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Dissertations / Theses on the topic 'Loops'

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1

Makkos, Joseph. "Recursive Loops." ScholarWorks@UNO, 2006. http://scholarworks.uno.edu/td/357.

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2

Taufer, Daniele. "Elliptic Loops." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. St
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3

Taufer, Daniele. "Elliptic Loops." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. St
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4

Spohr, Cristina. "Loops de Bol 2-nilpotentes e de expoente 2." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-16042010-133822/.

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Neste trabalho estudamos loops de Bol 2-nilpotentes e de expoente 2. Além disso, mostramos que o ideal de aumento de uma álgebra de loop, de um loop finito p-nilpotente em característica p > 0, é nilpotente. Com este resultado conseguimos caracterizar os elementos inversíveis da álgebra de loop de um loop 2-nilpotente sobre um corpo de dois elementos. Provamos também que loops de Bol finitos 2-nilpotentes e de expoente 2 podem ser mergulhados em um loop de Bol à direita de elementos inversíveis de uma álgebra alternativa à direita, sobre um corpo de característica dois.<br>In this work we stud
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5

Mehraban, Mehrdad. "Instant Feedback Loops – for short feedback loops and early quality assurance." Thesis, Blekinge Tekniska Högskola, Institutionen för kommunikationssystem, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-13379.

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Context. In recent years, Software Quality Assurance (SQA) has become a crucial part of software development processes. Therefore, modern software development processes led to an increase in demand for manual and automated code quality assurance. Manual code quality reviews can be a time-consuming and expensive process with varying results. Thus, automated code reviews turn out to be a preferred alternative for mitigating this process. However, commercial and open-source static code analyzer tools often offer deep analysis with long lead time. Objectives. In this thesis work, the main aim is t
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6

Gabrieli, Elisabetta. "Spiegelungsstrukturen und K-Loops." [S.l. : s.n.], 2000. http://www.sub.uni-hamburg.de/disse/113/inhalt.html.

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7

Stener, Mikael. "Moufang Loops : General theory and visualization of non-associative Moufang loops of order 16." Thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-295889.

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8

Fernández, Fuentes Narcís. "Classification of loops in protein structures: applications on loop modeling and protein function." Doctoral thesis, Universitat Autònoma de Barcelona, 2004. http://hdl.handle.net/10803/3516.

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Aquesta tesis esta estructurada en cinc capítols. Al capítol I, es fa una introducció als llaços, el subjecte d'estudi d'aquesta tesis. A més, es fa una petita introducció a les bases de dades biològiques de us corrent i de protocols bio-informàtics en comparacions de seqüències. Del capítol II al IV s'explora el paper que els llaços juguen a les proteïnes utilitzant un enfocament bio-informàtic, es realitza una classificació estructural de llaços (capítol II); es realitza un estudi per inferir relacions d'estructura i funció (capítol III) i es realitza un estudi de predicció d'estructura de l
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9

Gowanlock, Graham Keith. "Impulse noise on telephone loops." Thesis, University of Ottawa (Canada), 1993. http://hdl.handle.net/10393/6611.

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Impulse noise is an ever increasing impediment to successful digital data transmission in the telephone local cable plant. Two major factors have caused this to happen. Firstly, remedies have been found for nearly all the other causes of signal degradation, such as crosstalk and intersymbol interference, leaving impulse noise outstanding. Secondly, the user's demand for higher and higher data rates and the proliferation of repeaterless operation at extended loop ranges, have made the effects of impulse noise more prominent. This thesis covers the subject of impulse noise in the local plant. It
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10

Zhou, Yongxin. "Alternative algebras and RA loops." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/NQ42490.pdf.

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11

Horch, Alexander. "Condition Monitoring of Control Loops." Doctoral thesis, Stockholm : Tekniska högsk, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3050.

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12

Blacklaw, Grant Andrew. "Permutations, loops and difference sets." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406303.

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13

Steer, Daniele Ann. "Thermal fields and cosmic loops." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267263.

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14

Chintapalli, Sree Vamsee. "Closed loops in protein folding." Thesis, University of Essex, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.494193.

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15

Bordonalli, Aldario Chrestani. "Optical injection phase-lock loops." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244183.

