one-sided boundaries). The numerical evaluation of this formula can be done instantly and with the accuracy required for all practical purposes. The method followed can be extended to sequences of absorbing boundaries of higher dimension. It is also applied to sequences of two-sided boundaries.
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Chen, Yao, and Jian Feng. "Numerical Simulations on the Cable Clamp of a Concave Cable Arch." Applied Mechanics and Materials 105-107 (September 2011): 381–85. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.381.

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The inner concave cable arch structure has been adopted in some engineering applications in recent years. Geometric configuration of the cable clamp joint and its anti-sliding performance is the key to assure the bearing capacity for this type of structure. In this study, nonlinear finite element analysis on the cable clamp joint of a concave cable arch is performed using ABAQUS, with influences of the friction coefficients and the nonlinearity of materials are investigated. The pretension loss of bolts caused by different tightening sequences is also discussed. It is found that nearly 9% of the initial pretension force for each bolt gets lost during the tightening process, and mutual influence of the bolts can be significantly weakened by applying reasonable tightening sequence.
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Boruah, Khirod, and Bipan Hazarika. "Application of geometric calculus in numerical analysis and difference sequence spaces." Journal of Mathematical Analysis and Applications 449, no. 2 (May 2017): 1265–85. http://dx.doi.org/10.1016/j.jmaa.2016.12.066.

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Ji, Peng, Qing Hua Dai, Chen Bo Yin, Di Sheng Yi, Bin Wang, and Jie Zhu. "Influences of Welding Sequence on Residual Stress of Plate Butt Welding." Applied Mechanics and Materials 26-28 (June 2010): 568–72. http://dx.doi.org/10.4028/www.scientific.net/amm.26-28.568.

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For the plate butt welding of the same materials with different geometry structures, the numerical simulation was adopted to analyze the influences of welding sequence on transverse and longitudinal residual stress in the process of multi-layer and multi-pass welding. The results show that when welding from the small geometric side to the large side, the peak values of transverse and longitudinal residual stress are min along the bottom or top axis of the weld. And the welding sequences of the foremost welds have little effects on transverse and longitudinal residual stress along the bottom or top axis of the weld.
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He, Qi-Ming, and Marcel F. Neuts. "On the convergence and limits of certain matrix sequences arising in quasi-birth-and-death Markov chains." Journal of Applied Probability 38, no. 02 (June 2001): 519–41. http://dx.doi.org/10.1017/s0021900200020015.

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We study the convergence of certain matrix sequences that arise in quasi-birth-and-death (QBD) Markov chains and we identify their limits. In particular, we focus on a sequence of matrices whose elements are absorption probabilities into some boundary states of the QBD. We prove that, under certain technical conditions, that sequence converges. Its limit is either the minimal nonnegative solution G of the standard nonlinear matrix equation, or it is a stochastic solution that can be explicitly expressed in terms of G. Similar results are obtained relative to the standard matrix R that arises in the matrix-geometric solution of the QBD. We present numerical examples that clarify some of the technical issues of interest.
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He, Qi-Ming, and Marcel F. Neuts. "On the convergence and limits of certain matrix sequences arising in quasi-birth-and-death Markov chains." Journal of Applied Probability 38, no. 2 (June 2001): 519–41. http://dx.doi.org/10.1239/jap/996986760.

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We study the convergence of certain matrix sequences that arise in quasi-birth-and-death (QBD) Markov chains and we identify their limits. In particular, we focus on a sequence of matrices whose elements are absorption probabilities into some boundary states of the QBD. We prove that, under certain technical conditions, that sequence converges. Its limit is either the minimal nonnegative solution G of the standard nonlinear matrix equation, or it is a stochastic solution that can be explicitly expressed in terms of G. Similar results are obtained relative to the standard matrix R that arises in the matrix-geometric solution of the QBD. We present numerical examples that clarify some of the technical issues of interest.
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Makarov, V. L., N. O. Rossokhata, and B. I. Bandurskii. "Functional-Discrete Method with a High Order of Accuracy for the Eigenvalue Transmission Problem." Computational Methods in Applied Mathematics 4, no. 3 (2004): 324–49. http://dx.doi.org/10.2478/cmam-2004-0018.

