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1
Pribadi, Aaron. "Algebraic Methods for Log-Linear Models". Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/41.
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Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case of binary data.
2
Stefanov, Atanas. "On homogeneous Calderón-Zygmund operators with rough kernels /". free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9951125.
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Belloni, Alexandre, i Robert M. Freund. "Projective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System". Massachusetts Institute of Technology, Operations Research Center, 2005. http://hdl.handle.net/1721.1/17074.
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In this paper we present a general theory for transforming a normalized homogeneous conic system F : Ax = 0, s'x = 1, x in C to an equivalent system via projective transformation induced by the choice of a point w in the set H'(s) = { v : s - A'v in C*}. Such a projective transformation serves to pre-condition the conic system into a system that has both geometric and computational properties with certain guarantees. We characterize both the geometric behavior and the computational behavior of the transformed system as a function of the symmetry of w in H'(s) as well as the complexity parameter of the barrier for C. Under the assumption that F has an interior solution, H'(s) must contain a point w whose symmetry is at least 1/m; if we can find a point whose symmetry is O(1/m) then we can projectively transform the conic system to one whose geometric properties and computational complexity will be strongly-polynomial-time in m and the barrier parameter. We present a method for generating such a point w based on sampling and on a geometric random walk on H'(s) with associated complexity and probabilistic analysis. Finally, we implement this methodology on randomly generated homogeneous linear programming feasibility problems, constructed to be poorly behaved. Our computational results indicate that the projective pre-conditioning methodology holds the promise to markedly reduce the overall computation time for conic feasibility problems; for instance we observe a 46% decrease in average IPM iterations for 100 randomly generated poorly-behaved problem instances of dimension 1000 × 5000.
4
Kasperski, Michael William. "Multiple model estimation for linear stochastic hybrid systems with non-homogeneous transition probabilities". Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101496.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-64).
This thesis investigates the field of stochastic hybrid estimation. A broad introduction to the framework surrounding estimation, filtering, and multiple model based systems is presented. More specifically, the often made assumption of a constant time-invariant mode transition probability matrix is relaxed. Recent work done in the area of non-Markov jump stochastic hybrid systems is explored, including semi- Markov systems, non-homogeneous transition probability matrices, and continuous-state-dependent mode transitions. Algorithms needed to develop linear multiple model based filters with non-homogeneous transition probabilities are detailed. Finally, a case study for the practical implementation of an extended Kalman filter in the application of attitude heading and reference systems is conducted.
by Michael William Kasperski.
S.M.
5
Siletti, E. "Homogeneous Linear Predictor Models Specified by Constraints on the Goodman and Kruskal Tau Index". Doctoral thesis, Università degli Studi di Milano, 2008. http://hdl.handle.net/2434/484183.
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In this work we focus our research in Lang’s HLP models for contingency tables,
constraining the expected table counts through the Goodman and Kruskal tau-b and, or
the Gini’s index. Although we have used them, a lot of other measures can be used in
this kind of models. For example, to measure association in discrete variable we could
use odds ratios or coefficients derived from them such as the Goodman and Kruskal’s
gamma or Kendall’s tau. For HLP models link function is allowed to be many-to-one and
nonlinear. If the link functions are many to one as in our work, it is generally not
possible to re-express the likelihood in terms of the linear predictor parameter β alone.
This is one of the main reason that the ML approach has in the past typically been
abandoned in favour of alternative fitting methods. Although less of an issue today, ML
estimation was also avoided in the past because of computational complexity.
Following Lang’s approach we use ML estimation which is an attractive alternative to
non iterative weighted least squares for several reason: including model based estimates
of cell probabilities along with cell specific residuals are available; likelihood ratio and
score statistics are available and, unlike the Wald statistics, are invariant to the model
parameterization; profile likelihood confidence intervals are available; smoothed
estimates of the link function variance are used, mitigating potential problems with zero
counts; the ML estimation method does not require full rank link function Jacobian; ML
estimates are invariant; and estimators have higher order efficiency properties that are
not shared by WLS estimators.
In order to calculate the derivatives respect to the joint probabilities of the link functions
we have introduced the exp-log notation, in this way, only the derivative matrix of this
formula has been implemented and derived. Then, because following Lang the
constraint functions for HLP models must be function of the single variable m, to use the
Goodman and Kruskal measure of association and the Gini’s heterogeneity index as
constraints, we have specified them in the exp-log notation using the expected counts.
To use them in existing Lang’s computer procedure mph.fit, we have written some new
R’s functions. Two functions which calculate the measures using expected counts and
exp-log notation; and two function which calculate their derivatives.
6
Yuan, Chaogui. "On non-homogeneous quasi-linear PDEs involving the p-Laplacian and the critical Sobolev exponent". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/NQ27272.pdf.
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Person, Axelle. "Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order". Rennes 1, 2002. http://www.theses.fr/2002REN1A007.
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Koroma, Samuel Gerald. "Vibration of beams on non-linear and non-homogeneous elastic foundations with applications to railway tracks". Thesis, University of Nottingham, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.756108.
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The ever growing demand for public transportation and the need to integrate effective transport systems into urban life have led to an increase in the planning and construction of new railway systems in many countries around the world. These projects boast immense economic benefits, including high passenger capacity and reduction in commuting times. However, they are strongly opposed from an environmental point of view, not least the noise and vibration that are generated from their operations and subsequently transmitted into nearby buildings. In order to reduce the level of impact of the rail vehicles on the tracks, and subsequently the environment, railway tracks are commonly constructed with resilient elements, e.g. railpads. The dynamic properties of these elements have significant effects on noise generation, track and ground-borne vibration. It is important to develop understanding of the dynamic behaviour of railway tracks, through numerical modelling and/or experimental testing, in order to devise effective vibration countermeasures. To this end, many numerical models have been developed, most of which assumed linear and homogeneous track properties. However, many studies have shown that resilient elements exhibit pronounced nonlinear behaviour and that variability in track properties exists along the length of the track. In this study, novel approaches for incorporating nonhomogeneous and non-linear railpad properties in the modelling of railway track dynamics have been developed. A new method, called the Double Fourier Summation, have been used to account for nonhomogeneity in track foundation properties. To account for nonlinearity, on the other hand, constitutive relationships have been derived for the static and dynamic rail pad properties based on experimental data. These are then included into a time domain finite elements track model in order to study the effects of nonlinearity on track dynamics. The key findings of this research emphasise the necessity of including non-homogeneous and nonlinear behaviour of track resilience into the modelling of track dynamics. Large disparities in the track displacement, reaction-forces and wheel/rail interaction forces (more than 20 dB in some cases), have been observed between simplified linear homogeneous models and the more complex nonhomogeneous and nonlinear models presented in this work.