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16

Bauer, Sven. "Loops on real Stiefel-manifolds." Thesis, University of Aberdeen, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367371.

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The central object of the study in this thesis is ΩO(<I>n</I>), the space of closed continuous loops on an orthogonal group O(<I>n</I>) based at the identity-element 1 Ε O(<I>n</I>). The space ΩO(<I>n</I>) carries a group structure given by pointwise multiplication of paths in the group O(<I>n</I>). This makes it an infinite dimensional Lie group. A filtration of ΩO(<I>n</I>), more precisely of the subspace of 'polynomial' loops, is constructed. This can be thought of as the 'real' analogue of the Mitchell-Richter filtration of ΩSU(<I>n</I>). Our filtration of ΩO(<I>n</I>) splits stably and O(
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17

Anjos, Giliard Souza dos. "Half-Isomorfismos de loops automórficos." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-03052018-221550/.

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Loops automórficos, ou A-loops, são loops nos quais todas as aplicações internas são automorfismos. Esta variedade de loops inclui grupos e loops de Moufang comutativos. Loops automórficos diedrais formam uma classe de A-loops construda a partir da duplicação de grupos abelianos finitos, generalizando a construção do grupo diedral. Outra classe de A-loops é a dos loops automórficos de Lie, construda a partir de anéis de Lie, definindo-se uma nova operação entre seus elementos. Um half-isomorfismo é uma bijeção f entre loops L e L\' onde, para quaisquer x e y pertencentes a L, temos que f(xy) p
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18

FARIA, JUNIOR Joél. "Skew Loops e Superfícies Quádricas." reponame:Repositório Institucional da UNIFEI, 2017. http://repositorio.unifei.edu.br:8080/xmlui/handle/123456789/686.

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Submitted by repositorio repositorio (repositorio@unifei.edu.br) on 2017-03-15T18:01:49Z No. of bitstreams: 1 dissertacao_faria_junior_2017.pdf: 937266 bytes, checksum: 9969706623eab67e1e85bc07ef6bd2b1 (MD5)<br>Made available in DSpace on 2017-03-15T18:01:49Z (GMT). No. of bitstreams: 1 dissertacao_faria_junior_2017.pdf: 937266 bytes, checksum: 9969706623eab67e1e85bc07ef6bd2b1 (MD5) Previous issue date: 2017-03<br>O objetivo deste trabalho é o estudo da relação entre skew loops e superfícies quádricas. Mostramos que as únicas superfícies do ℝ³ com um ponto onde a curvatura é positiva e que
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19

Allegro, Matteo. "Un'introduzione a quasigruppi e loops." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/4160/.

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20

Larsen, Kasper J. "Maximal Unitarity at Two Loops : A New Method for Computing Two-Loop Scattering Amplitudes." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179203.

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The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation. Our main resu
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21

Dang, Francis Hoai Dinh. "Speculative parallelization of partially parallel loops." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1271.

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22

Scott, Jason Terrence. "Multi-instrument observations of coronal loops." Diss., Montana State University, 2012. http://etd.lib.montana.edu/etd/2012/scott/ScottJ0512.pdf.

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This document exhibits results of analysis from data collected with multiple EUV satellites (SOHO, TRACE, STEREO, Hinode, and SDO). The focus is the detailed observation of coronal loops using multiple instruments, i.e. filter imagers and spectrometers. Techniques for comparing the different instruments and deriving loop parameters are demonstrated. Attention is given to the effects the different instruments may introduce into the data and their interpretation. The assembled loop parameters are compared to basic energy balance equations and scaling laws. Discussion of the blue-shifted, asymmet
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23

Kurnik, Martin. "Protein folding without loops and charges." Doctoral thesis, Stockholms universitet, Institutionen för biokemi och biofysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-80512.

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Going down the folding funnel, proteins may sample a wide variety of conformations, some being outright detrimental to the organism. Yet, the vast majority of polypeptide molecules avoid such pitfalls. Not only do they reach the native minimum of the energy landscape; they do so via blazingly fast, biased, routes. This specificity and speed is remarkable, as the surrounding solution is filled to the brim with other molecules that could potentially interact with the protein and in doing so stabilise non-native, potentially toxic, conformations. How such incidents are avoided while maintaining n
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24

Rivera, Roberto Rafael. "On properties of completely flexible loops." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28841.