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AbstractWe develop a functional-discrete method with a high order of accuracy to find a numerical solution of an eigenvalue transmission problem. It allows to approximate the trial eigenvalue with any desired accuracy. This approach has no restriction on the number of eigenvalues, an approximation to which can be found. The convergence rate is proved as in the case of the geometric series. It is shown that depending on the data of the original problem, two kinds of eigenvalue sequences may exist. For the first one, the convergence rate increases as the ordinal number of the trial eigenvalue increases. For the second one, the convergence rate is the same for all eigenvalues and does not depend on the ordinal number of the trial eigenvalue. Based on the asymptotic behavior of the eigenvalues of the basic problem and the functional-discrete method, a qualitative result on the arrangement of eigenvalues of the original problem is established. A number of numerical examples are given to support the theory.
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Sahoo, Soumya Ranjan. "Active damping of geometrically nonlinear vibrations of smart composite shells using elliptical smart constrained layer damping treatment with fractional derivative viscoelastic layer." Journal of Intelligent Material Systems and Structures 31, no. 4 (December 25, 2019): 587–611. http://dx.doi.org/10.1177/1045389x19888800.

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In this article, the performance of elliptical smart constrained layer damping treatments on active damping of geometrically nonlinear vibrations of doubly curved smart laminated composite shells is analyzed. The constraining layers of the smart constrained layer damping treatments comprised vertically/obliquely reinforced 1–3 piezoelectric composites, while the constrained layers of isotropic viscoelastic materials are modeled using the three-dimensional fractional order derivative model. A mesh-free model of the smart composite shells is developed for analyzing their nonlinear transient responses within the framework of a layerwise shear and normal deformation theory considering the von Kármán–type geometric nonlinearity. Thin, doubly curved laminated composite shells integrated with elliptical/rectangular smart constrained layer damping patches with different stacking sequences and boundary conditions are considered for presenting the numerical results. The numerical analyses demonstrate the higher effectiveness of the elliptical smart constrained layer damping treatments over the rectangular ones in attenuating the nonlinear vibrations of laminated composite shells.
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Dissertations / Theses on the topic "Geometric and numerical sequences"

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TITONELI, LUANA MIRANDA BALTAZAR. "THE PATTERN OBSERVATION: MATHEMATICAL MODELING THROUGH NUMERICAL SEQUENCES AND GEOMETRIC OBJECTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33077@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL
Este trabalho é uma análise de padrões que são modelados matematicamente através de conceitos que envolvem as sequências numéricas bem como aspectos geométricos. São consideradas algumas aplicações práticas de conteúdos trabalhados na educação básica, muitas vezes estudados de forma mecânica através de fórmulas que tornam a Matemática enfadonha e até sem sentido para os discentes. O objetivo é mostrar que a Matemática transpõe os limites das salas de aula e que sua beleza pode ser vista em áreas diversas. As ideias e conceitos que envolvem as Progressões Aritméticas e Geométricas, por exemplo, são úteis na resolução de várias situações. A arte musical que está envolta em conhecimentos matemáticos desde os primórdios de seu desenvolvimento. Os estudos desenvolvidos com a sequência de Fibonacci e como está relacionada com a razão áurea e com fenômenos naturais que aparentemente nada teriam em comum. Além disso, a presença tão marcante na natureza das características dos fractais que traçam um padrão de formação para certos elementos naturais. É possível fazer com que o processo ensino- aprendizagem de Matemática torne-se efetivo através da abordagem dos conteúdos de forma prática, o que desperta no aluno o desejo de compreender o que é proposto. Este trabalho é inspirado na frase de Pitágoras: A Matemática é o alfabeto com o qual Deus escreveu o Universo e o que pretende-se é mostrar que esta ciência de fato está em toda a parte e que seu aprendizado pode ser significativo e interessante.
This work is an analysis of patterns that are modeled mathematically through concepts involving numerical sequences as well as geometric aspects. Some practical applications of content worked in basic education are considered, often mechanically studied through formulas that make Mathematics boring and even meaningless to students. The goal is to show that Mathematics transposes the boundaries of classrooms and that its beauty can be seen in several areas. The ideas and concepts that involve Arithmetic and Geometric Progressions, for example, are useful in solving various situations. The musical art that is shrouded in mathematical knowledge from the beginnings of its development. The studies developed with the Fibonacci sequence and how it is related to the golden ratio and with natural phenomena that apparently would have nothing in common. In addition, the presence so striking in the nature of the characteristics of the fractals that lay out a pattern of formation for certain natural elements. It is possible to make the teaching-learning process of Mathematics become effective by approaching the contents in a practical way, which awakens in the student the desire to understand what is proposed. This work is inspired by the phrase of Pythagoras: Mathematics is the alphabet with which God wrote the Universe and what is intended is to show that this science is indeed everywhere and that its learning can be meaningful and interesting.
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Batista, Bárbara Regina da Silveira. "SEQUÊNCIAS NUMÉRICAS A PARTIR DA GEOMETRIA FRACTAL PARA LICENCIANDOS EM MATEMÁTICA Santa Maria 2017." Centro Universitário Franciscano, 2017. http://www.tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/595.

