Дисертації з теми "Second order Hamiltonian systems"
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1
Montecchiari, Piero. "Homoclinic Solutions for Asymptotically Periodic Second Order Hamiltonian Systems." Doctoral thesis, SISSA, 1994. http://hdl.handle.net/20.500.11767/4531.
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2
Caldiroli, Paolo. "Homoclinic and heteroclinic orbits for some classes of second order Hamiltonian systems." Doctoral thesis, SISSA, 1995. http://hdl.handle.net/20.500.11767/4455.
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3
Teixeira, Randall Guedes [UNESP]. "Formalismo de Hamilton-Jacobi para sistemas singulares." Universidade Estadual Paulista (UNESP), 1996. http://hdl.handle.net/11449/91863.
Повний текст джерелаАнотація:
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teixeira_rg_me_ift.pdf: 565736 bytes, checksum: 47638723d76926fa1da8cc7e9ede904d (MD5)Neste trabalho apresentamos o formalismo Hamiltoniano de Dirac para sistemas singulares, analisando inclusive a construção do gerador de transformações de gauge. A seguir discutimos brevemente a generalização, já conhecida, desse formalismo para o caso de Lagrangeanos singulares de segunda ordem fazendo também uma análise da estrutura de vínculos presente em tais teorias. Desenvolvemos então o formalismo de Hamilton-Jacobi para sistemas singulares fazendo sua generalização para Lagrangeanos de segunda ordem. Por último, ambos formalismos são aplicados à Eletrodinâmica de Podols y e os resultados obtidos são comparados.
In this work we study Dirac's Hamiltonian formulation for singular systems including the construction of the gauge transformations generator. Next we briefy discuss the generalization, already developed, of this formalism for singular second order La grangians. Besides that we also make an anlysis of the constrains structure present in such theories. Then we develop the Hamilton-Jacobi formalism for singular systems making its generalization for the case of second order Lagrangians. Finally, both formalisms are applied to Podols y's eletrodynamics and the obtained results are comparad.
4
Teixeira, Randall Guedes. "Formalismo de Hamilton-Jacobi para sistemas singulares /." São Paulo : [s.n.], 1996. http://hdl.handle.net/11449/91863.
Повний текст джерелаАнотація:
Orientador: Bruto Max Pimentel EscobarResumo: Neste trabalho apresentamos o formalismo Hamiltoniano de Dirac para sistemas singulares, analisando inclusive a construção do gerador de transformações de gauge. A seguir discutimos brevemente a generalização, já conhecida, desse formalismo para o caso de Lagrangeanos singulares de segunda ordem fazendo também uma análise da estrutura de vínculos presente em tais teorias. Desenvolvemos então o formalismo de Hamilton-Jacobi para sistemas singulares fazendo sua generalização para Lagrangeanos de segunda ordem. Por último, ambos formalismos são aplicados à Eletrodinâmica de Podols y e os resultados obtidos são comparados.
Abstract: In this work we study Dirac's Hamiltonian formulation for singular systems including the construction of the gauge transformations generator. Next we briefy discuss the generalization, already developed, of this formalism for singular second order La grangians. Besides that we also make an anlysis of the constrains structure present in such theories. Then we develop the Hamilton-Jacobi formalism for singular systems making its generalization for the case of second order Lagrangians. Finally, both formalisms are applied to Podols y's eletrodynamics and the obtained results are comparad.
Mestre
5
Muzzulini, Marco. "Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order." [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007403.
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6
Bird, Craig Malcolm. "Second order interactions in solid state systems." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388768.
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7
Kau, Chung-Ta. "Robust stability margin and LQR of second-order systems." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/12044.
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Courouge, Olivier Franck. "Robust positive real controllers for dynamical second-order systems." Thesis, Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/12425.
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Wierda, F. "Information Systems for Managing Second Order Dynamics of Organizations." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-210868.
Повний текст джерелаАнотація:
"From the point of view of information technology the past decade can be designated the “decade of ERP”. A global movement of implementing integrated systems for optimising the fulfilment of orders has dominated both investments from large and medium corporations and the focus of research and educational institutions. The results of these implementations sometimes have been dramatic: Significant improvements of throughput time, and at the same time clear decreases in inventory. Organisations have become like machines. Interesting material - though not in all aspects consistent - on the improvement of productivity is collected in (Potthof, 1998). Unfortunately, and strangely enough, only little research has been done in the consequences of ERP systems on the flexibility and adaptability of organisations."
10
Wierda, F. "Information Systems for Managing Second Order Dynamics of Organizations." Josef Eul Verlag GmbH, 1999. https://tud.qucosa.de/id/qucosa%3A29861.
Повний текст джерелаАнотація:
From the point of view of information technology the past decade can be designated the “decade of ERP”. A global movement of implementing integrated systems for optimising the fulfilment of orders has dominated both investments from large and medium corporations and the focus of research and educational institutions. The results of these implementations sometimes have been dramatic: Significant improvements of throughput time, and at the same time clear decreases in inventory. Organisations have become like machines. Interesting material - though not in all aspects consistent - on the improvement of productivity is collected in (Potthof, 1998). Unfortunately, and strangely enough, only little research has been done in the consequences of ERP systems on the flexibility and adaptability of organisations.
11
Sundgren, David. "The Apparent Arbitrariness of Second-Order Probability Distributions." Doctoral thesis, Stockholms universitet, Institutionen för data- och systemvetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-54697.
Повний текст джерелаАнотація:
Adequate representation of imprecise probabilities is a crucial and non-trivial problem in decision analysis. Second-order probability distributions is the model for imprecise probabilities whose merits are discussed in this thesis. That imprecise probabilities may be represented by second-order probability distributions is well known but there has been little attention to specific distributions. Since different probability distributions have different properties, the study of the desired properties of models of imprecise probabilities with respect to second-order models require analysis of particular second-order distributions. An often held objection to second-order probabilities is the apparent arbitrariness in the choice of distribution. We find some evidence that the structure of second-order distributions is an important factor that prohibits arbitrary choice of distributions. In particular, the properties of two second-order distributions are investigated; the uniform joint distribution and a variant of the Dirichlet distribution that has the property of being the normalised product of its own marginal distributions. The joint uniform distribution is in this thesis shown to have marginal distributions that belie the supposed non-informativeness of a uniform distribution. On the other hand, the modified Dirichlet distribution discovered here has its information content evenly divided among the joint and marginal distributions in that the total correlation of the variables is minimal. It is also argued in the thesis that discrete distributions, as opposed to the continuous distributions mentioned above, would have the advantage of providing a natural setting for updating of lower bounds, and computation of expected utility is made more efficient.In placitorum scrutatione maxima et mehercle minime levis difficultas eo spectat, quomodo probabilitates dubiae bene ostendantur. In hac thesi de utilitate distributionum probabilitatum secundi ordinis disseremus, in quantum ad probabilitates dubias ostendendas valeant. Omnibus fere notum est probabilitates dubias ostendi posse per distributiones probabilitatum secundi ordinis, sed pauci operam distributionibus singulis operam contulerunt. Cum tamen distributiones probabilitatum valde inter se diversae sint, si quis proprietatibus desideratis probabilitatum dubiarum secundi ordinis studium conferre vult, primum debet quasdam praescriptas distributiones secundi ordinis investigare. Sed fortasse, quod saepenumero fieri solet, quispiam dixerit probabilitates secundi ordinis nulla, ut videtur, ratione habita quasi vagari quoad delectum distributionis. Nos tamen nonnulla indicia comperimus quibus freti confirmare audemus ipsam formam distributionum secundi ordinis multum valere ad praedictum distributionum secundi ordinis delectum rationabiliter peragendum. Imprimis proprietates duarum distributionum secundi ordinis investigabimus, nimirum distributionis uniformis coniunctae et alterius cuiusdam speciei distributionis quae ‘Dirichleti’ vocatur, quae ex ipsius distributionibus marginalibus ad normam correcta oritur. In hac thesi probamus illam coniunctam uniformem distributionem continere distributiones marginales eius modi quae illos refellant qui negant distributionem uniformem quicquam alicuius momenti afferre. Attamen in illa distributione Dirichleti paulo mutata, quam hoc loco patefacimus, omnia aequaliter inter coniunctas et marginales distributiones divisa sunt, in quantum tota ratio quae inter variantia intercessit ad minimum reducitur. Insuper in hac thesi confirmamus distributiones discretas potius quam antedictas distributiones continuas in hoc utiliores esse, quod per eas limites inferiores in melius mutare licet, et beneficia exspectata accuratius computari possunt.