9
Junkins, Caroline. "The Grothendieck Gamma Filtration, the Tits Algebras, and the J-invariant of a Linear Algebraic Group". Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31331.
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Consider a semisimple linear algebraic group G over an arbitrary field F, and a projective homogeneous G-variety X. The geometry of such varieties has been a consistently active subject of research in algebraic geometry for decades, with significant contributions made by Grothendieck, Demazure, Tits, Panin, and Merkurjev, among others. An effective tool for the classification of these varieties is the notion of a cohomological (or alternatively, a motivic) invariant. Two such invariants are the set of Tits algebras of G defined by J. Tits, and the J-invariant of G defined by Petrov, Semenov, and Zainoulline. Quéguiner-Mathieu, Semenov and Zainoulline discovered a connection between these invariants, which they developed through use of the second Chern class map.
The first goal of the present thesis is to extend this connection through the use of higher Chern class maps. Our main technical tool is the Steinberg basis, which provides explicit generators for the γ-filtration on the Grothendieck group K_0(X) in terms of characteristic classes of line bundles over X. As an application, we establish a connection between the J-invariant and the Tits algebras of a group G of inner type E6.
The second goal of this thesis is to relate the indices of the Tits algebras of G to nontrivial torsion elements in the γ-filtration on K_0(X). While the Steinberg basis provides an explicit set of generators of the γ-filtration, the relations are not easily computed. A tool introduced by Zainoulline called the twisted γ-filtration acts as a surjective image of the γ-filtration, with explicit sets of both generators and relations. We use this tool to construct torsion elements in the degree 2 component of the γ-filtration for groups of inner type D2n. Such a group corresponds to an algebra A endowed with an orthogonal involution having trivial discriminant. In the trialitarian case (i.e. type D4), we construct a specific element in the γ-filtration which detects splitting of the associated Tits algebras. We then relate the non-triviality of this element to other properties of the trialitarian triple such as decomposability and hyperbolicity.
10
Montcalm, Michael R. "Scheduling Algorithms for Instruction Set Extended Symmetrical Homogeneous Multiprocessor Systems-on-Chip". Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20056.
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Embedded system designers face multiple challenges in fulfilling the runtime requirements of programs. Effective scheduling of programs is required to extract as much parallelism as possible. These scheduling algorithms must also improve speedup after instruction-set extensions have occurred. Scheduling of dynamic code at run time is made more difficult when the static components of the program are scheduled inefficiently. This research aims to optimize a program’s static code at compile time. This is achieved with four algorithms designed to schedule code at the task and instruction level. Additionally, the algorithms improve scheduling using instruction set extended code on symmetrical homogeneous multiprocessor systems. Using these algorithms, we achieve speedups up to 3.86X over sequential execution for a 4-issue 2-processor system, and show better performance than recent heuristic techniques for small programs. Finally, the algorithms generate speedup values for a 64-point FFT that are similar to the test runs.
11
Yoerger, Edward J. Jr. "Vertical Acoustic Propagation in the Non-Homogeneous Layered Atmosphere for a Time-Harmonic, Compact Source". ScholarWorks@UNO, 2019. https://scholarworks.uno.edu/td/2709.
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In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer.
In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method.
In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions.
For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP.
Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method
12
Lawson, Brodie Alexander James. "Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations". Thesis, Queensland University of Technology, 2013. https://eprints.qut.edu.au/61066/1/Brodie_Lawson_Thesis.pdf.
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Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo.
However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here.
The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment.
This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations.
These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography.
Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised.
Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.
13
Agrell, Fredrik. "Control of HCCI by aid of Variable Valve Timings with Specialization in Usage of a Non-Linear Quasi-Static Compensation". Doctoral thesis, Stockholm : Department of Machine Design, Royal Institute of Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4070.
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Willden, Charles C. "Using an Experimental Mixture Design to Identify Experimental Regions with High Probability of Creating a Homogeneous Monolithic Column Capable of Flow". BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3167.
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Graduate students in the Brigham Young University Chemistry Department are working to develop a filtering device that can be used to separate substances into their constituent parts. The device consists of a monomer and water mixture that is polymerized into a monolith inside of a capillary. The ideal monolith is completely solid with interconnected pores that are small enough to cause the constituent parts to pass through the capillary at different rates, effectively separating the substance. Although the end objective is to minimize pore sizes, it is necessary to first identify an experimental region where any combination of input variables will consistently yield homogeneous monoliths capable of flow. To accomplish this task, an experimental mixture design is used to model the relationship between the variables related to the creation of the monolith and the probability of creating an acceptable polymer. The results of the mixture design suggest that, inside of the constrained experimental region, mixtures with higher proportions of monomer and surfactant, low amounts of initiator and salt, and DEGDA as the monomer have the highest probability of producing a workable monolith. Confirmatory experiments are needed before future experimentation to minimize pore sizes is performed using the refined constrained experimental region determined by the results of this analysis.
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Dey, Prasenjit. "Exciton Dynamics and Many Body Interactions in Layered Semiconducting Materials Revealed with Non-linear Coherent Spectroscopy". Thesis, University of South Florida, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10076073.