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Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T17:13:03Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_BarbaraReginaDaSilveiraBatista.pdf: 2388062 bytes, checksum: 2cec4c9f6c44ba531dba7b28764e1215 (MD5)
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This dissertation is a result of a mathematic investigation carried out in an university, located in Santa Maria/RS, that had as objective investigate which contributions of Fractal Geometry, when was used to introduce the content of numerical sequences, to Mathematics students. This is a mathematical investigation, as a research methodology, for systematization of teaching, complemented by the qualitative approach. Fractal Geometry allows the integration of many Mathematic fields and others sciences and, when inserted in teaching process, can develop the experimental side of students and understand as a facilitator to apropration of numerical sequences concepts. The data collect was by means of photographical register, notes, material made by participants and constructions and performed registered activities in a field journal, during two horas in each workshop. Previously, the application was developed in a pilot Project, with a activities sequence, involving three licenced Mathematics professor, belonging at the institution that the researcher acts and they had experience with calculation, Statistics, discrete mathematics, analytical geometry and linear algebra subjects. Such professors never had worked with fractal geometry, even though they had some superficial knowledge about the subject, without however using it in their activities. Workshop application with professor allowed a reflexion of the referrals given by the researcher and provided the correction of ways to posterior reapplication with the graduates.in a first meeting, the researcher made a survey about the students framing on a logical sequence of graduation, concluding every graduates had finished some calculation subject. At the same meeting, explored a fractal construction by materials resources as ruler and compass, recovering some contents, forgetted by them. In the second meeting, was resumed the Snowflake fractal, builded at first meeting, to obtain sequences, involving perimeters and áreas. In a survey, applied to participants, was verified the relevance of project to recover knowledges of numerical sequences convergence, that the same indicated possibilities of using in a future professional practic, since the application was made in Mathematic Analysis and the focus in the workshop had given a new sight about the contente in a direction of teaching, main object of professor training.
Esta dissertação é resultante de uma investigação matemática realizada em uma Instituição de Ensino Superior no Município de Santa Maria/RS, a qual teve como objetivo investigar quais as contribuições da Geometria Fractal quando utilizada para introdução do conteúdo de sequências numéricas para licenciandos em Matemática. Trata-se da Investigação Matemática, como metodologia de pesquisa, para a sistematização do ensino, complementando-se por meio de uma abordagem qualitativa. A Geometria Fractal permite a integração de vários campos da Matemática e de outras ciências e, quando inserida no ensino, pode desenvolver o lado experimental dos alunos e entender Geometria como facilitadora para apropriação de conceitos de sequências numéricas. A coleta de dados deu-se por meio de registro fotográfico, anotações, material confeccionado pelos participantes e as construções e atividades realizadas e registradas em diário de campo durante dois encontros de 2 horas cada em uma oficina. Anteriormente à aplicação com os estudantes foi desenvolvido um projeto piloto com a sequência de atividades, envolvendo três professores com Licenciatura em Matemática, pertencentes à instituição em que a pesquisadora atua e que já tinham experiência com as disciplinas de Cálculo, Estatística, Matemática Discreta, Geometria Analítica e Álgebra Linear. Tais professores nunca haviam trabalhado com Geometria Fractal, muito embora tivessem algum conhecimento superficial da mesma, sem, entretanto, a utilizarem em suas atividades. A aplicação da oficina com os professores permitiu reflexão sobre os encaminhamentos dados pela pesquisadora e proporcionou correção de