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25

Robertson, David. "Transverse oscillations of interacting coronal loops." Thesis, University of Sheffield, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.538010.

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26

Serna, Martínez Pablo. "Simulaciones numéricas en modelos de loops." Doctoral thesis, Universidad de Murcia, 2014. http://hdl.handle.net/10803/146182.

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El objetivo de esta tesis consiste en el estudio de varias familias de modelos de loops en dos y tres dimensiones, donde se encuentran dos fases diferentes: una con loops finitos y otra donde hay al menos uno infinito. En concreto, se han estudiado tres clases de modelos de loops. El primero, un modelo de loops tridimensionales con orientación y color, definidos en redes con número de coordinación cuatro. El segundo, una modificación de estos modelos de loops que es un firme candidato a presentar una transición de fase de deconfinamiento. El tercero, un modelo de loops bidimensionales en la re
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27

Garreau-Iles, Angelique Genevieve Lucie. "Triblock copolymers : the quest for loops." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394068.

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28

Dean, John Scott. "An Aspect Pointcut for Parallelizable Loops." NSUWorks, 2013. http://nsuworks.nova.edu/gscis_etd/131.

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This study investigated the need for a pointcut for parallelizable loops in an aspect-oriented programming environment. Several prototype solutions exist for loop pointcuts, but the solutions are not very granular. In particular, they are not able to differentiate between loops that are parallelizable and those that are not. Being able to identify parallelizable loops automatically, as part of an aspect-oriented compiler's weaving process, is particularly important because (1) manually identifying parallelizable loops is known to be a difficult problem and (2) aspectizing parallelized loops ca
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29

Yeomans, Maria Elena Tejeda. "Parton-parton scattering at two-loops." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3773/.

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We present an algorithm for the calculation of scalar and tensor one- and two-loop integrals that contribute to the virtual corrections of 2 →2 partonic scattering. First, the tensor integrals are related to scalar integrals that contain an irreducible propagator-like structure in the numerator. Then, we use Integration by Parts and Lorentz Invariance recurrence relations to build a general system of equations that enables the reduction of any scalar integral (with and without structure in the numerator) to a basis set of master integrals. Their expansions in e = 2-D/2 have already been calcul
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30

Blasi, Junior Francisco. "Otimização em loops no Projeto Xingo." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276316.

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Orientador: Rodolfo Jardim de Azevedo<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Computação<br>Made available in DSpace on 2018-08-05T13:01:34Z (GMT). No. of bitstreams: 1 BlasiJunior_Francisco_M.pdf: 934725 bytes, checksum: 6a13eaaaee52e0aabb1a74f3c2c4669f (MD5) Previous issue date: 2005<br>Resumo: As otimizações implementadas em compiladores proporcionam uma melhora significativa de desempenho dos programas. Em muitos casos, proporcionam também a redução do tamanho do programa. Quase todos os programas em produção são compilados com diretivas
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31

Pires, Rosemary Miguel. "Loops de código: automorfismos e representações." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-10072011-093023/.

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Neste trabalho, estudamos Loops de Código. Para este estudo, introduzimos os loops de código a partir de códigos pares e depois, provamos que loops de código de posto $n$ podem ser caracterizados como imagem homomórfica de certos loops de Moufang livres com n geradores. Além disso, introduzimos o conceito de vetores característicos associados a um loop de código. Com os resultados da teoria estudada, classificamos todos os loops de código de posto 3 e 4, encontramos todos os grupos de automorfismos externos destes loops e, finalmente, determinamos todas as suas respectivas representações básic
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32

Reis, Márcio Alexandre de Oliveira. "Loops de Bol algébricos e analíticos." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-27062010-143306/.