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Atomically thin, semiconducting transition metal dichalogenides (TMDs), a special class of layered semiconductors, that can be shaped as a perfect two dimensional material, have garnered a lot of attention owing to their fascinating electronic properties which are achievable at the extreme nanoscale. In contrast to graphene, the most celebrated two-dimensional (2D) material thus far; TMDs exhibit a direct band gap in the monolayer regime. The presence of a non-zero bandgap along with the broken inversion symmetry in the monolayer limit brands semiconducting TMDs as the perfect candidate for future optoelectronic and valleytronics-based device application. These remarkable discoveries demand exploration of different materials that possess similar properties alike TMDs. Recently, III-VI layered semiconducting materials (example: InSe, GaSe etc.) have also emerged as potential materials for optical device based applications as, similar to TMDs, they can be shaped into a perfect two-dimensional form as well as possess a sizable band gap in their nano-regime. The perfect 2D character in layered materials cause enhancement of strong Coulomb interaction. As a result, excitons, a coulomb bound quasiparticle made of electron-hole pair, dominate the optical properties near the bandgap. The basis of development for future optoelectronic-based devices requires accurate characterization of the essential properties of excitons. Two fundamental parameters that characterize the quantum dynamics of excitons are: a) the dephasing rate, γ, which represents the coherence loss due to the interaction of the excitons with their environment (for example- phonons, impurities, other excitons, etc.) and b) excited state population decay rate arising from radiative and non-radiative relaxation processes. The dephasing rate is representative of the time scale over which excitons can be coherently manipulated, therefore accurately probing the source of exciton decoherence is crucial for understanding the basic unexplored science as well as creating technological developments. The dephasing dynamics in semiconductors typically occur in the picosecond to femtosecond timescale, thus the use of ultrafast laser spectroscopy is a potential route to probe such excitonic responses.
The focus of this dissertation is two-fold: firstly, to develop the necessary instrumentation to accurately probe the aforementioned parameters and secondly, to explore the quantum dynamics and the underlying many-body interactions in different layered semiconducting materials. A custom-built multidimensional optical non-linear spectrometer was developed in order to perform two-dimensional spectroscopic (2DFT) measurements. The advantages of this technique are multifaceted compared to regular one-dimensional and non-linear incoherent techniques. 2DFT technique is based on an enhanced version of Four wave mixing experiments. This powerful tool is capable of identifying the resonant coupling, probing the coherent pathways, unambiguously extracting the homogeneous linewidth in the presence of inhomogeneity and decomposing a complex spectra into real and imaginary parts. It is not possible to uncover such crucial features by employing one dimensional non-linear technique.
Monolayers as well as bulk TMDs and group III-VI bulk layered materials are explored in this dissertation. The exciton quantum dynamics is explored with three pulse four-wave mixing whereas the phase sensitive measurements are obtained by employing two-dimensional Fourier transform spectroscopy. Temperature and excitation density dependent 2DFT experiments unfold the information associated with the many-body interactions in the layered semiconducting samples.
16
Eslick, John. "A Dynamical Study of the Evolution of Pressure Waves Propagating through a Semi-Infinite Region of Homogeneous Gas Combustion Subject to a Time-Harmonic Signal at the Boundary". ScholarWorks@UNO, 2011. http://scholarworks.uno.edu/td/1367.
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In this dissertation, the evolution of a pressure wave driven by a harmonic signal on the boundary during gas combustion is studied. The problem is modeled by a nonlinear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for any transient effects to have dissipated. The zeroth, first and second-order perturbation solutions are obtained and their moduli are plotted against frequency. It is seen that the first and second-order corrections have unique maxima that shift to the right as the frequency decreases and to the left as the frequency increases. Dispersion relations are determined and their limiting behavior investigated in the low and high frequency regimes. It is seen that for low frequencies, the medium assumes a diffusive-like nature. However, for high frequencies the medium behaves similarly to one exhibiting relaxation. The phase speed is determined and its limiting behavior examined. For low frequencies, the phase speed is approximately equal to sqrt[ω/(n+1)] and for high frequencies, it behaves as 1/(n+1), where n is the mode number. Additionally, a maximum allowable value of the perturbation parameter, ε = 0.8, is determined that ensures boundedness of the solution. The location of the peak of the first-order correction, xmax, as a function of frequency is determined and is seen to approach the limiting value of 0.828/sqrt(ω) as the frequency tends to zero and the constant value of 2 ln 2 as the frequency tends to infinity. Analytic expressions are obtained for the approximate general perturbation solution in the low and high-frequency regimes and are plotted together with the perturbation solution in the corresponding frequency regimes, where the agreement is seen to be excellent. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from the boundary will be negligible. The perturbation solution and the finite-difference solution are found to be in excellent agreement. Thus, the validity of the perturbation method is established.
17
Dauguet, Simon. "Généralisations du critère d’indépendance linéaire de Nesterenko". Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112085/document.
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Cette thèse s'inscrit dans le prolongement du résultat d'Apéry donnant l'irrationalité de ζ (3) et de celui de Ball-Rivoal prouvant qu'il existe une infinité d'entiers impairs en lesquels la fonction zêta de Riemann prend des valeurs irrationnelles. Un outil crucial dans la démonstration de Ball-Rivoal est le critère d'indépendance linéaire de Nesterenko, qui a été généralisé par Fischler et Zudilin pour exploiter sous des hypothèses très restrictives la présence de diviseurs communs aux coefficients des formes linéaires. Une généralisation ultérieure due à Fischler s'applique lorsqu'on dispose d'approximations simultanées des nombres réels en question (et non plus de combinaisons Z-linéaires petites de ces nombres).Dans cette thèse, on améliore ce dernier résultat en affaiblissant considérablement les hypothèses sur les diviseurs. On démontre aussi un critère d'indépendance linéaire analogue, dans l'esprit de celui de Siegel. Dans une autre partie en commun avec Zudilin, on construit, en utilisant des identités hypergéométriques, des approximations simultanées de ζ (2) et ζ (3) qui permettent de démontrer en même temps l'irrationalité de ces deux nombres. En appliquant essentiellement le critère démontré précédemment, on en déduit une minoration des combinaisons Z-linéaires de 1, ζ 2) et ζ (3), sous des hypothèses de divisibilité très fortes sur les coefficients (si bien que l'indépendance linéaire sur Q de ces trois nombres est toujours conjecturale)This Ph.D. thesis lies in the path opened by Apéry who proved the irrationality of ζ(3) andalready followed by Ball-Rivoal who proved that there are infinitely many odd integers at which Riemann zeta function takes irrational values. A fundamental tool in the proof of Ball-Rivoal is Nesterenko’s linear independence criterion. This criterion has been generalized by Fischler and Zudilin to use common divisors of the coefficients of linear forms, under some restrictive assumptions. Then Fischler gave another generalization for simultaneous approximations (instead of small Z-linear combinations).In this Ph.D. thesis, we improve this last result by greatly weakening the assumption on thedivisors. We prove also an analogous linear independence criterion in the spirit of Siegel. Inanother part joint with Zudilin, we construct simultaneous linear approximations to ζ(2) and ζ(3) using hypergeometric identitites. These linear approximations allow one to prove at thesame time the irrationality of ζ(2) and that of ζ(3). Then, using a criterion from the previouspart, we deduce a lower bound on Z-linear combinations of 1, ζ(2) and ζ(3), under somestrong divisibility hypotheses on the coefficients (so that the Q-linear independence of thesethree numbers still remains an open problem)
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Oliveira, Ricardo Coração de Leão Fontoura de 1978. "Estudo de robustez em sistemas lineares por meio de relaxações em termos de desigualdades matriciais lineares". [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260563.