rumos para replicação posterior com os licenciandos. Num primeiro encontro a pesquisadora fez um levantamento sobre o enquadramento dos estudantes no quadro de sequência lógica do curso, tendo concluído que todos já haviam cursado alguma disciplina de Cálculo. No mesmo encontro explorou a construção de um fractal por meio de recursos materiais como régua e compasso, resgatando alguns conteúdos já esquecidos por eles. No segundo encontro, foi retomado o fractal Floco de Neve, construído no primeiro encontro, para obtenção de sequências envolvendo perímetros e áreas. Num questionário aplicado aos participantes foi constatada a relevância do projeto para resgatar conhecimentos de convergência de sequência numéricas, sendo que os mesmos indicaram possibilidades de utilização na prática profissional futura, uma vez que a aplicação foi realizada na disciplina de Análise Matemática e o foco dado na oficina proporcionou um novo olhar sobre o conteúdo voltado ao ensino, objeto principal da formação de professores.
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Brum, Maria Gorete Nascimento. "ATIVIDADES INVESTIGATIVAS PARA O ENSINO DE MATEMÁTICA PARA ALUNOS DE 5º SÉRIE DO ENSINO FUNDAMENTAL." Universidade Franciscana, 2012. http://tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/128.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present research investigated the contributions of the use of investigative activities in the exploration of standards and regularities in numerical and geometric sequences as elements that become easy the learning of the pupils of 5º series of Basic Education. This work was carried through with a group of 5º degree with 30 pupils of the State school of Basic Education Marechal Rondon in the periphery of the city of Santa Maria, RS. The date of the research, qualitative matrix, had been gotten of the direct action teacher s in the classroom with the pupils by means of the observation and the registers in its diary beyond the analysis of the pupils, work and the presentations to the great group. It can be inferred that the objectives considered in the sessions as explore the standard concept, to recognize, to describe standards, to continue the drawing of the sequence was reached. The objectives to generalize, to explore the notion and properties of the numbers pairs, uneven and multiple, as well as the involution of natural numbers and to work the concept of area and perimeter of plain figures, partially had been reached. The results presented for the pupils it can be concluded that the investigative activities worked with the pupils of 5ª degree, had propitiated the increase of interest, the motivation in the accomplishment of the activities proposals in classroom and as consequence had an improvement in the learning.
A presente pesquisa investigou as contribuições da utilização de atividades investigativas na exploração de padrões e regularidades em sequências numéricas e geométricas como elementos facilitadores da aprendizagem dos alunos de 5º série do Ensino Fundamental. Este trabalho foi realizado com uma turma de 5º série com 30 alunos da escola Estadual de Ensino Fundamental Marechal Rondon na periferia de Santa Maria R.S. Os dados da pesquisa, de cunho qualitativo, foram obtidos da ação direta do professor na sala de aula com os alunos por meio da observação e dos registros no seu diário de campo, além da análise dos trabalhos dos alunos e de suas apresentações ao grande grupo. Pode-se inferir que os objetivos propostos nas sessões como explorar o conceito de padrões, reconhecer, descrever padrões, continuar o desenho da sequência foram plenamente atingidos. Os objetivos de generalizar, explorar a noção e propriedade dos números pares, ímpares e múltiplos, bem como a potenciação de números naturais e trabalhar o conceito de área e perímetro de figuras planas, foram parcialmente atingidos. Dos resultados apresentados pelos alunos pode-se concluir que as atividades investigativas trabalhadas com os alunos de 5º série, propiciaram o aumento de interesse, a motivação na realização das atividades propostas em sala de aula e como consequência houve uma melhoria na aprendizagem.
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Kaneko, Hajime. "LIMIT POINTS OF FRACTIONAL PARTS OF GEOMETRIC SEQUENCES." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120624.