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Neste trabalho classificamos, a menos de isomorfismos, as álgebras de Bol de dimensão 2 sobre um corpo de característica 0. Também determinamos suas álgebras de Lie envolvente e, mostramos que existem álgebras de Bol não isomorfas cujas álgebras de Lie envolventes coorrespondentes são isomorfas. Calculamos os grupos algébricos (locais) correspondentes a cada uma das álgebras de Lie envolventes e provamos que todo loop de Bol analítico (algébrico) global de dimensão 2 sobre um corpo de característica 0 é um grupo. Exibimos exemplos de loops de Bol algébricos globais de dimensão n, para todo n >
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33

Anjos, Giliard Souza dos. "Grupo de automorfismos de A-loops." reponame:Repositório Institucional da UFABC, 2014.

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34

GOMEZ, CAROLINA VALERIA. "Wilson loops in supersymmetric gauge theories." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2020. http://hdl.handle.net/10281/258696.

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This thesis is dedicated to the study of Wilson loops in supersymmetric gauge theories, we will study their properties and how they are related to physical observables, such as the Bremsstrahlung function that controls to the energy radiated by an accelerating particle. We will give various examples of the computation of their expectations values using perturbative and non-perturbative techniques. For SU(N) superconformal QCD we perform a three-loop calculation of the generalized cusp anomalous dimension of the BPS Wilson loop operator using HQET formalism. We obtain an expression which is val
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35

Fili, Thomas. "Studio, implementazione e test di phase-locked loops per segnali "open loop" da sonde interplanetarie." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14372/.

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La tesi tratta di studio, test ed implementazione di Phase-Locked Loops, ovvero sistemi di controllo automatico il cui obiettivo è rigenerare segnali di telecomunicazione di input soggetti a jitter di fase. Dalla definizione delle trasformate di Laplace del controllore si passa all'implementazione delle analoghe equazioni in tempo discreto (z-transform) in Matlab & Simulink per studiare il comportamento di questi sistemi con segnali sintetici e reali (provenienti dalla sonda Juno).
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36

Wu, Chia-Ying (Charles). "Musical and Dramatic Functions of Loops and Loop Breakers in Philip Glass's Opera The Voyage." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc849734/.

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Philip Glass's minimalist opera The Voyage commemorates the 500th Anniversary of Christopher Columbus's discovery of America. In the opera, Philip Glass, like other composers, expresses singers' and non-singers' words and activities by means of melodies, rhythms, chords, textures, timbres, and dynamics. In addition to these traditional musical expressions, successions of reiterating materials (RMs, two or more iterations of materials) and non reiterating materials (NRMs) become new musical expressions. However, dividing materials into theses two categories only distinguishes NRMs from RMs with
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37

Souder, William Dai Foster. "A low power 10 GHz phase locked loop for radar applications implemented in 0.13 um SiGe technology." Auburn, Ala, 2009. http://hdl.handle.net/10415/1631.

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38

Li, Xiang, and xiali@cs rmit edu au. "Utilising Restricted For-Loops in Genetic Programming." RMIT University. Computer Science and Information Technology, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080110.122751.

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Genetic programming is an approach that utilises the power of evolution to allow computers to evolve programs. While loops are natural components of most programming languages and appear in every reasonably-sized application, they are rarely used in genetic programming. The work is to investigate a number of restricted looping constructs to determine whether any significant benefits can be obtained in genetic programming. Possible benefits include: Solving problems which cannot be solved without loops, evolving smaller sized solutions which can be more easily understood by human programmers
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39

Saksena, Mayank. "Verifying Absence of ∞ Loops in Parameterized Protocols." Doctoral thesis, Uppsala University, Department of Information Technology, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8605.

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<p>The complex behavior of computer systems offers many challenges for <i>formal verification</i>. The analysis quickly becomes difficult as the number of participating processes increases.</p><p>A <i>parameterized system</i> is a family of systems parameterized on a number <i>n</i>, typically representing the number of participating processes. The <i>uniform verification problem</i> — to check whether a property holds for each instance — is an infinite-state problem. The automated analysis of parameterized and infinite-state systems has been the subject of research over the last 15–20 years.
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40

Terlemez, Bortecene. "Oscillation Control in CMOS Phase-Locked Loops." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4841.