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Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-06T10:51:24Z (GMT). No. of bitstreams: 1 Oliveira_RicardoCoracaodeLeaoFontourade_D.pdf: 881205 bytes, checksum: 053263f18afcf3085a0fc073e1594d2d (MD5) Previous issue date: 2006
Resumo: A principal contribuição desta tese é a proposta de uma metodologia para solução de desigualdades matriciais lineares dependentes de parâmetros que freqüentemente aparecem em problemas de análise e controle robusto de sistema lineares com incertezas na forma politópica. O método consiste na parametrização das soluções em termos de polinômios homogêneos com coeficientes matriciais de grau arbitrário. Para a construção dessas soluções, um procedimento baseado em resoluções de problemas de otimiza¸c¿ao na forma de um número finito de desigualdades matriciais lineares 'e proposto, resultando em seqüências de relaxações que convergem para uma solução polinomial homogênea sempre que uma solução existe. Problemas de análise robusta e custo garantido s¿ao analisados em detalhes tanto para sistemas a tempo contínuo quanto para sistemas discretos no tempo. Vários exemplos numéricos são apresentados ilustrando a eficiência dos métodos propostos em termos da acurácia dos resultados e do esforço computacional quando comparados com outros métodos da literatura
Abstract: This thesis proposes, as main contribution, a new methodology to solve parameterdependent linear matrix inequalities which frequently appear in robust analysis and control problems of linear system with polytopic uncertainties. The proposed method relies on the parametrization of the solutions in terms of homogeneous polynomials of arbitrary degree with matrix valued coefficients. For constructing such solutions, a procedure based on optimization problems formulated in terms of a finite number of linear matrix inequalities is proposed, yielding sequences of relaxations which converge to a homogeneous polynomial solution whenever a solution exists. Problems of robust analysis and guaranteed costs are analyzed in details for continuous and discrete-time uncertain systems. Several numerical examples are presented illustrating the efficiency of the proposed methods in terms of accuracy and computational burden when compared to other methods from the literature
Doutorado
Automação
Doutor em Engenharia Elétrica
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Miyamura, Mauricio Yudi. "Reflexidade de espaços de operadores lineares e espaços de polinomios homogeneos". [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307330.
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Orientador: Jorge Tulio Mujica AscuiDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Sejam E e F espaços de Banach. Os principais resultados que iremos expor serão teoremas sobre a reflexividade de L (E; F) e P (mE; F).. No capítulo 2, estudamos alguns conceitos básicos da teoria de produtos tensoriais de espaços de Banach. A importância do capítulo 2 para o trabalho seria, essencialmente, a identificação do espaço de operadores lineares contínuos L (E; F) com o dual do produto tensorial projetivo E ÄpF?. No capítulo 3, que trata de espaços de polinômios homogêneos, incluímos de noções e resultados básicos e estudamos um teorema de linearização que permitirá transferir resultados em espaços de operadores lineares para espaços de polinômios homogêneos.
Abstract: Let E and F be Banach spaces. The main results in this work are theorems concerning the reflexivity of L (E; F) and P (mE; F). In Chapter 2, we study basic concepts of the theory of tensor products of Banach spaces. The importance of Chapter 2 will be, essentially, the identification of the space of continuous linear operators L(E; F) with the dual of the projective tensor product E ÄpF?. In Chapter 3, that deals with homogeneous polynomials, we include basic definitions and results and we study a linearization theorem that will allow to transfer results from spaces of linear operators to spaces of homogeneous polynomials.
Mestrado
Matematica
Mestre em Matemática
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Nasr, Alexandre. "De la compréhension vers la conception de nouveaux complexes au molybdène pour la métathèse des oléfines linéaires". Thesis, Lyon 1, 2013. http://www.theses.fr/2013LYO10177/document.