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Palmacci, Matthew Stephen. "Escher's problem and numerical sequences." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-042706-133106/.

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Lawver, Jordan D. "Robust Feature Tracking in Image Sequences Using View Geometric Constraints." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365611706.

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Alsallami, Shami Ali M. "Discrete integrable systems and geometric numerical integration." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22291/.

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This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplectic schemes for Hamiltonian systems are accurate over long times. However, for nonlinear systems the series defining the modified Hamiltonian equation usually diverges. The first part of the thesis demonstrates that there are nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. Specifically, they arise as reductions of a lattice version of the Korteweg-de Vries (KdV) partial differential equation. We present cases of one and two degrees of freedom symplectic mappings, for which the modified Hamiltonian equations can be computed as a closed form expression using techniques of action-angle variables, separation of variables and finite-gap integration. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example is a system of an implicit dependence on the time step, which is obtained by dimensional reduction of a lattice version of the modified KdV equation. The second part of the thesis contains a different class of discrete-time system, namely the Boussinesq type, which can be considered as a higher-order counterpart of the KdV type. The development and analysis of this class by means of the B{\"a}cklund transformation, staircase reductions and Dubrovin equations forms one of the major parts of the thesis. First, we present a new derivation of the main equation, which is a nine-point lattice Boussinesq equation, from the B{\"a}cklund transformation for the continuous Boussinesq equation. Second, we focus on periodic reductions of the lattice equation and derive all necessary ingredients of the corresponding finite-dimensional models. Using the corresponding monodromy matrix and applying techniques from Lax pair and $r$-matrix structure analysis to the Boussinesq mappings, we study the dynamics in terms of the so-called Dubrovin equations for the separated variables.
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San, Juan Camilo Andrés Méndez. "Texts, numerical sequences and patterns in my recent music." Thesis, Royal College of Music, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.691366.

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Radvar-Esfahlan, Hassan. "Fixtureless geometric inspection of nonrigid parts using "generalized numerical inspection fixture"." Mémoire, École de technologie supérieure, 2014. http://espace.etsmtl.ca/1294/1/RADVAR_ESFAHLAN_Hassan.pdf.

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Aujourd’hui les pièces mécaniques de forme libre et qui sont souples (non rigides) sont fréquentes dans les industries automobile et aéronautique. Ces pièces possèdent des formes significativement différentes à l'état libre que leurs formes nominales, telles que définies dans un modeleur numérique, en raison de leurs variations dimensionnelles et géométriques, l’effet de la gravité et les contraintes résiduelles induites par le procédé de fabrication. Pour l'inspection géométrique de ces pièces flexibles, des appareils d'inspection spécialisés tel que les gabarits de conformation, en combinaison avec les machines à mesure tridimensionnelle (MMT) et/ou des dispositifs d'acquisition de données optiques (scanners) sont utilisés. Ce qui se traduit immanquablement par des coûts et des délais additionnels qui se traduisent par une carence de compétitivité pour l’industrie. L'objectif de cette thèse est de faciliter l'inspection dimensionnelle et géométrique des composants flexibles à partir d'un nuage de points sans l'aide d’un gabarit ou autre opération de conformation secondaire. Plus précisément, nous visons à développer une méthodologie pour localiser et quantifier les défauts de profil dans le cas des coques minces qui sont typiques pour les industries aéronautique et automobile. La méthodologie présentée est basée sur le fait que la distance géodésique entre deux points d'une forme demeure invariante au cours d'une déformation isométrique (absence d’étirement, stretch). Cette étude développe donc la théorie générale, les méthodes et outils pour une métrologie des pièces non rigides en se basant sur l’hypothèse d’une déformation isométrique. Nous avons ainsi développé une méthode originale que nous avons nommée ‘Gabarit d'Inspection Numérique Généralisée (GNIF)’. C’est une méthodologie robuste qui utilise les découvertes et technologies récemment développées en géométrie métrique et algorithmique. Les techniques de réduction dimensionnelle non linéaire sont employées pour identifier les meilleures correspondances entre deux sets de points (CAD et nuage mesuré). Finalement, la méthode des éléments finis est employée en post-traitement pour ‘caler’ les deux nuages de points et produire un état numérique ‘virtuel’ d’une opération de conformation pour atteindre le but du projet qui est de développer une approche générale de l'inspection géométrique sans gabarit pour les pièces non rigides. La validation et l’exploration des performances métrologiques de notre approche sont réalisées sur des composants typiques de l’industrie.
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Fasi, Massimiliano. "Weighted geometric mean of large-scale matrices: numerical analysis and algorithms." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8274/.