Adekvat representation av osäkra eller imprecisa sannolikheter är ett avgörande och icke-trivialt problem i beslutsanalys. I denna avhandling diskuteras förtjänsterna hos andra ordningens sannolikheter som en modell för imprecisa sannolikeheter. Att imprecisa sannolikheter kan representeras med andra ordningens sannolikheter är välkänt, men hittills har särskilda andra ordningens föredelningar inte ägnats någon större uppmärksamhet. Då olika sannolikhetsfördelningar har olika egenskaper kräver studiet av önskvärda egenskaper hos modeller för imprecisa sannolikheter en granskning av specifika andra ordningens fördelningar. Den godtycklighet som tycks vidhäfta valet av andra ordningens fördelning är en ofta förekommande invändning mot andra ordingens sannolikhetsfördelningar. Vi finner vissa belägg för at strukturen hos andra ordningens fördelningar är en omständighet som hindrar godtyckligt val av fördelningar. I synnerhet undersöks egenskaper hos två andra ordningens fördelningar; den likformiga simultana fördelningen och en variant av Dirichletfördelningen med egenskapen att vara lika med den normaliserade produkten av sina egna marginalfördelningar. Den likformiga simultana fördelningen visas i avhandligen ha marginalfördelningar som motsäger den förmodat icke-informativa strukturen hos en likformig fördelning. Å andra sidan gäller för den modifierade Dirichletfördelningen som upptäckts här att informationsinnehållet är jämnt fördelat mellan den simultana fördelningen och marginalfördelningarna; den totala korrelationen mellan variablerna är minimal. Det hävdas också i avhandlingen att diskreta sannolikhetsfördelningar i motsats till de kontinuerliga fördelningar som nämnts ovan har fördelen att utgöra en naturlig miljö för uppdatering av undre gränser och dessutom tillåta en mer effektiv beräkning av förväntad nytta.
12
Causey, Richard Todd. "Blind multiuser detection based on second-order statistics." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/15486.
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13
Tin, Albert Chu Yu. "Design of steel scaffolding systems using practical second-order analysis /." St. Lucia, Qld, 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18037.pdf.
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Abuazoum, Latifa Abdalla. "Advanced model updating methods for generally damped second order systems." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12063/.
Повний текст джерелаАнотація:
This thesis is mostly about the analysis of second order linear vibrating systems. The main purpose of this study is to extend methods which have previously been developed for either undamped or proportionally damped or classically damped systems to the general case. These methods are commonly used in aerospace industries. Ground vibration testing of aircraft is performed to identify the dynamic behaviour of the structure. New aircraft materials and joining methods - composite materials and/or novel adhesive bonding approaches in place of riveted or welded joints - cause higher levels of damping that have not been seen before in aircraft structure. Any change occurring in an original structure causes associated changes of the dynamic behaviour of the structure. Analytical finite element analyses and experimental modal testing have become essential tools for engineers. These techniques are used to determine the dynamic characteristics of mechanical structures. In Chapters 3 and 4, structural analysis and modal testing have been carried out an aircraft-like structure. Modal analysis techniques are used to extract modal data which are identified from a single column of the frequency response matrix. The proposed method is presented for fitting modal peaks one by one. This technique overcomes the difficulty due to the conventional methods which require a series of measured FRFs at different points of excitation. New methods presented in this thesis are developed and implemented initially for undamped systems in all cases. These ideas are subsequently extended for generally damped linear systems. The equations of motion of second order damped systems are represented in state space. These methods have been developed based on Lancaster Augmented Matrices (LAMs) and diagonalising structure preserving equivalences (DSPEs). In Chapter 5, new methods are developed for computing the derivatives of the non-zeros of the diagonalised system and the derivatives of the diagonalising SPEs with respect to modifications in the system matrices. These methods have provided a new approach to the evaluation and the understanding of eigenvalue and eigenvector derivatives. This approach resolves the quandary where eigenvalue and eigenvector derivatives become undefined when a pair of complex eigenvalues turns into a pair of real eigenvalues or vice-versa. They also have resolved when any one or more of the system matrices is singular. Numerical examples have illustrated the new methods and they have shown that the method results overcome certain difficulties of conventional methods. In Chapter 6, Möbius transformations are used to address a problem where the mass matrix is singular. Two new transformations are investigated called system spectral transformation SSTNQ and diagonalising spectral/similarity transformation DSTOQ. The transformation SSTNQ maps between matrices of two systems having the same short eigenvectors and their diagonalised system matrices. The transformation DSTOQ maps between two diagonalising SPE‟s having identical eigenvalues. Modal correlation methods are implemented to evaluate and quantify the differences between the output results from these techniques. Different cross orthogonality measures represent a class of methods which are recently performed as modal correlation for damped systems. In Chapter 7, cross orthogonality measures and mutual orthogonality measures are developed for undamped systems. These measures are defined in terms of real matrices - the diagonalising structure preserving equivalences (DSPEs). New methods are well developed for ill-conditioned system such that they work for all occasions and not only for cases where mass matrix is non-singular. Also a measure of the residuals is introduced which does not demand invertibility of diagonalised system matrices. Model updating methods are used in order to update models of systems by matching the output results from analytical system models with the experimentally obtained values. In Chapter 8, both cross-orthogonality measures and mutual-orthogonality measures are developed and used in the model updating of generally damped linear systems. Model updating based on the mutual orthogonality measures exhibits monotonic convergence from every starting position. That is to say, the ball of convergence has an infinite radius whereas updating procedures based on comparing eigenvectors exhibit a finite ball of convergence. Craig Bampton transformations are one of component methods which are used to reduce and decouple large structure systems. In Chapter 9 Craig Bampton transformations are developed for undamped systems and extended for damped second order systems in state space. Craig Bampton transformations are generalised and presented in SPEs forms. The two parts of the Craig Bampton transformations are extended in the full sizes of the substructure. The extended Craig Bampton transformations are modified to format each block of transformed substructure matrices as LAMs matrices format. This thesis generalises and develops the methods mentioned above and illustrates these concepts with an experimental modal test and some examples. The thesis also contains brief information about basic vibration properties of general linear structures and literature review relevant to this project.
15
Sundgren, David. "Distribution of expected utility in second-order decision analysis." Licentiate thesis, Kista : Data- och systemvetenskap, Kungliga Tekniska högskolan, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4442.
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16
Dzacka, Charles Nunya. "A Variation of the Carleman Embedding Method for Second Order Systems." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1877.
Повний текст джерелаАнотація:
The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential equations, it is difficult to use the Carleman Embedding method. This project will examine the Carleman Embedding and a variation of the method which is very convenient in applying to second order systems of nonlinear equations.
17
High, Chris. "Opening spaces for learning : a systems approach to sustainable development." Thesis, Open University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251404.
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Wyatt, Sarah Alice. "Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27668.
Повний текст джерелаАнотація:
Dynamical systems are mathematical models characterized by a set of differential or difference equations.
Model reduction aims to replace the original system with a reduced system of significantly smaller dimension that still describes the important dynamics of the large-scale
model. Interpolatory model reduction methods define a reduced model that interpolates the full model at selected interpolation points. The reduced model may be obtained through a Krylov reduction process or by using the Iterative Rational Krylov Algorithm (IRKA), which iterates this Krylov reduction process to obtain an optimal $\mathcal{H}_2$ reduced model.
This dissertation studies interpolatory model reduction for first-order descriptor systems, second-order systems, and DAEs. The main computational cost of interpolatory model reduction is the associated linear systems. Especially in the large-scale setting, inexact solves become desirable if not necessary. With the introduction of inexact solutions, however, exact interpolation no longer holds. While the effect of this loss of interpolation has previously been studied, we extend the discussion to the preconditioned case. Then we utilize IRKA's convergence behavior to develop preconditioner updates.
We also consider the interpolatory framework for DAEs and second-order systems. While interpolation results still hold, the singularity associated with the DAE often results in unbounded model reduction errors. Therefore, we present a theorem that guarantees interpolation and a bounded model reduction error. Since this theorem relies on expensive projectors, we demonstrate how interpolation can be achieved without explicitly computing the projectors for index-1 and Hessenberg index-2 DAEs. Finally, we study reduction techniques for second-order systems. Many of the existing methods for second-order systems rely on the model's associated first-order system, which results in computations of a $2n$ system. As a result, we present an IRKA framework for the reduction of second-order systems that does not involve the associated $2n$ system. The resulting algorithm is shown to be effective for several dynamical systems.Ph. D.
19
Diwekar, Anjali M. "Stability analysis, robustness and controller design for matrix second order dynamical systems /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu148786342909184.
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Abuhamdia, Tariq Maysarah. "Wavelets Based on Second Order Linear Time Invariant Systems, Theory and Applications." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/85439.