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Cette thèse porte sur l'élaboration de nouveaux complexes au molybdène bien définis pour la métathèse des oléfines. La majeure partie des travaux porte sur la synthèse et l'étude de la réactivité des acides arylboriniques avec un précurseur au molybdène. La fonction hydroxyle des acides permet de substituer un des deux ligands pyrroles du précurseur Mo(N(2,6 iPr2C6H3))(CHCMe2Ph)(2,5- Me2NC4H2)2 pour conduire à de nouveaux complexes comportant une liaison Mo–O–B. La résolution par diffraction des rayons X a permis de confirmer la structure du complexe Mo(N(2,6- iPr2C6H3))(CHCMe2Ph)(2,5-Me2NC4H2)(OB(Mes)2) (Mes = 2,4,6-Me3C6H2) obtenu ainsi que la nature covalente des liaison Mo–O et O–B. Ce complexe mono boroxy pyrrolure (MBP) s'est avéré actif pour l'homométathèse sélective d'oléfines linéaires modèles (octène-1 et octène-2). L'utilisation d'autres acides arylboriniques synthétisés au laboratoire a permis de générer in situ de nouveaux complexes mono boroxy pyrrolure et de comparer leur réactivité pour la métathèse de l'octène-1 et de l'octène-2 sans les isoler. Nous nous sommes également intéressés à la réactivité de ligands alkoxy fonctionnalisés par une phosphine avec un précurseur du molybdène. L'étude par diffraction des rayons X du complexe chélate pentavalent Mo(N(2,6-iPr2C6H3))(CHCMe2Ph)(2,5- Me2NC4H2)(OCMe2(CH2)2PPh2) a confirmé la formation d'une liaison Mo–P covalente de coordination. Cette liaison renforce la stabilité du complexe vis-à vis de l'air et de l'humidité. Il n'est cependant pas actif pour la métathèse des oléfines linéaires. L'emploi d'acides de Lewis et d'acides de Brønsted comme activateurs de ces complexes chélates a été abordéThis thesis is about the design of new well-defined molybdenum-based complexes for olefin metathesis. The main part of this work dealt with the synthesis and the reactivity of arylborinic acids with molybdenum complexes precursor. Mo(N(2,6-iPr2C6H3))(CHCMe2Ph)(2,5-Me2NC4H2)2 precursor reacted with the hydroxyl moiety of the acid to remove one pyrrolide ligand leading to new complexes bearing a Mo–O–B bond. X-ray diffraction confirmed such structure for Mo(N(2,6- iPr2C6H3))(CHCMe2Ph)(2,5-Me2NC4H2)(OB(Mes)2) (Mes = 2,4,6-Me3C6H2) complex. This mono boroxy pyrrolide (MBP) complex showed activity for model linear olefins homometathesis (1-octene and 2-octene). Screening of more synthesized arylborinic acids lead to in situ generation of new MBP complexes which demonstrated activity for 1-octene and 2-octene homometathesis without requiring their isolation. We also focused on the reactivity of alkoxy ligands bearing phosphine moieties with molybdenum complexes precursor. X-ray diffraction of the five-coordinated Mo(N(2,6- iPr2C6H3))(CHCMe2Ph)(2,5-Me2NC4H2)(OCMe2(CH2)2PPh2) adduct confirmed formation on an strong Mo–P covalent bond. This bond strengthen stability of the complexe towair air and moisture. Nonetheless, this complex did not show activity for linear olefin metathesis. The use of Lewis acids and Brønsted acids as activators for these adducts has been studied and described
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Žilėnaitė, Judita. "Koliestinių sluoksniuočių homogeninės beveik kompleksinės struktūros". Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120813_131717-04146.
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Darbe nagrinėjamos koliestinės sluoksniuotės su apibrėžta metrika. Parodyta kaip šių erdvių metrinis tenzorius indukuoja tiesinę ir afiniąją sietį, surasti šių siečių kreivumo objektai. Įrodyta, kad šiose sluoksniuotėse egzistuoja vidinės homogeninės beveik kompleksinės struktūros. Nustatytos šių struktūrų integruojamumo sąlygos, surastos sąlygos, kad šį struktūra būtų Kelerio tipo.In this paper cotangent bundle with determinate metrics are analysed. It is shown how metrical tensor of those spaces induces linear and affine connections, also objects of those connections‘ curvature are found. It is proved that intrinsic homogeneous almost complex structure exists in that bundle. Conditions of those structure integration are identified as well as conditions for this structure to be Kahler‘s type are found.
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Almeida, Valério da Silva. "Análise da interação solo não-homogêneo/estrutura via acoplamento MEC/MEF". Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-31032016-094320/.
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O estudo do comportamento mecânico do complexo sistema advindo da interação entre solo/subestrutura/superestrutura é o tema do trabalho. Neste contexto, a representação do maciço é feita usando-se o método dos elementos de contorno (MEC) em abordagem 3D, de maneira que se possa simular o maciço com características mecânicas não-homogêneas, além de se considerar uma camada de apoio indeslocável a distâncias prescritas a priori e condição de aderência perfeita. A subestrutura também é representada via MEC tridimensional, a qual está imersa dentro deste meio heterogêneo. A infra e a superestrutura são modeladas empregando o método dos elementos finitos (MEF), com o uso de elementos estruturais reticulares e elementos laminares. São apresentados alguns exemplos em que se valida a formulação e outros que demonstram a potencialidade e a necessidade de se empregar a formulação para a melhor análise do complexo fenômeno em estudo. Por fim, demonstra-se a obrigatoriedade de se otimizar a formulação, empregando-se duas grandes ferramentas numéricas: o paralelismo e o emprego de um adequado método de resolução de sistemas esparsos.The analysis of the soil-structure system interaction is a vast field of interest in the area of civil engineering. A realistic representation of its behaviour. Thus, in the present research, the soil is considered a non-homogeneous continuum supported by a rigid and adhesive interface and modelled by boundary element method via Kelvin solution in 3D space. The foundation is also modelled by this above-mentioned modelling technique. The raft foundation and the superstructure are represented by finite shell and 3D frame elements. In order to estimate the accuracy and the potentiality of the proposed numerical formulation, some examples are validated when compared to similar approaches, and others simulations are presented to stress the necessity of coupling the non-homogeneous soil-foundation-radier-superstructure system as a whole. Finally, to acquire numerical time efficiency, it is shown that it is imperative to apply parallel processing and sparse techniques for the solution of the final system.
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Leveneur, Sébastien. "Catalytic synthesis and decomposition of peroxycarboxylic acids". Phd thesis, INSA de Rouen, 2009. http://tel.archives-ouvertes.fr/tel-00560883.
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L'objectif de cette thèse fut de développer un process pour la production d'acide peroxycarbolique à partir du peroxyde d'hydrogène et d'un acide carboxylique dans un réacteur continu. Dans un premier temps, la stabilité des espèces peroxydées fut étudiée en utilisant une méthode d'analyse en direct (spectromètre de masse). Un effort particulier a été apporté pour trouver un catalyseur hétérogène ne provoquant pas la décomposition des espèces peroxydées et ayant une activité catalytique similaire à l'acide sulfurique. Un réacteur en continu en lit fixe a été construit en utilisant des résines échangeuses de cation.
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Moura, Fernanda Ribeiro de. "Ideais algebricos de aplicações multilineares e polinômios homogêneos". Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/16812.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorThe main purpose of this dissertation is the study of ideals of multilinear mappings and homogeneous polynomials between linear spaces. By an ideal we mean a class that is stable under the composition with linear operators. First we study multilinear mappings and spaces of multilinear mappings. We also show how to obtain, from a given multilinear mapping, other multilinear mappings with degrees of multilinearity greater than, equal to or smaller than the degree of the original multilinear mapping. Next we study homogeneous polynomials and spaces of homogeneous polynomials, and we also show how to obtain, from a given n-homogeneous polynomial, other polynomials with degrees of homogeneity greater than, equal to or smaller than the degree of the original polynomial. Next we study ideals of multilinear mappings, or multi-ideals, and ideals of homogeneous polynomial, or polynomial ideals, giving several examples and presenting methods to generated multi-ideals and polynomial ideals from a given operator ideal. Finally we dene and give several examples of coherent multi-ideals and coherent polynomial ideals.