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Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.
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Books on the topic "Geometric and numerical sequences"

1

Hairer, Ernst, Gerhard Wanner, and Christian Lubich. Geometric Numerical Integration. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-05018-7.

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K, Agarwal Pankaj, ed. Davenport-Schinzel sequences and their geometric applications. Cambridge: Cambridge University Press, 1995.

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Bonnard, Bernard, Monique Chyba, and Jérémy Rouot. Geometric and Numerical Optimal Control. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94791-4.

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Geometric Numerical Integration and Schrödinger Equations. Zürich, Switzerland: European Mathematical Society, 2012.

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Laumond, Jean-Paul, Nicolas Mansard, and Jean-Bernard Lasserre, eds. Geometric and Numerical Foundations of Movements. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51547-2.

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Hasle, Geir, Knut-Andreas Lie, and Ewald Quak, eds. Geometric Modelling, Numerical Simulation, and Optimization. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-68783-2.

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Borouchaki, Houman, and Paul Louis George. Meshing, Geometric Modeling and Numerical Simulation 1. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119384335.

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George, Paul Louis, Houman Borouchaki, Frédéric Alauzet, Patrick Laug, Adrien Loseille, and Loïc Maréchal. Meshing, Geometric Modeling and Numerical Simulation 2. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781119384380.

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Whitney, Hassler. Geometric integration theory. Mineola, N.Y: Dover Publications, 2005.

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Udriște, Constantin. Geometric dynamics. Dordrecht: Kluwer Academic Publishers, 2000.

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Book chapters on the topic "Geometric and numerical sequences"

1

Loureiro-Ga, Marcos, Maria F. Garcia, Cesar Veiga, G. Fdez-Manin, Emilio Paredes, Victor Jimenez, Francisco Calvo-Iglesias, and Andrés Iñiguez. "An Aortic Root Geometric Model, Based on Transesophageal Echocardiographic Image Sequences (TEE), for Biomechanical Simulation." In Computational Mathematics, Numerical Analysis and Applications, 249–54. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49631-3_15.

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Davies, T. J. G., R. R. Martin, and A. Bowyer. "Computing Volume Properties Using Low-Discrepancy Sequences." In Geometric Modelling, 55–72. Vienna: Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-6270-5_4.

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An, Myoung, Andrzej K. Brodzik, and Richard Tolimieri. "Permutation Sequences." In Applied and Numerical Harmonic Analysis, 1–17. Boston: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4738-4_11.

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Iserles, Arieh, and G. R. W. Quispel. "Why Geometric Numerical Integration?" In Discrete Mechanics, Geometric Integration and Lie–Butcher Series, 1–28. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01397-4_1.

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Moraglio, Alberto, Riccardo Poli, and Rolv Seehuus. "Geometric Crossover for Biological Sequences." In Lecture Notes in Computer Science, 121–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11729976_11.