Повний текст джерелаАнотація:
This study introduces new families of wavelets. The first is directly derived from the response of Second Order Underdamped Linear-Time-Invariant (SOULTI) systems, while the second is a generalization of the first to the complex domain and is similar to the Laplace transform kernel function. The first takes the acronym of SOULTI wavelet, while the second is named the Laplace wavelet. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. It is shown that it is possible to recover back the original signal once the SOULTI or the Laplace wavelet transform is applied to decompose the signal. It is found that both wavelet transforms satisfy linear differential equations called the reconstructing differential equations, which are closely related to the differential equations that produce the wavelets. The new wavelets can have well defined Time-Frequency resolutions, and they have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification and modal decomposition of LTI Multi-Degree of Freedom (MDOF) systems and it showed better results than the Short-time Fourier Transform (STFT) and the other harmonic wavelets used in time-frequency analysis. The modal decomposition is applied for modal parameters identification, and the properties of the Laplace and the SOULTI wavelet transforms allows analytical and accurate identification methods.Ph. D.
21
Brown, James Robert. "Development of second order understanding as a basis for organisational improvement." Thesis, Northumbria University, 2009. http://nrl.northumbria.ac.uk/2180/.
Повний текст джерелаАнотація:
Most if not all organisations claim to pursue a continued improvement philosophy. The processes often adopted are predominantly concerned with the collection and analysis of data. Such approaches take little account of the opinions or varying points of view of the affected groups or individuals. Within this research, these processes are referred to as first order processes. The thesis explores what is termed the second order of organisational improvement, placing the emphasis of the inquiry on the worldviews of those involved. The research includes a study of peoples' attitudes towards organisational improvement and an in depth review of the relevant literature. Initial research consisting of questionnaires and interviews, gave an indication of the willingness within the workforce to engage in improvement activities. This led to the development of a model looking to understand and incorporate the differing worldviews of individuals, into action plans to improve the situations of concern, and an improvement process embedding understanding of others' perspectives and worldviews, dialogical communication and systems thinking. Incorporation of the differentiation of opinions and views of the people affected is central to the second order process. Implementation is possible in any organisation that enjoys an open trusting environment, irrespective of the operational sector. The major contribution of the process is in the change of emphasis from establishment of a commonly held shared view of a situation, to understanding the differences between worldviews of those involved. In effect, the second order process explores the differences in opinions and beliefs that underlie how individuals view a situation. The aim is to understand peoples' different views and incorporate those views in any agreed action.
22
Mongol, Bayarpurev, Takaya Yamazato, Hiraku Okada, and Masaaki Katayama. "On the Second-order Statistics of the Channel Parameters for BFDM/OQAM Systems." IEEE, 2005. http://hdl.handle.net/2237/7761.
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Yantır, Ahmet Ufuktepe Ünal. "Oscillation theory for second order differential equations and dynamic equations on time scales/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000418.pdf.
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Perkins, Skyler Knox. "Becoming Eco-Logical With Second-Order Systems Theory: Sustainability In Re-Organization Of Economies And Food Systems." ScholarWorks @ UVM, 2018. https://scholarworks.uvm.edu/graddis/869.
Повний текст джерелаАнотація:
Ecological Economics has emerged across disciplines, and has begun to disentangle, not only the relationship between biophysical earth systems and economic activity, but also, fundamental relationships between objectivity, power, value, ethics, perspective and purpose.
In part, this thesis represents an effort to illustrate basic transdisciplinary concepts necessary for understanding the project of Ecological Economics. At present, Ecological Economics is challenged by a seemingly infinite number of available considerations, with a relatively narrow repertoire of impactful mechanisms of control. Given this, it is apparent that the application of Cybernetics to Ecological Economics might provide insights. Cybernetics can help to lend concise language to manners for implementing control and also help to navigate the paradoxes which arise for self- regulating systems. While Cybernetics played an early role in the formulation of the relationship between the economy and an environment with available energy, second- order cybernetics can help to formulate the autonomy of Ecological Economics as a self-regulating system and shed light on the epistemology and ethics of circularity. The first article of this thesis identifies occasions when Ecological Economics has confronted circularity, and explores options moving forward. Ultimately, confronting paradox and circularity provide the means for the substantiation of Ecological Economics.
The food system is prominent within Ecological Economics discourse. It serves as a good example of the ‘emergence’ of coordinated activity. In Cybernetics jargon, we can think of the ‘Food System’ as a symbol for the redundancy found in linked characteristics of particular Ecological-Economic inquiry. For instance, when we consider the food system we can be sure that we are dealing with resources that are essential, both rival and non-rival, excludable and non-excludable, and also highly sensitive to boundaries in scope, and scale, and thus highly sensitive to political and social change. In this sense, the food system acts as a symbol for the coordination of activity, and produces an output which is an input to the Ecological Economic ‘boundary’ between the Economy and the Ecosystem.
The second article of this thesis provides an analysis of GHG emissions within the Chittenden County Foodshed. We conclude that urban agriculture, dietary change and agro-ecological production in concert, provide emission reductions which are not achieved when these options are considered separately. Given these conditions, we see mitigation beyond 90% of current emissions.
25
Burovskiy, Pavel Andreevich. "Second order quasilinear PDEs in 3D : integrability, classification and geometric aspects." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/26691.
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Bruschetta, Mattia. "A variational integrators approach to second order modeling and identification of linear mechanical systems." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3421654.
Повний текст джерелаАнотація:
The identication of linear second order models of mechanical systems has been object of intensive research and of several papers in the last decades. In this thesis the interest is focused on mechanical systems which can be described by the classical second order vector model defined by the generalized stiffness K, damping D, and inerzia M. All current identication techniques operate in discrete time. Noisy data obtained by sampling the system must be used to stimate the continuous time physical parameters M;K and D. Since identication operates in discrete time one needs to convert the discrete time identied system into a continuous time one. There are structural constraints that need to be imposed to obtain the second order structure.
In short, the procedure is composed of three main steps:
1. Discrete-time Identication, mostly using subspace methods, from sampled input-output data;
2. Implementation of a set of constraints which force the dentied system to the form;
3. Conversion from the discrete to a continuous model and conversion of the relative system parameters.
The usual procedure assumes that the discrete time identied system is a Zero-Order-Hold (ZOH) discretization of the underlying continuous time system.
This assumption may lead to serious numerical problems, since the conversion discrete-to-continuous (d2c) requires the computation of the matrix logarithm of a 2n 2n matrix, which is well-known to be an ill conditioned problem resulting in a serious amplication of the noisy errors in the discrete estimates.
The proposed solution to this problem is to introduce a new discretization technique of the equations of motion of a mechanical systems introduced by Veselov, and further developed by J.Marsden and co-workers. This technique has been developed for general mechanical system and leads to discrete systems characterized by a sort of "discrete mechanical structure". Unlike the usual discretization procedures familiar in control, e.g. ZOH, it can lead to linear algebraic transformation formulas for the recovery of the continuous time parameters from the discretized model.
In this thesis variational integrators are applied to linear second order mechanical systems and it is shown that physically meaningful properties of the continuous-time model, like passivity, are preserved in the discretization.L'identicazione di modelli di sistemi meccanici del secondo ordine e stata oggetto di un'intensa attivita di ricerca negli ultimi decenni. In questa tesi ci si focalizza nei sistemi meccanici che si posso descrivere con un modello classic del secondo ordine definito dalle classiche matrici di inerzia generalizzata M, stiffness K e damping D. Tutte le attuali tecniche di identicazione operano a tempo discreto. I dati rumorosi ottenuti dal campionamento del sistema devono essere utilizzati per stimare i parametri sici del sistema a tempo continuo M;K e D. Poiche il processo di identicazione opera a tempo discreto si rende necessaria una conversione del sistema discreto identicato in uno a tempo continuo. Ci sono vincoli strutturali che devono essere imposti per ottenere la struttura del secondo ordine. In breve, la procedure si compone di tre parti principali: 1. Identicazione a tempo discreto, per lo pi metodi a sottospazi, dai dati ingresso-uscita campionati; 2. Implementazione di un set di vincoli che forzi il sistema identicato alla forma; 3. Conversione dal dominio di tempo discreto a quello continuo and conversione dei relativi parametri del sistema. La procedura classica prevede che il sistema identicato a tempo discreto sia ottenuto per discretizzazione di tipo Zero-Order-Hold (ZOH) del sottostante modello continuo. Quest'assunzione porta a gravi problemi di tipo numerico, poiche la conversione dal discreto al continuo (d2c) richiede il calcolo del logaritmo per una matrice 2n 2n. E' noto che tale operazione comporta problemi di malcondizionamento numerico che producono un amplicazione degli errori di stima nel sistema discreto. La soluzione proposta al problema e di introdurre una nuova tecnica di discretizzazione delle equazioni del moto per sistemi meccanici, introdotta da Veselov, e successivamente sviluppata da J.Marden e dai suoi collaboratori. Questa tecnica e stata sviluppata per sistemi meccanici generici e porta a sistemi discreti caratterizzati da una sorta di "struttura meccanica discreta". Diversamente dalle procedure di discretizzazione classiche, familiari nel mondo del controllo, e.g. ZOH, tale metodo porta a una formula di trasformazione algebrica lineare per il recupero dei parametri continui da quelli discreti. Nella tesi gli integratori variazionali sono applicati ai sistemi meccanici lineari del secondo ordine e verra provato che nella discretizzazione vengono preservate proprieta con intrinseco signicato fisico del modello a tempo continuo, ad esempio la passivita.