O principal objetivo desta dissertação e estudar os ideais de aplicações multilineares e polinômios homogêneos entre espaços vetoriais. Por um ideal entendemos uma classe de aplicações que e estavel atraves da composição com operadores lineares. Primeiramente estudamos as aplicações multilineares e os espaços de aplicações multilineares. Mostramos tambem como obter, a partir de uma aplicação multilinear dada, outras aplicações com graus de multilinearidade maiores, iguais ou menores que o da aplicação original. Em seguida estudamos os polinômios homogêneos e os espacos de polinômios homogêneos, e mostramos que, a partir de um polinômio n-homogêneo, tambem podemos construir novos polinômios homogêneos com graus de homogeneidade maiores, iguais ou menores que n. Posteriormente estudamos os ideais de aplicações multilineares, ou multi-ideais, e os ideais de polinômios homogêneos, exibindo varios exemplos e apresentando metodos para se obter um multi-ideais, ou ideais de polinômios, a partir de ideais de operadores lineares dados. Por m, denimos e exibimos varios exemplos de multi-ideais coerentes e de ideais coerentes de polinômios.
Mestre em Matemática
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Genovés, Gómez Vicente. "New non-destructive testing techniques based on mechanical waves: Development and application to damage characterization on non-homogeneus materials". Doctoral thesis, Universitat Politècnica de València, 2019. http://hdl.handle.net/10251/114799.
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Esta tesis doctoral se encuentra desarrollada en los ámbitos de materiales, ensayos
no destructivos y procesado de señal. Su propósito es aportar nuevas técnicas no
destructivas centrándose tanto en su desarrollo como en su aplicación a sistemas
reales. La evaluación de durabilidad y daño en materiales no homogéneos es el
eje central de este documento, articulándolo en dos capítulos fundamentales. En
primera instancia se evalúa el comportamiento del cemento reforzado con fibra de
vidrio bajo esfuerzo de flexión. Múltiples señales ultrasónicas fueron adquiridas
en todo el proceso de deformación de los elementos implementando una nueva
técnica de adquisición multifrecuencia. En la fase posterior a la adquisición se
determinaron parámetros lineales y no lineales de las señales ultrasónicas pulsadas
correlacionando dichos parámetros con las curvas tensión - deformación
descritas por los elementos ensayados. En el último bloque se expone el análisis
de espectroscopía por impacto sobre probetas de mortero dañadas química y térmicamente.
Se profundizó sobre el comportamiento dinámico no-lineal e histéretico
de los elementos de mortero. El análisis del ablandamiento del módulo dinámico
con el incremento de la amplitud de excitación es un tema de gran interés para
la evaluación de daño, siendo la técnica actual dependiente de la adquisición de
múltiples señales. En este contexto, se propone nueva técnica de procesado de
señal capaz de extraer parámetros de esta naturaleza a partir de una única señal.Aquesta tesi doctoral està desenvolupada als àmbits de materials, assajos no destructius i processament de senyals. El seu propòsit és aportar noves tècniques no destructives, centrades tant en el seu desenvolupament com en la seua aplicació a sistemes reals. L'avaluació de durabilitat i dany en materials no homogenis és l'eix central d'aquest document, format per dos capítols fonamentals. En primer lloc s'avalua el comportament del ciment reforçat amb fibra de vidre sotmès a esforç de flexió. Diverses senyals ultrasòniques van ser adquirides durant tot el procés de deformació dels elements que implementa una nova tècnica d'adquisició multifreqüència. En la fase posterior a l'adquisició es van determinar paràmetres lineals i no lineals de les senyals ultrasòniques polsades que correlacionen aquests paràmetres amb les corbes de tensió-deformació descrites pels elements assajats. Al tercer bloc s'exposa l'anàlisi d'espectroscòpia per impacte en provetes de morter malmeses químicament i tèrmicament. Es va aprofundir en el comportament dinàmic no lineal i histerètic dels elements de morter. L'anàlisi de l'estovament del mòdul dinàmic amb l'increment de l'amplitud de l'excitació és un aspecte molt interessant per a l'avaluació de dany, tècnica que actualment depèn de l'adquisició de diverses senyals. En aquest context, es proposa una nova tècnica de processament de senyal capaç d'extraure paràmetres d'aquesta natura a partir d'una única senyal.
This doctoral thesis is developed in materials, Non-Destructive Testing (NDT) and signal processing fields. Its purpose is to make a contribution in new non destructive techniques focusing in its development and application to real systems. Durability and damage evaluation in non-homogeneous materials is the keystone of this document, assembling the structure in two main chapters. In the first instance the behaviour of Glass-fiber Reinforced Cement under bending test is evaluated. Multiple ultrasonic signals during the deformation process of the specimens were acquired, implementing a new multi-frequency acquisition technique. After the acquisition stage, linear and non-linear parameters were calculated from the pulsed ultrasonic signals correlating those parameters with the stress strain curve described during the test. In the third chapter, the impact spectroscopy analysis applied to chemical and thermal damaged mortar samples is exposed. The non-linear histeretic behaviour of the mortar specimens was studied more in depth. The analysis of the dynamic modulus softening with increment of the excitation amplitude is a hot spot at this moment for damage evaluation, being the current technique depending on the multiple signals acquisition. In this context, a new technique is proposed which allows a non-linear parameters extraction from a single reverberation signal.
Genovés Gómez, V. (2018). New non-destructive testing techniques based on mechanical waves: Development and application to damage characterization on non-homogeneus materials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/114799
TESIS
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Křehlík, Štěpán. "Strukturované multisystémy a multiautomaty indukované časovými procesy". Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2015. http://www.nusl.cz/ntk/nusl-234457.