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Chan, Agnes Hui, Mark Goresky, and Andrew Klapper. "Correlation Functions of Geometric Sequences." In Advances in Cryptology — EUROCRYPT ’90, 214–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-46877-3_19.

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Rabinowitz, Philip, Jaroslav Kautsky, Sylvan Elhay, and John C. Butcher. "On Sequences of Imbedded Integration Rules." In Numerical Integration, 113–39. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3889-2_13.

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Rohwer, Carl. "Operators on Sequences." In International Series of Numerical Mathematics, 1–7. Basel: Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7382-2_1.

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Winter, Steffen. "Geometric Measures for Fractals." In Applied and Numerical Harmonic Analysis, 73–89. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4888-6_6.

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Kimmel, Ron. "Geometric Framework in Image Processing." In Numerical Geometry of Images, 141–62. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-21637-9_10.

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Conference papers on the topic "Geometric and numerical sequences"

1

Konca, Şükran, and Mahpeyker Öztürk. "Some topological and geometric properties of sequence spaces involving lacunary sequence in n-normed spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756302.

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Wang, Hua, and Jun Liu. "Study on the Effect of Clamping Sequence on Bulk Stress Redistribution of Long Edge." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50272.

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For a given assembly process, fixture-related operations contribute to the dimensional variations of compliant part. When the manufactured components are within the specified tolerances, the bulk stresses distribution of the assembly are respected. In addition to fixture geometric errors and clamping forces, the clamping sequence can also affect part bulk stress redistribution. This paper presents a numerical simulation of bulk stress redistribution in a long edge assembling with different clamping sequences. A finite element model of the plate with residual stresses after quenching and stretching is constructed. The edge is milled from the numerical plate, and the edge with the initial deformation and residual stresses is ready for clamping. The contact model between the clamper and edge is constructed to simulate the practical clamping process, especially considering the friction contact between the clamper and edge. Then the edge is virtually clamped in different clamping sequences, and its deformation and bulk stresses are obtained. The simulation results show that there are differences in the stains of edge under different clamping sequences, and the edge’s bulk stresses under different clamping sequences are different with each other also. The proposed numerical model could predict the edge’s bulk stresses under different clamping sequences. It will help obtaining optimal stresses of the edge by certain clamping sequence, and help systematically improving the compliant assembling efficiency in civil aircraft industry.
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Evaristo, Jerónimo, Paula Catarino, Helena Campos, and Ana Paula Aires. "TEACHING NUMERICAL SEQUENCES FROM GEOMETRY IN THE 2ND CYCLE OF SECONDARY EDUCATION." In 14th International Technology, Education and Development Conference. IATED, 2020. http://dx.doi.org/10.21125/inted.2020.1052.

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Panta Pazos, Rube´n. "Behavior of a Sequence of Geometric Transformations for a Truncated Ellipsoid Geometry in Transport Theory." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75758.

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The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8, but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5. Horseshoe domain: for that it is used the complex function: f:D→C,definedasf(z)=12ez+1ezwhereD=z∈C−0.5≤Re(z)≤0.5,−12π≤Im(z)≤12π(0.1) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.
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Gou, J. B., Y. X. Chu, and Z. X. Li. "A Geometric Theory for Form, Profile and Orientation Tolerances: Evaluation Algorithms and Simulation Results." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dfm-5744.

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Abstract Using the geometric theory for formulation of form, profile and orientation tolerances, we develop a simple geometric algorithm, called the Symmetric Minimum Zone (SMZ) algorithm, to unify the computation of form, profile and orientation tolerances. First, using a technique of numerical analysis, we transform the non-differentiable minimization problem into a differentiable minimization problem over an extended configuration space. Then, we solve the latter problem by computing the solutions of a sequence of linear programming problems which can be easily derived using the geometric properties of SE(3)/G0. The SMZ algorithm is incorporated into a software package called GTPack for tolerance verification. Numerous simulation experiments show that the SMZ algorithm has several important features which could lead to its rapid acceptance in the industry: (1) consistency with the Y14.5M standard, (2) computational efficiency, (3) robustness with respect to variations in initial conditions; and (4) implementational simplicity. We also give extensive simulation results comparing the performances of the SMZ algorithm against the best known algorithms in the literature.
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Yaghoubi, A. Seyed, and B. Liaw. "Determination of Ballistic Limits of GLARE 5 Fiber-Metal Laminates: The Influences of Geometry, Thickness and Stacking Sequence." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62139.