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Dube, Sibusisiwe. "A paradox of the second order digital divide in higher education institutions of developing countries: case of Zimbabwe." Doctoral thesis, Faculty of Commerce, 2021. http://hdl.handle.net/11427/33697.
Повний текст джерелаАнотація:
Although this is not a new research phenomenon, the literature has often associated the digital divide (second order or otherwise) with sociodemographic, sociocultural and socioeconomical factors as reasons for the digital divide. However, there is little presence in the literature into the underlying structures (physical or abstract arrangement) leading to the divide. This means that the underlying structures leading to this problem have so far been ignored and require scholarly attention. This study, therefore, identifies and explains the structures leading to the second order digital divide, a problem relating to the unequal use of information and communication technologies (ICTs) which is more prevalent in the higher education institutions (HEIs) of developing countries. Before the structures that lead to the second order digital divide could be explained the interlocking dynamics of ICT adoption needed to be identified. Structuration Theory was employed as a sensitising tool for collecting, analysing, and interpreting qualitative data for this interpretivist research. Novel qualitative data were collected from a purposive sample drawn from a single HEI of Zimbabwe, a developing country of high literacy. Directed content analysis generated insightful explanations of the structures leading to the second order digital divide at the HEI case. Preliminary analysis based on a deductive logic approach identified signification, domination, and legitimation as some of the structures leading to the second order digital divide at the HEI case. Further analysis based on an inductive logic approach revealed additional belief, institutional and governance structures which manifested from the interlocking dynamics of ICT adoption, involving resources, leadership, adoption behaviours and empowerment. These findings contributed to practice by explaining the underlying structures of the second order digital divide, for the benefit of ICT4D researchers, and by suggesting interventions to HEI policy-makers for reducing the second order digital divide. The results also make an iv explanatory contribution to theory by presenting a model of the interlocking dynamics of ICT adoption for theorising about the complex second order digital divide.
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Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.
Повний текст джерелаАнотація:
Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since then, there has been a strong development in the intrinsic treatment of a variety of topics in theoretical physics, applied mathematics and control theory using methods of differential geometry.
Most of the work done in geometrical physics since its first days has been devoted to study first-order theories, that is, those theories whose physical information depends on (at most) first-order derivatives of the generalized coordinates of position (velocities). However, there are theories in physics in which the physical information depends explicitly on accelerations or higher-order derivatives of the generalized coordinates of position, and thus more sophisticated geometrical tools are needed to model them acurately.
In this Ph.D. Thesis we pretend to give a geometrical description of some of these higher-order theories. In particular, we focus on dynamical systems and field theories whose dynamical information can be given in terms of a Lagrangian function, or a Hamiltonian that admits Lagrangian counterpart. More precisely, we will use the Lagrangian-Hamiltonian unified approach in order to develop a geometric framework for autonomous and non-autonomous higher-order dynamical system, and for second-order field theories. This geometric framework will be used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
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Junkermeier, Chad Everett. "Iteration Methods For Approximating The Lowest Order Energy Eigenstate of A Given Symmetry For One- and Two-Dimensional Systems." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/85.
Повний текст джерелаАнотація:
Using the idea that a quantum mechanical system drops to its ground state as its temperature goes to absolute zero several operators are devised to enable the approximation of the lowest order energy eigenstate of a given symmetry; as well as an approximation to the energy eigenvalue of the same order.
30
Wong, Ho-ting, and 黃浩霆. "Hand-written Chinese character recognition by first and second order Hidden Markov Models and radical modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B27770862.
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Frénoy, Antoine. "Second order selection pressures promoting the evolution and maintenance of cooperation in microbial and in silico systems." Thesis, Paris 5, 2014. http://www.theses.fr/2014PA05T050/document.
Повний текст джерелаАнотація:
Cette thèse s'intéresse aux liens entre l'évolution de la coopération et la sélection de second ordre. Dans une première partie, nous montrons comment des organismes digitaux adaptent leurs génomes pour encoder les gènes liées à la coopération d'une manière plus contrainte (suppression d'évolvabilité), notamment à l'aide d'opérons et d'overlaps impliquant aussi des gènes essentiels. Dans une deuxième partie, nous testons expérimentalement cette vision des overlaps de gènes comme "contrainte évolutive" grâce à des outils d'algorithmique et de biologie synthétique que nous avons développés. Dans une troisième partie, nous utilisons des simulations par agents pour montrer comment une forme de division du travail peut être interprétée comme un système coopératif à la lumière de la théorie évolutive moderne. Dans une dernière partie, nous montrons que la dispersion spatiale des allèles coopératives obtenue par des phénomènes de "genetic hitchiking" joue un rôle important dans l'évolution de la coopération, quand bien même ce mécanisme de dispersion s'applique aussi à des allèles non coopératives, grâce à la "relatedness" (aux loci codant pour la coopération) crée par l'invasion locale de mutations bénéfiques (à des loci non liés à la coopération) et par l'équilibre complexe entre ces mutations bénéfiques et la robustesse mutationnelle. L'ensemble de ces résultats appelle à une prise en compte plus importante des pressions sélectives de second ordre dans l'étude de l'évolution sociale, et au développement de modèles plus réalistes qui permettraient d'intégrer de telles forces évolutives. Nous insistons également sur l'importance du paysage mutationnel dans l'étude des populations bactériennes, et montrons le potentiel croissant de la biologie synthétique comme outil d'étude de ce paysage et de l'évolution microbienne en généralIn the first part, I show how digital organisms adapt their genomes to encode cooperation-related genes in a more constrained way (evolvability suppression), especially using operons and overlaps also involving essential genes. In the second part, we experimentally test this view of gene overlaps as an evolutionary constraint, using both algorithmic and synthetic biology tools that we have developed. In the third part, I use agent-based simulations to show how a form of division of labour can be interpreted as a cooperative system in the light of modern evolutionary theory. In the final part, I show that the patterns of dispersal of cooperative alleles due to hitchhiking phenomena play an important role in the evolution of cooperation. The last result holds even though the hitchhiking mechanisms also applies to non-cooperative alleles, thanks to the relatedness (at cooperation-related loci) created by the local invasion of beneficial mutations (at loci not related to cooperation). The beneficial mutations form a complex and interesting equilibrium with mutational robustness, which I investigate using in silico evolution. On the whole, these results call for a more careful consideration of the second-order selection pressures in the study of social evolution, and show the necessity for more realistic models allowing to integrate such evolutionary forces. My thesis research specifically highlights the importance of the mutational landscape in the study of microbial populations and shows the increasing potential of synthetic biology as a tool to study such landscape and microbial evolution in general
32
Haque, Md Z. "An adaptive finite element method for systems of second-order hyperbolic partial differential equations in one space dimension." Ann Arbor, Mich. : ProQuest, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3316356.
Повний текст джерелаАнотація:
Thesis (Ph.D. in Computational and Applied Mathematics)--S.M.U.Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-08, Section: B Adviser: Peter K. Moore. Includes bibliographical references.
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Lawrie, Sofía. "Information representation and processing in neuronal networks: from biological to artificial systems and from first to second-order statistics." Doctoral thesis, Universitat Pompeu Fabra, 2022. http://hdl.handle.net/10803/673989.