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In the thesis we discuss binary hyperstructures of linear differential operators of the second order both in general and (inspired by models of specific time processes) in a special case of the Jacobi form. We also study binary hyperstructures constructed from distributive lattices and suggest transfer of this construction to n-ary hyperstructures. We use these hyperstructures to construct multiautomata and quasi-multiautomata. The input sets of all these automata structures are constructed so that the transfer of information for certain specific modeling time functions is facilitated. For this reason we use smooth positive functions or vectors components of which are real numbers or smooth positive functions. The above hyperstructures are state-sets of these automata structures. Finally, we investigate various types of compositions of the above multiautomata and quasi-multiautomata. In order to this we have to generalize the classical definitions of Dörfler. While some of the concepts can be transferred to the hyperstructure context rather easily, in the case of Cartesian composition the attempt to generalize it leads to some interesting results.
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MARINHO, Sheyla Silva. "Sobre existência de soluções para equações diferenciais ordinárias envolvendo operadores não-lineares via Métodos de Shooting e Ponto fixo". Universidade Federal de Campina Grande, 2010. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1227.
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Capes
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GANDINI, JACOPO. "Simple linear compactifications of spherical homogeneous spaces". Doctoral thesis, 2011. http://hdl.handle.net/11573/918775.
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Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module. If G/H is a spherical orbit in P(V) and if X is its closure, then we describe the orbits of X and those of its normalization X. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient
combinatorial conditions so that the normalization morphism X → X is a
homeomorphism. Such conditions are trivially fulfilled if G is simply laced or
if H is a symmetric subgroup. In the special case of an odd orthogonal group G regarded as a GxG variety, we give an explicit classification of its simple linear compactifications, namely those equivariant compactifications with a unique closed orbit which are obtained by taking the closure of the GxG-orbit of the identity in a projective space P(End(V)), where V is a finite dimensional rational G-module.
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Awasthi, Ambrish. "Primitive transformation shift registers and primitive elements over finite fields". Thesis, 2018. http://localhost:8080/xmlui/handle/12345678/7720.
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"Mode-dependent finite-difference discretization of linear homogeneous differential equations". Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1987. http://hdl.handle.net/1721.1/2983.
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C.-C. Jay Kuo, Bernard C. Levy.Bibliography: p. 32-35.
Supported in part by the Army Research Office under grant no. DAAG-29-84-K-0005 Supported in part by the Advanced Research projects Agency monitored by ONR under contract N00014-81-K-0742 Supported in part by AFOSR contract F49620-84-K-0742
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Tang, Chaio-Ling, i 唐巧玲. "Homogeneous tests for linear and quadractic drift functions of brownian motions". Thesis, 2005. http://ndltd.ncl.edu.tw/handle/67862391844771939793.
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碩士國立中央大學
數學研究所
93
Testing equality of mean functions is important in multivariate analysis.The application can be found in analysis of variance,analysis of covariance and regression.However,this testing problem is relatively less explored for stochastic processes datum.In this paper,we present homogeneous tests for linear quadratic drift functions of Brownian motions.
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Mahony, Robert. "Optimization algorithms on homogeneous spaces : with applications in linear systems theory". Phd thesis, 1994. http://hdl.handle.net/1885/138389.
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Chia-WeiChu i 朱嘉葦. "Distributing non-linear divisible loads on homogeneous processors with daisy chain networks". Thesis, 2013. http://ndltd.ncl.edu.tw/handle/09834049559776681924.
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碩士國立成功大學
資訊工程學系碩博士班
101
In many diverse areas with divisible loads, the computational cost of the algo-rithm is a nonlinear function of the load size. The main purpose of the Divisible Load Theory (DLT) is obtaining the optimal load fraction in each processor to minimize the entire load processing time. This thesis proposed two different nonlinear computational load distribution algorithms for the homogeneous processors with daisy chain networks, to which the entire loads are originated from root processor located on the boundary initially. If the entire loads are originated form the interior (root) processor, this thesis also proposed a divisible load distribution algorithm. In order to reduce the idle time before each processor starts to compute, we also address a nonlinear computational load distribution algorithm for boundary root processor case with multiple installments. For these algorithms, the closed-form expression of the load fraction for each processor and the entire processing time are derived. Moreover, the entire load processing time and the proper number of the processors are also obtained for the case the start-up cost is considered. At the end, the performance of the proposed algorithms significantly outperforms the classic algorithm is also proved in the thesis.
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Liao, Yu-Fan, i 廖宇凡. "Identifying essence codings and effects in functional linear models with homogeneous and independent errors". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/75ragk.
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Hagelberg, Carl R. "Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulation". Thesis, 1989. http://hdl.handle.net/1957/28933.
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The stability of steady-state solutions of the equations governing two-dimensional,
homogeneous, incompressible fluid flow are analyzed in the context
of shear-flow in a channel. Both the linear and nonlinear theories are
reviewed and compared. In proving nonlinear stability of an equilibrium,
emphasis is placed on using the stability algorithm developed in Holm et al.
(1985). It is shown that for certain types of equilibria the linear theory is
inconclusive, although nonlinear stability can be proven.
Establishing nonlinear stability is dependent on the definition of a norm
on the space of perturbations. McIntyre and Shepherd (1987) specifically
define five norms, two for corresponding to one flow state and three to a
different flow state, and suggest that still others are possible. Here, the
norms given by McIntyre and Shepherd (1987) are shown to induce the same
topology (for the corresponding flow states), establishing their equivalence as
norms, and hence their equivalence as measures of stability. Summaries of the
different types of stability and their mathematical definitions are presented.
Additionally, a summary of conditions on shear-flow equilibria under which
the various types of stability have been proven is presented.
The Hamiltonian structure of the two-dimensional Euler equations is
outlined following Olver (1986). A coordinate-free approach is adopted emphasizing
the role of the Poisson bracket structure. Direct calculations are
given to show that the Casimir invariants, or distinguished functionals, are
time-independent and therefore are conserved quantities in the usual sense.Graduation date: 1990
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Person, Axelle Claude. "Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order". 2002. http://www.lib.ncsu.edu/theses/available/etd-08062002-104315/unrestricted/etd.pdf.
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Wirnata, René. "Universal electromagnetic response relations: applied to the free homogeneous electron gas". 2020. https://tubaf.qucosa.de/id/qucosa%3A74721.