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In this paper, GLARE 5 fiber-metal laminates (FMLs) of two different geometries: 152.4mm×101.6mm (6″×4″) plate and 254mm×25.4mm (10″×1″) beam and with various thicknesses and stacking sequences were impacted by a 0.22 caliber bullet-shaped projectile using a high-speed gas gun. Velocities of the projectile along the ballistic trajectory were measured at different locations. For both geometries, the incident projectile impact velocity versus the residual velocity was plotted and numerically fitted according to the classical Lambert–Jonas equation for the determination of ballistic limit velocity, V50. The results showed that V50 varied in a parabolic trend with respect to the metal volume fraction (MVF) and the specimen thickness for both geometries. It was found that by changing the geometry from a plate to a beam, the ballistic limit velocity increased. On the other hand, changing the stacking sequence had a less pronounced effect on V50 for both geometries. The quasi-isotropic beam and plate specimens offered relatively higher ballistic limit velocities compared to other types of stacking sequences in their own geometrical groups. Furthermore, the cross-ply and unidirectional beam specimens showed relatively higher V50 compared to their plate counterparts. Experimental results showed that the ballistic limit was almost the same for the quasi-isotropic layup FMLs of both plate and beam geometries.
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Pomier Ba´ez, L. E., J. E. Nun˜ez Mac Leod, and J. H. Baro´n. "Severe Accident Improvements for CAREM-25 to Arrest Reactor Vessel Meltdown Sequences." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22304.

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Advanced nuclear reactor designs, such as the CAREM reactor, include several improvements related to safety issues either enhancing the passive safety functions or allowing plant operators more time to undertake different management actions against radioactive releases to the environment. In the development of the nuclear power plant CAREM, the possibility of including a passive metallic in-vessel container in its design is being considered, to arrest the reactor pressure vessel meltdown sequence during a core damaging event, and thereof prevent its failure. The paper comprises the analyses, via numerical simulation, for the conceptual design of such a container type. Simulation model characteristics helping to establish geometrical dimensions, materials and container compatibility with power plant engineering features is addressed. The paper also presents the first model developed to analyze the complex relocation phenomena in the core of CAREM during a severe accident sequence caused by a loss of coolant. The PC version of MELCOR 1.8.4 code has been used to predict the transient behavior of core parameters. The finite element analysis (FEA) system ALGOR has been used to evaluate the thermal regime of the reactor pressure vessel wall, when the in-vessel metallic core catcher is present and when it is not present. Two different scenarios have been considered for heat transfer outside the reactor vessel, a pessimistic (dry) and optimistic (wet) conditions in the reactor cavity. This paper presents reactor variables behavior during the first hours of the event being studied, giving preliminary conclusions about the use and capability of a metallic in-vessel core catcher.
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8

Rui Ling, Yuanjun He, and Kairen Deng. "Automatic generation of geometric base sequences." In 2010 International Conference on Progress in Informatics and Computing (PIC). IEEE, 2010. http://dx.doi.org/10.1109/pic.2010.5687899.

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Sharir, Micha, Richard Cole, Klara Kedem, Daniel Leven, Richard Pollack, and Shmuel Sifrony. "Geometric applications of Davenport-Schinzel sequences." In 27th Annual Symposium on Foundations of Computer Science (sfcs 1986). IEEE, 1986. http://dx.doi.org/10.1109/sfcs.1986.23.

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Gu, Shengyin, Olivier Poch, Bernd Hamann, and Patrice Koehl. "A Geometric Representation of Protein Sequences." In 2007 IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2007). IEEE, 2007. http://dx.doi.org/10.1109/bibm.2007.22.

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