Повний текст джерелаАнотація:
Neuronal networks are today hypothesized to the basis for the computing capabilities of biological nervous systems. In the same manner, artificial neuronal systems are intensively exploited for a diversity of industrial and scientific applications. However, how information is represented and processed by these networks remains under debate, meaning that it is not clear which sets of neuronal activity features are useful for computation. In this thesis, I present a set of results that link the first-order statistics of neuronal activity with behavior, in the general context of encoding/decoding to analyse experimental data collected while non human primates performed a working memory task. Subsequently, I go beyond the first-order and show that the second-order statistics of neuronal activity in reservoir computing, a recurrent artificial network model, make up a robust candidate for information representation and transmission for the classification of multivariate inputs.Las redes neuronales se presentan hoy, hipotéticamente, como las responsables de las capacidades computacionales de los sistemas nerviosos biológicos. De la misma manera, los sistemas neuronales artificiales son intensamente explotados en una diversidad de aplicaciones industriales y científicas. No obstante, cómo la información es representada y procesada por estas redes está aún sujeto a debate. Es decir, no está claro qué propiedades de la actividad neuronal son útiles para llevar a cabo computaciones. En esta tesis, presento un conjunto de resultados que relaciona el primer orden estadístico de la actividad neuronal con comportamiento, en el contexto general de codificación/decodificación, para analizar datos recolectados mientras primates no humanos realizaban una tarea de memoria de trabajo. Subsecuentemente, voy más allá del primer orden y muestro que las estadísticas de segundo orden en computación de reservorios, un modelo de red neuronal artificial y recurrente, constituyen un candidato robusto para la representación y transmisión de información con el fin de clasificar señales multidimensionales.
34
Tran, Dai Quang. "Toward improved flange bracing requirements for metal building frame systems." Thesis, Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/33908.
Повний текст джерелаАнотація:
This research investigates the application of the AISC Direct Analysis Method for stability bracing design of columns, beams, beam-columns and frames. Emphasis is placed on out-of-plane flange bracing design in metal building frame systems. Potential improvements and extensions to the 2005 AISC Appendix 6 stability bracing provisions are studied and evaluated. The structural attributes considered include various general conditions encountered in practical metal building design: unequal brace spacing, unequal brace stiffness, nonprismatic member geometry, variable axial load or bending moment along the member length, cross-section double or single symmetry, combined bending and axial load, combined torsional and lateral bracing from girts/purlins with or without diagonal braces from these components to the inside flanges, load height, cross-section distortion, and non-rigid end boundary conditions. The research addresses both the simplification to basic bracing design rules as well as direct computation for more complex cases. The primary goal is improved assessment of the demands on flange bracing systems in metal building frames.
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Sroczinski, Matthias [Verfasser]. "Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluids / Matthias Sroczinski." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1184795460/34.
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Opalka, Daniel [Verfasser], Wolfgang [Akademischer Betreuer] Domcke, Grafenstein Ulrich [Akademischer Betreuer] Boesl-von, and Moniek [Akademischer Betreuer] Tromp. "New aspects of the Jahn-Teller effect in tetrahedral systems : high-order expansions of the electrostatic Hamiltonian and relativistic Jahn-Teller couplings / Daniel Opalka. Gutachter: Ulrich Boesl-von Grafenstein ; Moniek Tromp. Betreuer: Wolfgang Domcke." München : Universitätsbibliothek der TU München, 2011. http://d-nb.info/1019589434/34.
Повний текст джерела
37
Kim, Jae-Hak, and Jae-Hak Kim@anu edu au. "Camera Motion Estimation for Multi-Camera Systems." The Australian National University. Research School of Information Sciences and Engineering, 2008. http://thesis.anu.edu.au./public/adt-ANU20081211.011120.
Повний текст джерелаАнотація:
The estimation of motion of multi-camera systems is one of the most important tasks in computer vision research. Recently, some issues have been raised about general camera models and multi-camera systems. Using many cameras as a single camera is studied [60], and the epipolar geometry constraints of general camera models is theoretically derived. Methods for calibration, including a self-calibration method for general camera models, are studied [78, 62]. Multi-camera systems are an example of practically implementable general camera models and they are widely used in many applications nowadays because of both the low cost of digital charge-coupled device (CCD) cameras and the high resolution of multiple images from the wide field of views. To our knowledge, no research has been conducted on the relative motion of multi-camera systems with non-overlapping views to obtain a geometrically optimal solution. ¶
In this thesis, we solve the camera motion problem for multi-camera systems by using linear methods and convex optimization techniques, and we make five substantial and original contributions to the field of computer vision. First, we focus on the problem of translational motion of omnidirectional cameras, which are multi-camera systems, and present a constrained minimization method to obtain robust estimation results. Given known rotation, we show that bilinear and trilinear relations can be used to build a system of linear equations, and singular value decomposition (SVD) is used to solve the equations. Second, we present a linear method that estimates the relative motion of generalized cameras, in particular, in the case of non-overlapping views. We also present four types of generalized cameras, which can be solvable using our proposed, modified SVD method. This is the first study finding linear relations for certain types of generalized cameras and performing experiments using our proposed linear method. Third, we present a linear 6-point method (5 points from the same camera and 1 point from another camera) that estimates the relative motion of multi-camera systems, where cameras have no overlapping views. In addition, we discuss the theoretical and geometric analyses of multi-camera systems as well as certain critical configurations where the scale of translation cannot be determined. Fourth, we develop a global solution under an L∞ norm error for the relative motion problem of multi-camera systems using second-order cone programming. Finally, we present a fast searching method to obtain a global solution under an L∞ norm error for the relative motion problem of multi-camera systems, with non-overlapping views, using a branch-and-bound algorithm and linear programming (LP). By testing the feasibility of LP at the earlier stage, we reduced the time of computation of solving LP.¶
We tested our proposed methods by performing experiments with synthetic and real data. The Ladybug2 camera, for example, was used in the experiment on estimation of the translation of omnidirectional cameras and in the estimation of the relative motion of non-overlapping multi-camera systems. These experiments showed that a global solution using L∞ to estimate the relative motion of multi-camera systems could be achieved.
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Yan, Xinming. "Development of robust control based on sliding mode for nonlinear uncertain systems." Thesis, Ecole centrale de Nantes, 2016. http://www.theses.fr/2016ECDN0012.
Повний текст джерелаАнотація:
Le travail de thèse présenté dans ce mémoire s’inscrit dans le cadre du développement de lois de commande pour des systèmes non linéaires incertains, basées sur la théorie des modes glissants. Les méthodes classiques de la commande par modes glissants sont des lois de commande par retour d’état, où la variable de glissement et ses dérivées sont nécessaires. Le premier objectif de cette thèse est de proposer des lois de commande par modes glissants d’ordre supérieur avec une réduction de l’ordre de dérivation de la variable de glissement. Le deuxième objectif est de combiner les nouvelles lois de commande avec un mécanisme de gain adaptatif. L’utilisation d’un gain adaptatif permet de simplifier le réglage du gain, de réduire le temps de convergence et d’améliorer la précision. Enfin, l’applicabilité de ces approches est démontrée à travers leur application au banc d’essais électropneumatique de l’IRCCyN, et à un système volant à trois degrés de libertéThis work deals with the development of control laws for nonlinear uncertain systems based onsliding mode theory. The standard sliding mode control approaches are state feedback ones, in which the sliding variable and its time derivatives are required. This first objective of this thesis is to propose high order sliding mode control laws with a reduced use of sliding variable time derivatives. The contributions are made for the second and third order sliding mode control. The second objective is to combine the proposed control laws with a gain adaptation mechanism. The use of adaptive gain law allows to simplify the tuning process, to reduce the convergence time and to improve the accuracy. Finally, the applicability of the proposed approaches is shown on IRCCyN pneumatic benchmark. Applications are also made on 3DOF flying system
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Cyriac, Aiswarya. "Verification of communicating recursive programs via split-width." Thesis, Cachan, Ecole normale supérieure, 2014. http://www.theses.fr/2014DENS0004/document.