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Die vorliegende Arbeit befasst sich mit der Anwendung des kürzlich entwickelten 'Functional Approach' zur Elektrodynamik in Medien auf das Modell des freien homogenen Elektronengases. Basierend auf einer ausschließlich mikroskopischen Feldtheorie wird gezeigt, dass mittels universell gültiger Relationen zwischen Antwortfunktionen sowohl alle relevanten optischen als auch magnetischen (linearen) Materialeigenschaften allein aus der Strom-Strom-Korrelation gewonnen werden können. Dabei ist es essentiell, alle Berechnungen auf dem vollen Stromdichteoperator aufzubauen, also auf der Summe aus diamagnetischem, orbitalem und spinoriellem Anteil. Weiterhin wird anhand der magnetischen Suszeptibilität demonstriert, dass im Allgemeinen die Unterscheidung zwischen eigenen und direkten Antwortfunktionen nicht zu vernachlässigen ist. Schließlich wird mit dem „Lindhard-Integral-Theorem“ bewiesen, dass nicht nur der longitudinale, sondern auch der transversale Anteil des vollen frequenz- und wellenvektorabhängigen fundamentalen Antworttensors des freien Elektronengases komplett durch das charakteristische Lindhard-Integral bestimmt ist.:Introduction
I Microscopic electrodynamics in media
1 Classical electrodynamics
1.1 Covariant formulation
1.2 Temporal gauge
1.3 Free Green function
1.4 Total functional derivatives
2 Electrodynamics in media
2.1 Field identifications
2.2 Fundamental response tensor
2.3 Universal response relations
2.4 Direct and proper response
2.5 Isotropic and combined limits
2.6 Full Green function
2.7 Wave equations in media and dispersion relations
II Application to the free electron gas
3 Fundamental response tensor
3.1 Electromagnetic current density
3.2 Kubo-Greenwood formulae
3.3 Diamagnetic, orbital and spinorial contribution
3.4 Spin susceptibility vs. spinorial current response
4 London model and diamagnetic response
4.1 Interpretation as response function
4.2 Application of universal response relations
4.3 Spin correction
5 Full current response
5.1 Dimensionless formulae
5.2 Lindhard integral theorem
5.3 Laurent expansions
5.4 Optical properties
5.5 Magnetic properties
Conclusion
Appendix A - Notation
Appendix B - Formulary
B.1 Basic analysis and vector calculus
B.2 Special relativity theory
B.3 Fourier transformation
B.4 Functional derivatives
B.5 Projectors and Helmholtz' theorem
B.6 Complex analysis
Appendix C - Yang-Mills gauge theory
C.1 Field strength tensor
C.2 Minimal coupling principle
C.3 Gauge invariant quantities and equations
Appendix D - Periodic solids
D.1 Partitioning of reciprocal space
D.2 Homogeneous limit
Appendix E - Electromagnetic spectrum
Bibliography
Acknowledgements
ErrataThis thesis is concerned with the application of the recently developed 'Functional Approach' to electrodynamics of media to the model of the free homogeneous electron gas. Based on an exclusively microscopic field theory it is shown that with the help of universally valid relations between response functions, all relevant optical and magnetic (linear) materials properties can be extracted from the mere current-current response. For this purpose, it is essential to base all calculations on the full current density operator, i.e. the sum of diamagnetic, orbital and spinorial contributions. Furthermore, we use the example of the magnetic susceptibility to demonstrate that the distinction between proper and direct response functions is in general crucial. Lastly, with the “Lindhard integral theorem” we prove that not only the longitudinal but also the transverse part of the full frequency- and wavevector-dependent fundamental response tensor of the free electron gas is completely determined by the characteristic Lindhard integral.:Introduction I Microscopic electrodynamics in media 1 Classical electrodynamics 1.1 Covariant formulation 1.2 Temporal gauge 1.3 Free Green function 1.4 Total functional derivatives 2 Electrodynamics in media 2.1 Field identifications 2.2 Fundamental response tensor 2.3 Universal response relations 2.4 Direct and proper response 2.5 Isotropic and combined limits 2.6 Full Green function 2.7 Wave equations in media and dispersion relations II Application to the free electron gas 3 Fundamental response tensor 3.1 Electromagnetic current density 3.2 Kubo-Greenwood formulae 3.3 Diamagnetic, orbital and spinorial contribution 3.4 Spin susceptibility vs. spinorial current response 4 London model and diamagnetic response 4.1 Interpretation as response function 4.2 Application of universal response relations 4.3 Spin correction 5 Full current response 5.1 Dimensionless formulae 5.2 Lindhard integral theorem 5.3 Laurent expansions 5.4 Optical properties 5.5 Magnetic properties Conclusion Appendix A - Notation Appendix B - Formulary B.1 Basic analysis and vector calculus B.2 Special relativity theory B.3 Fourier transformation B.4 Functional derivatives B.5 Projectors and Helmholtz' theorem B.6 Complex analysis Appendix C - Yang-Mills gauge theory C.1 Field strength tensor C.2 Minimal coupling principle C.3 Gauge invariant quantities and equations Appendix D - Periodic solids D.1 Partitioning of reciprocal space D.2 Homogeneous limit Appendix E - Electromagnetic spectrum Bibliography Acknowledgements Errata
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Boniface, Vinodkumar. "Small Scale Yielding And Mixed Mode Fracture In Homogeneous And Composite Media". Thesis, 1995. https://etd.iisc.ac.in/handle/2005/1631.
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Boniface, Vinodkumar. "Small Scale Yielding And Mixed Mode Fracture In Homogeneous And Composite Media". Thesis, 1995. http://etd.iisc.ernet.in/handle/2005/1631.
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Makhabane, Paul Suunyboy. "Analysis of a boundary value problem for a system on non-homogeneous ordinary differential equations (ODE), with variable coefficients". Diss., 2015. http://hdl.handle.net/11602/212.
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ŽELEZNÝ, Zdeněk. "Diferenciální rovnice 1. řádu --- Sbírka řešených příkladů". Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-112121.
Pełny tekst źródłaStreszczenie:
This thesis deals with the solution of differential equations of the first degree. The work is intended to serve as a textbook (a collection of exercises) for students of teaching mathematics at lower secondary schools. Each chapter contains a summary of basic concepts, solved task models of the related topic, sorted by difficulty, and finally tasks assigned for independent practicing. This thesis aims to present basic knowledge about ways of solving differential equations of the first degree, including practical skills for their solution.