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Recent advances in voltage-controlled oscillator (VCO) design and the trend of CMOS processing indicate that the oscillator control is quickly becoming one of the forefront problems in high-frequency and low-phase-noise phase-locked loop (PLL) design. This control centric study explores the limitations and challenges in high-performance analog charge-pump PLLs when they are extended to multiple gigahertz applications. Several problems with performance enhancement and precise oscillator control using analog circuits in low-voltage submicron CMOS processes, coupled with the fact that analo
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41

Myllylä, K. (Kari). "On the solvability of groups and loops." Doctoral thesis, University of Oulu, 2003. http://urn.fi/urn:isbn:9514269055.

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Abstract The dissertation consists of three articles in which the solvability of groups and the solvability of loops are considered. The first parts of the thesis survey some basic information and results on transversals and loops. The summarizing parts provide the three main results for the solvability of groups and loops.
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42

Berndtsson, Magnus. "Fault detection in lambda-tuned control loops." Licentiate thesis, Luleå : Luleå University of Technology, 2006. http://epubl.ltu.se/1402-1757/2006/47/LTU-LIC-0647-SE.pdf.

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43

Hennion, Benjamin. "Formal loops spaces and tangent Lie algebras." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS160/document.

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L'espace des lacets lisses C(S^1,M) associé à une variété symplectique M se voit doté d'une structure (quasi-)symplectique induite par celle de M.Nous traiterons dans cette thèse d'un analogue algébrique de cet énoncé.Dans leur article, Kapranov et Vasserot ont introduit l'espace des lacets formels associé à un schéma. Il s'agit d'un analogue algébrique à l'espace des lacets lisses.Nous generalisons ici leur construction à des lacets de dimension supérieure. Nous associons à tout schéma X -- pas forcément lisse -- l'espace L^d(X) de ses lacets formels de dimension d.Nous démontrerons que ce de
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44

Kling, Michael (Michael W. ). "Detecting and escaping infinite loops using Bolt." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77024.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 89-91).<br>In this thesis we present Bolt, a novel system for escaping infinite loops. If a user suspects that an executing program is stuck in an infinite loop, the user can use the Bolt user interface, which attaches to the running process and determines if the program is executing in an infinite loop. If that is the case, the user can direct the interface to automatically explore multiple stra
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45

Durant, Kevin. "Investigating the non-termination of affine loops." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80052.

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Thesis (MSc)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: The search for non-terminating paths within a program is a crucial part of software verification, as the detection of anfinite path is often the only manner of falsifying program termination - the failure of a termination prover to verify termination does not necessarily imply that a program is non-terminating. This document describes the development and implementation of two focussed techniques for investigating the non-termination of affine loops. The developed techniques depend on the known non-termination concepts of re
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46

Mikkelson, Rana Catherine. "Minimum rank of graphs that allow loops." [Ames, Iowa : Iowa State University], 2008.

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47

Högstedt, Karin Dyveke. "Predicting performance for tiled perfectly nested loops /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9951422.

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48

Ko, Byung-su. "On performance assessment of feedback control loops /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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49

Williamson, Alastair. "Time-dependent resonant damping in coronal loops." Thesis, University of Sheffield, 2013. http://etheses.whiterose.ac.uk/4803/.

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Abstract:
This Thesis will extend the current theory of propagating, linear MHD waves into a cylindrical model containing a time-dependent background density. The current observations of propagating waves in the solar corona clearly show that the magnetic waveguides contain many time-dependent features which have, to date, been excluded from the majority of theoretical models investigating MHD wave propagation. Analysing a straight magnetic flux tube, to leading order in the WKB approximation, allows for the derivation of two governing equations describing the perturbed total pressure and the radial dis
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50

Scott, Amy. "Transverse oscillations of non-planar coronal loops." Thesis, University of Sheffield, 2012. http://etheses.whiterose.ac.uk/3213/.

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Abstract:
In this thesis a non-planar coronal loop model is introduced. The loop has helical geometry and therefore has non-zero curvature and torsion. A curvilinear coordinate system is introduced, which uses the loop axis as a coordinate line and the loop boundary as a coordinate surface. We assume that the density along the loop is stratified. The governing equation for kink oscillations of the loop is derived under the assumption of the thin tube approximation. It is found that the governing equation has the same form as the governing equation for a straight loop with density varying along the tube.
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