Повний текст джерелаАнотація:
Cette thèse développe des techniques à base d'automates pour la vérification formelle de systèmes physiquement distribués communiquant via des canaux fiables de tailles non bornées. Chaque machine peut exécuter localement plusieurs programmes récursifs (multi-threading). Un programme récursif peut également utiliser pour ses calculs locaux des structures de données non bornées, comme des files ou des piles. Ces systèmes, utilisés en pratique, sont si puissants que tous leurs problèmes de vérification deviennent indécidables. Nous introduisons et étudions un nouveau paramètre, appelé largeur de coupe (split-width), pour l'analyse de ces systèmes. Cette largeur de coupe est définie comme le nombre minimum de scissions nécessaires pour partitioner le graphe d'une exécution en parties sur lesquelles on pourra raisonner de manière indépendante. L'analyse est ainsi réalisée avec une approche diviser pour régner. Lorsqu'on se restreint à la classe des comportements ayant une largeur de coupe bornée par une constante, on obtient des procédures de décision optimales pour divers problèmes de vérification sur ces systèmes tels que l'accessibilité, l'inclusion, etc. ainsi que pour la satisfaisabilité et le model checking par rapport à divers formalismes comme la logique monadique du second ordre, la logique dynamique propositionnelle et des logiques temporelles. On montre aussi que les comportements d'un système ont une largeur de coupe bornée si et seulement si ils ont une largeur de clique bornée. Ainsi, grâce aux résultats de Courcelle sur les graphes de degré uniformément borné, la largeur de coupe est non seulement suffisante, mais aussi nécessaire pour obtenir la décidabilité du problème de satisfaisabilité d'une formule de la logique monadique du second ordre. Nous étudions ensuite l'existence de contrôleurs distribués génériques pour nos systèmes distribués. Nous proposons plusieurs contrôleurs, certains ayant un nombre fini d'états et d'autres étant déterministes, qui assurent que les comportements du système sont des graphes ayant une largeur de coupe bornée. Un système ainsi contrôlé de manière distribuée hérite des procédures de décision optimales pour les différents problèmes de vérification lorsque la largeur de coupe est bornée. Cette classe décidable de système généralise plusieurs sous-classes décidables étudiées précédemmentThis thesis investigates automata-theoretic techniques for the verification of physically distributed machines communicating via unbounded reliable channels. Each of these machines may run several recursive programs (multi-threading). A recursive program may also use several unbounded stack and queue data-structures for its local-computation needs. Such real-world systems are so powerful that all verification problems become undecidable. We introduce and study a new parameter called split-width for the under-approximate analysis of such systems. Split-width is the minimum number of splits required in the behaviour graphs to obtain disjoint parts which can be reasoned about independently. Thus it provides a divide-and-conquer approach for their analysis. With the parameter split-width, we obtain optimal decision procedures for various verification problems on these systems like reachability, inclusion, etc. and also for satisfiability and model checking against various logical formalisms such as monadic second-order logic, propositional dynamic logic and temporal logics. It is shown that behaviours of a system have bounded split-width if and only if they have bounded clique-width. Thus, by Courcelle's results on uniformly bounded-degree graphs, split-width is not only sufficient but also necessary to get decidability for MSO satisfiability checking. We then study the feasibility of distributed controllers for our generic distributed systems. We propose several controllers, some finite state and some deterministic, which ensure that the behaviours of the system have bounded split-width. Such a distributedly controlled system yields decidability for the various verification problems by inheriting the optimal decision procedures for split-width. These also extend or complement many known decidable subclasses of systems studied previously
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Vignoni, Alejandro. "Invariance and Sliding Modes. Application to coordination of multi-agent systems, bioprocesses estimation, and control in living cells." Doctoral thesis, Editorial Universitat Politècnica de València, 2014. http://hdl.handle.net/10251/37743.
Повний текст джерелаАнотація:
The present thesis employs ideas of set invariance and sliding modes
in order to deal with different relevant problems control of nonlinear
systems. Initially, it reviews the techniques of set invariance as well as
the more relevant results about sliding modes control. Then the main
methodologies used are presented: sliding mode reference conditioning,
second order sliding modes and continuous approximation of sliding
modes. Finally, the methodologies are applied to different problems in
control theory and to a variety of biologically inspired applications.
The contributions of the thesis are:
The development of a method to coordinate dynamical systems
with different dynamic properties by means of a sliding mode auxiliary
loop shaping the references given to the systems as function
of the local and global goals, the achievable performance of each
system and the available information of each system.
Design methods for second order sliding mode algorithms. The
methods decouple the problem of stability analysis from that of
finite-time convergence of the super-twisting sliding mode algorithm.
A nonlinear change of coordinates and a time-scaling are
used to provide simple, yet flexible design methods and stability
proofs. Application of the method to the design of finite-time convergence
estimators of bioprocess kinetic rates and specific biomass
growth rate, from biomass measurements. Also the estimators are
validated with experimental data.
The proposal of a strategy to reduce the variability of a cell-to-cell
communication signal in synthetic genetic circuits. The method
uses set invariance and sliding mode ideas applied to gene expression
networks to obtain a reduction in the variance of the communication signal. Experimental approaches available to modify the
characteristics of the gene regulation function are described.Vignoni, A. (2014). Invariance and Sliding Modes. Application to coordination of multi-agent systems, bioprocesses estimation, and control in living cells [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/37743
Alfresco
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Scheunert, Christian. "Über die Modellierung und Simulation zufälliger Phasenfluktuationen." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-64272.
Повний текст джерелаАнотація:
Nachrichtentechnische Systeme werden stets durch unvermeidbare zufällige Störungen beeinflußt. Neben anderen Komponenten sind davon besonders Oszillatoren betroffen. Die durch die Störungen verursachten zufälligen Schwankungen in der Oszillatorausgabe können als Amplituden- und Phasenabweichungen modelliert werden. Dabei zeigt sich, daß vor allem zufällige Phasenfluktuationen von Bedeutung sind. Zufällige Phasenfluktuationen können unter Verwendung stochastischer Prozesse zweiter Ordnung mit kurzem oder langem Gedächtnis modelliert werden. Inhalt der Dissertation ist die Herleitung eines Verfahrens zur Simulation zufälliger Phasenfluktuationen von Oszillatoren mit kurzem Gedächtnis unter Berücksichtigung von Datenblattangaben.
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Casiulis, Mathias. "Étude d'un modèle Hamiltonien de liquide non-Galiléen : du mouvement collectif sans activité." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS647.
Повний текст джерелаАнотація:
Le mouvement collectif, l'ordre spontané des vitesses dans un système macroscopique, est une propriété marquante des systèmes vivants tels que les vols d'oiseaux. Il est prédit par des modèles de particules auto-propulsées, qui sont actives : elles ne conservent ni énergie, ni impulsion. Dans ma thèse, j'étudie un modèle conservatif de mouvement collectif, composé de particules portant des spins couplés à leur vitesse, en m'aidant de notions de physique des liquides, de magnétisme, et de mécanique statistique. Je montre que l'alignement des spins génère une attraction effective, qui est responsable d'une séparation de phase entre un gaz isotrope et un ferroliquide se terminant en un point triple, d'où émerge la ligne de Curie. Je dresse ensuite le diagramme des phases du modèle en présence d'un couplage spin-vitesse, en faisant varier son intensité, le nombre de particules, la densité, et la température. La conservation de l'impulsion impose que les phases polaire soient en mouvement collectif. A basse température et basse densité, je montre que le système peut créer spontanément des défauts d'alignement pour ne pas avoir à se mouvoir et ainsi échapper à un coût élevé en énergie cinétique. Je montre que le système peut transiter d'un état apolaire vers un état polaire lorsque la température augmente, trahissant un phénomène d'ordre par le désordre. Enfin, je montre que le mouvement du système est bien décrit par un modèle effectif de particules auto-propulsées avec de l'inertie de rotation, qui augmente fortement à la transition de rigidité. A haute inertie, le système présente des virages et des rotations spontanées dus à la conservation du moment cinétiqueCollective motion, the spontaneous ordering of the velocities across a macroscopic system, is a hallmark of living systems like flocks of birds.It is captured by models of self-propelled particles, that are usually active: they do not conserve energy nor momentum. In my thesis, using notions from the theory of liquids, magnetism, and statistical mechanics, I study a conservative model of collective motion, composed of particles that carry spins, which are coupled to their velocities. I show that the alignment of spins creates an effective attraction, that is responsible for a phase separation between an isotropic gas and a ferroliquid. This phase separation ends in a tricritical point, from which stems the Curie line. I then establish the full phase diagram of the model with a spin-velocity coupling, varying its amplitude, the number of particles, the density, and the temperature.The conservation of momentum imposes that all polar phases move collectively. At low temperatures and densities, I show that the system spontaneously generates alignment defects so as to stop moving, and thus escapes a high kinetic energy cost. I also show that the system can go from an apolar state to a polar one as the temperature increases, betraying an order-by-disorder phenomenon. Finally, I show that the dynamics of the system is well described by an effective model of self-propelled particles, with a rotational inertia that soars at the rigidity transition. At high inertia, the system moves with spontaneous turns and rotations caused by the conservation of angular momentum
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Ayad, Mohammad. "Homogenization-based, higher-gradient dynamical response of micro-structured media." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0062.
Повний текст джерелаАнотація:
Une approche dynamique discrète (DDM) est proposée dans le contexte de la mécanique des poutres pour calculer les caractéristiques de dispersion des structures périodiques. Cette démarche permet de calculer les caractéristiques de dispersion de milieux périodiques unidimensionnels et bidimensionnels. Il est montré qu’un développement d'ordre supérieur suffisamment élevé des forces et des moments d’éléments structuraux est nécessaire pour décrire avec précision les modes de propagation d’ordre supérieur. Ces résultats montrent dans l’ensemble que les calculs des caractéristiques de dispersion de systèmes structurels périodiques peuvent être abordés avec une bonne précision par la dynamique des éléments discrets. Les comportements non classiques peuvent être capturés non seulement par une expansion d'ordre supérieur mais aussi par des formulations à gradient supérieur. Nous calculons ainsi les paramètres constitutifs macroscopiques jusqu'au deuxième gradient du déplacement en utilisant deux formulations différentes, soit selon une méthode d'homogénéisation dynamique à gradient supérieur (DHGE) prenant en compte les effets de micro-inertie, ou alternativement selon le principe de Hamilton. Nous analysons ensuite la sensibilité des termes constitutifs du second gradient aux paramètres microstructuraux pour des matériaux composites à microstructure périodique de type laminés. En plus, on montre que les modèles du deuxième gradient formulés à partir de l'énergie interne totale en tenant compte des termes de gradient d'ordre supérieur donnent la meilleure description du propagation d’onde à travers ces milieux. On analyse les contributions d'ordre supérieur et de micro-inertie sur le comportement mécanique de structures composites en utilisant une méthode d'homogénéisation dynamique d'ordre supérieur qui intègre les effets de micro-inertie. Nous calculons la réponse effective statique longitudinale à gradient d’ordre supérieur, en quantifiant la différence relative par rapport à la formulation classique de type Cauchy qui repose sur le premier gradient du déplacement. Nous analysons ensuite les propriétés de propagation d’ondes longitudinales en termes de fréquence propre de composites, en tenant compte de la contribution de la micro-inertie. La longueur interne joue un rôle crucial dans les contributions de micro-inertie avec un effet substantiel pour les faibles valeurs de longueur interne, et qui correspond à une large gamme de matériaux utilisés en ingénierie des structures. La méthode d’homogénéisation développée montre un effet de taille important pour les modules élastiques homogénéisés d’ordre supérieur. Par conséquent, nous développons une formulation indépendante de la taille qui est basée sur des termes de correction liée aux moment quadratique. Dans ce contexte, on analyse l’influence des termes de correction sur le comportement statique et dynamique de composites à inclusionA discrete dynamic approach (DDM) is developed in the context of beam mechanics to calculate the dispersion characteristics of periodic structures. Subsequently, based on this dynamical beam formulation, we calculate the dispersion characteristics of one-dimensional and two-dimensional periodic media. A sufficiently high order development of the forces and moments of the structural elements is necessary to accurately describe the propagation modes of higher order. These results show that the calculations of the dispersion characteristics of structural systems can be approached with good accuracy by the dynamics of the discrete elements. Besides, non-classical behaviors can be captured not only by higher order expansion but also by higher gradient formulations. To that scope, we develop a higher gradient dynamic homogenization method with micro-inertia effects. Using this formulation, we compute the macroscopic constitutive parameters up to the second gradient, using two distinct approaches, namely Hamilton’s principle and a total internal energy formulation. We analyze the sensitivity of the second gradient constitutive terms on the inner material and geometric parameters for the case of composite materials made of a periodic, layered microstructure. Moreover, we show that the formulations based on the total internal energy taking into account higher order gradient terms give the best description of wave propagation through the composite. We analyze the higher order and micro-inertia contributions on the mechanical behavior of composite structures by calculating the effective static and dynamic properties of composite beams using a higher order dynamic homogenization method. We compute the effective longitudinal static response with higher order gradient, by quantifying the relative difference compared to the classical formulation of Cauchy type, which is based on the first gradient of displacement. We then analyze the propagation properties of longitudinal waves in terms of the natural frequency of composite structural elements, taking into account the contribution of micro-inertia. The internal length plays a crucial role in the contributions of micro-inertia, which is particularly significant for low internal length values, therefore for a wide range of materials used in structural engineering. The developed method shows an important size effect for the higher gradients, and to remove these effects correction terms have been incorporated which are related to the quadratic moment of inertia. We analyze in this context the influence of the correction terms on the static and dynamic behavior of composites with a central inclusion
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Bernstein, David. "Entwurf einer fehlerüberwachten Modellreduktion basierend auf Krylov-Unterraumverfahren und Anwendung auf ein strukturmechanisches Modell." Master's thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-151975.
Повний текст джерелаАнотація:
Die FEM-MKS-Kopplung erfordert Modellordnungsreduktions-Verfahren, die mit kleiner reduzierter Systemdimension das Übertragungsverhalten mechanischer Strukturen abbilden. Rationale Krylov-Unterraum-Verfahren, basierend auf dem Arnoldi-Algorithmen, ermöglichen solche Abbildungen in frei wählbaren, breiten Frequenzbereichen. Ziel ist der Entwurf einer fehlerüberwachten Modelreduktion auf Basis von Krylov-Unterraumverfahren und Anwendung auf ein strukturmechanisches Model. Auf Grundlage der Software MORPACK wird eine Arnoldi-Funktion erster Ordnung um interpolativen Startvektor, Eliminierung der Starrkörperbewegung und Reorthogonalisierung erweitert. Diese Operationen beinhaltend, wird ein rationales, interpolatives SOAR-Verfahren entwickelt. Ein rationales Block-SOAR-Verfahren erweist sich im Vergleich als unterlegen. Es wird interpolative Gleichwichtung verwendet. Das Arnoldi-Verfahren zeichnet kleiner Berechnungsaufwand aus. Das rationale, interpolative SOAR liefert kleinere reduzierte Systemdimensionen für gleichen abgebildeten Frequenzbereich. Die Funktionen werden auf Rahmen-, Getriebegehäuse- und Treibsatzwellen-Modelle angewendet. Zur Fehlerbewertung wird eigenfrequenzbasiert ein H2-Integrationsbereich festgelegt und der übertragungsfunktionsbasierte, relative H2-Fehler berechnet. Es werden zur Lösung linearer Gleichungssysteme mit Matlab entsprechende Löser-Funktionen, auf Permutation und Faktorisierung basierend, implementiertFEM-MKS-coupling requires model order reduction methods to simulate the frequency response of mechanical structures using a smaller reduced representation of the original system. Most of the rational Krylov-subspace methods are based on Arnoldi-algorithms. They allow to represent the frequency response in freely selectable, wide frequency ranges. Subject of this thesis is the implementation of an error-controlled model order reduction based on Krylov-subspace methods and the application to a mechanical model. Based on the MORPACK software, a first-order-Arnoldi function is extended by an interpolative start vector, the elimination of rigid body motion and a reorthogonalization. Containing these functions, a rational, interpolative Second Order Arnoldi (SOAR) method is designed that works well compared to a rational Block-SOAR-method. Interpolative equal weighting is used. The first-order-Arnoldi method requires less computational effort compared to the rational, interpolative SOAR that is able to compute a smaller reduction size for same frequency range of interest. The methods are applied to the models of a frame, a gear case and a drive shaft. Error-control is realized by eigenfrequency-based H2-integration-limit and relative H2-error based on the frequency response function. For solving linear systems of equations in Matlab, solver functions based on permutation and factorization are implemented
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Cyriac, Aiswarya, and Aiswarya Cyriac. "Verification of communicating recursive programs via split-width." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2014. http://tel.archives-ouvertes.fr/tel-01015561.
Повний текст джерелаАнотація:
This thesis investigates automata-theoretic techniques for the verification of physically distributed machines communicating via unbounded reliable channels. Each of these machines may run several recursive programs (multi-threading). A recursive program may also use several unbounded stack and queue data-structures for its local-computation needs. Such real-world systems are so powerful that all verification problems become undecidable. We introduce and study a new parameter called split-width for the under-approximate analysis of such systems. Split-width is the minimum number of splits required in the behaviour graphs to obtain disjoint parts which can be reasoned about independently. Thus it provides a divide-and-conquer approach for their analysis. With the parameter split-width, we obtain optimal decision procedures for various verification problems on these systems like reachability, inclusion, etc. and also for satisfiability and model checking against various logical formalisms such as monadic second-order logic, propositional dynamic logic and temporal logics. It is shown that behaviours of a system have bounded split-width if and only if they have bounded clique-width. Thus, by Courcelle's results on uniformly bounded-degree graphs, split-width is not only sufficient but also necessary to get decidability for MSO satisfiability checking. We then study the feasibility of distributed controllers for our generic distributed systems. We propose several controllers, some finite state and some deterministic, which ensure that the behaviours of the system have bounded split-width. Such a distributedly controlled system yields decidability for the various verification problems by inheriting the optimal decision procedures for split-width. These also extend or complement many known decidable subclasses of systems studied previously.
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Raei, Mohammed. "Development and Validation of the Adaptive Leadership with Authority Scale." Antioch University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=antioch153684122004308.
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Camargo, Rafael Eclache Moreira de. "Contribuição ao estudo da estabilidade de edifícios de andares múltiplos em aço." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23102012-095939/.
Повний текст джерелаАнотація:
Este trabalho apresenta uma análise comparativa de diferentes sistemas estruturais para um edifício de 20 pavimentos. Cada um dos modelos foi dimensionado através dos princípios do método da análise direta, presente na ABNT NBR 8800:2008. O método da amplificação dos esforços solicitantes (MAES) foi usado para se obter de forma simplificada os esforços atuantes nos elementos do edifício considerando os efeitos locais e globais de segunda ordem. A incidência do vento foi simulada de duas formas diferentes. Na primeira, chamada de uniforme, o vento foi aplicado sem excentricidade, gerando apenas o efeito de tombamento nas estruturas. Na segunda hipótese, considerou-se uma excentricidade devida aos efeitos de vizinhança, prescrita pela ABNT NBR 6123:1988, responsável por ocasionar o tombamento e a torção dos edifícios. Todas as análises numéricas foram repetidas fazendo o uso de outro método simplificado de segunda ordem, conhecido como P-Delta. Por meio dos resultados obtidos, constatou-se que a possibilidade de se reduzir a sobrecarga para o dimensionamento de pilares proporciona uma economia de material, mas, por outro lado, tem como consequência o aumento do tempo de análise, pois exige a utilização de diferentes combinações de cálculo para o dimensionamento de vigas e pilares. A estratégia utilizada para simular os efeitos de vizinhança mostrou-se satisfatória, pois permitiu introduzir de maneira fácil e prática a torção ocasionada pela incidência excêntrica do vento. Observou-se também que esses efeitos ocasionaram o aumento dos momentos fletores e dos deslocamentos das estruturas analisadas. Em relação à avaliação dos efeitos de segunda ordem, comprovou-se que, para a classificação da deslocabilidade, a combinação de cálculo crítica é aquela que possui o maior carregamento gravitacional. Entretanto, para o dimensionamento dos elementos, foi constatado que outras hipóteses de cálculo, principalmente aquelas em que o vento é a ação variável principal, podem ser determinantes. Por fim, foi observado que os resultados obtidos pelo método P-Delta ficaram bastante semelhantes àqueles calculados pelo MAES, com desvios desprezíveis. O MAES, por sua vez, mostrou-se bastante trabalhoso, pois exige a modelagem de diferentes tipos de estruturas para a determinação dos esforços.This work presents a comparative analysis of different structural systems for a 20-storey building. Each model has been designed using the principles of the direct analysis method (DAM), present in the ABNT NBR 8800:2008. The first-order amplification method (FOAM) was used to obtain, in a simplified manner, the forces acting on the building elements, including local and global second-order effects. The incidence of the wind was simulated in two different ways. In the first case, named uniform, the wind was applied without eccentricity, generating only structure overturning. In the second case, it was considered an eccentricity due to vicinity effects, prescribed by the ABNT NBR 6123:1988, responsible for causing twisting and building overturning. All numerical analysis were carried out a simplified second-order method known as P-Delta. From the results obtained it was found that the reduction of live loads in the design of columns provides material economy, but on the other hand, increases analysis time, since it requires different combinations for beams and columns. The strategy used to simulate the vicinity effects was satisfactory, because it allowed, in an easy and practical way, the consideration of the torsion produced by the wind eccentric impact. It was also observed that these effects increased the bending moments and the displacements of the structures. About the second-order effects, it was shown that, for sway or non-sway classification, the critical combination is one with greatest gravitational loading. However, for the design of the elements, it was observed that other loading conditions can be critical, especially those in which the wind is the main live load. Finally, the results obtained by the P-Delta method were very similar to those calculated by the first-order amplification method. The FOAM was, in turn, very laborious, because it requires the modeling of different types of structures for the determination of the forces.
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Janin, David. "Contribution aux fondements des méthodes formelles : jeux, logique et automates." Habilitation à diriger des recherches, Université Sciences et Technologies - Bordeaux I, 2005. http://tel.archives-ouvertes.fr/tel-00659990.
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Ryšavý, Marek. "Zlomkooktává analýza akustických signálů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-241138.
Повний текст джерелаАнотація:
The diploma thesis is focused on design and optimalization of digital octave and fraction-octave band filters. This thesis describe the behavior of filters in systems with fixed point arithmetics and investigate the impact of quantization coefficients for frequency response of filter. Filters, whitch has been designed, are implemented into simple software in C. Designed filters are in accordance with standard IEC 61260.
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Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.
Повний текст джерелаАнотація:
Doutoramento em MatemáticaNesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias são representadas pelas chamadas séries de Chen. Estuda-se a representação formal destas séries através da introdução de várias álgebras não associativas e técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo e de segundo tipo. Apresenta-se uma demonstração alternativa para as coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas de primeiro tipo. Estas últimas estão intimamente ligadas ao logaritmo da série de Chen que, por sua vez, tem fortes relações com uma fórmula designada na literatura por “continuous Baker-Campbell- Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia de um campo de vectores não linear e periódico no tempo em relação a uma truncatura do logaritmo de Chen. No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer dois corpos que rolem um sobre o outro sem deslizar ou torcer. Constroem-se controlos fechados e dependentes do tempo que tornam a origem do sistema de dois corpos num sistema localmente assimptoticamente estável. Vários exemplos e algumas implementações em Maple°c são discutidos. No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o valor de várias funções fundamentais na aritmética digital, sendo possível a sua implementação em microprocessadores. São também obtidos os seus domínios de convergência. No último tópico, também em apêndice, demonstra-se a existência e unicidade de solução para uma classe de equações integrais não lineares com atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade no sentido de Fréchet da solução em relação à função de atraso.
In this PhD thesis several subjects are studied regarding the following topics: formulas for nonlinear control systems on free Lie algebras, stabilizability of nonlinear control systems, digital arithmetic algorithms, and nonlinear Fredholm integral equations with delay. The first and principal topic is mainly related with a problem known as the continuous Baker-Campbell-Hausdorff exponents. We propose a calculus to deal with formal nonautonomous ordinary differential equations evolving on the algebra of formal series defined on an alphabet. We introduce and connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel, chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of those notions were also introduced into the universal enveloping algebra of a free Lie algebra. We study Chen series and iterated integrals by relating them with nonlinear control systems linear in control. At the heart of all the theory of Chen series resides a zinbiel and shuffle homomorphism that allows us to construct a purely formal representation of Chen series on algebras of words. It is also given a pre-zinbiel representation of the chronological exponential, introduced by A.Agrachev and R.Gamkrelidze on the context of a tool to deal with nonlinear nonautonomous ordinary differential equations over a manifold, the so-called chronological calculus. An extensive description of that calculus is made, collecting some fragmented results on several publications. It is a fundamental tool of study along the thesis. We also present an alternative demonstration of the result of H.Sussmann about coordinates of second kind using the mentioned tools. This simple and comprehensive proof shows that coordinates of second kind are exactly the image of elements of the dual basis of a Hall basis, under the above discussed homomorphism. We obtain explicit expressions for the logarithm of Chen series and the respective coordinates of first kind, by defining several operations on a forest of leaf-labelled trees. It is the same as saying that we have an explicit formula for the functional coefficients of the Lie brackets on a continuous Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We apply those formulas to relate some noncommutative symmetric functions, and we also connect the monodromy map of a time-periodic nonlinear vector field with a truncation of the Chen logarithm. On the second topic, we study any system of two bodies rolling one over the other without twisting or slipping. By using the Chen logarithm expressions, the monodromy map of a flow and Lyapunov functions, we construct time-variant controls that turn the origin of a control system linear in control into a locally asymptotically stable equilibrium point. Stabilizers for control systems whose vector fields generate a nilpotent Lie algebra with degree of nilpotency · 3 are also given. Some examples are presented and Maple°c were implemented. The third topic, on appendix, concerns the construction of efficient algorithms for Digital Arithmetic, potentially for the implementation in microprocessors. The algorithms are intended for the computation of several functions as the division, square root, sines, cosines, exponential, logarithm, etc. By using redundant number representations and methods of Lyapunov stability for discrete dynamical systems, we obtain several algorithms (that can be glued together into an algorithm for parallel execution) having the same core and selection scheme in each iteration. We also prove their domains of convergence and discuss possible extensions. The last topic, also on appendix, studies the set of solutions of a class of nonlinear Fredholm integral equations with general delay. The delay is of functional character modelled by a continuous lag function. We ensure existence and uniqueness of a continuous (positive) solution of such equation. Moreover, under additional conditions, it is obtained the Fr´echet differentiability of the solution with respect to the lag function.