Дисертації: "Decomposition for BV functions"

1

Tonon, Daniela. "Regularity results for Hamilton-Jacobi equations." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4210.

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2

De, Cicco Virginia. "Some Lower Semicontinuity and Relaxation Results for Functionals Defined on BV (Ω)". Doctoral thesis, SISSA, 1992. http://hdl.handle.net/20.500.11767/4325.

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3

BUFFA, Vito. "BV Functions in Metric Measure Spaces: Traces and Integration by Parts Formulæ." Doctoral thesis, Università degli studi di Ferrara, 2018. http://hdl.handle.net/11392/2488124.

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Questa tesi fornisce una panoramica sulla teoria delle funzioni Sobolev e BV nel contesto degli spazi metrici con misura. Vengono messe a confronto diverse caratterizzazioni di tali spazi al fine di evidenziarne le interconnessioni e le condizioni che garantiscono l'equivalenza delle definizioni. Dunque, si discute la struttura differenziale introdotta da N. Gigli in un articolo del 2014 per dare una nuova definizione di funzioni BV nel setting RCD(K,\infty) attraverso opportuni campi vettoriali. Di seguito, nel contesto metrico doubling con disuguaglianza di Poincaré, si danno nuove formule di integrazione per parti utilizzando campi a "divergenza-misura" per trattare poi il problema delle tracce delle funzioni BV. Si confronta la teoria delle "rough traces" (riadattata al presente setting, cfr. V. Maz'ya) con l'operatore di traccia definito mediante punti di Lebesgue, trovando le condizioni in cui le due caratterizzazioni coincidono.
This thesis offers a survey on the theory of Sobolev and BV functions in the setting of metric measure spaces. We compare different characterizations of such spaces in order to emphasize their relationships along with the conditions which ensure the equivalence of the definitions. Then, we discuss the differential structure introduced by N. Gigli in a paper of 2014 to give a new definition of BV functions in the RCD(K,\infty) setting, making use of suitable vector fileds. Later, in the metric doubling setting with Poincaré inequality, we give new integration by parts formulæ via "divergence-measure" vector fields to attack the issue of traces of BV functions. We compare the theory of "rough traces" (re-adapted to the present setting, cfr. V. Maz'ya) with the trace operator defined via Lebesgue points, finding the conditions under which the two characterizations coincide.

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4

Korey, Michael Brian. "A decomposition of functions with vanishing mean oscillation." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2592/.

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A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO.

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5

Lanagan, Gareth Daniel Edward. "Weather forecast error decomposition using rearrangements of functions." Thesis, Aberystwyth University, 2012. http://hdl.handle.net/2160/b489892f-7607-4125-90fb-46d8376edf8f.

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This thesis applies rearrangement and optimal mass transfer theory to weather forecast error decomposition. Errors in weather forecasting are often due to displacement of key features; conventional error scores do not necessarily favour good forecasts, nor are they descriptive of how the forecast failed. We study forecast error decomposition, where error is split into an error due to displacement and an error due to differences in qualitative features. In its simple formulation, we seek re-arrangements of the forecast which are a best fit to the actual data, and then find the “least kinetic energy” of a notional velocity transporting the forecast to a best fit. In mathematical terms, we are characterising those elements of a set of rearrangements which are closest (in the sense of L2) to a prescribed square integrable function, and seeking the least 2-Wasserstein distance squared between the forecast and the closest displaced forecasts. We demonstrate that there are closest rearrangements, and characterise this set; the best fitting rearrangements are determined up to rearrangement on the level sets of positive size of the prescribed function. Displacement error is calculated by finding the minimum value of an optimal mass transfer problem; we review previous work, demonstrating the connection with transport of the forecast to the best fit. A problem with the simple formulation of forecast error decomposition is that because the qualitative features error is taken first, an error in qualitative features may be penalise as a large displacement error. We conclude this thesis by considering a formulation which minimises both errors simultaneously.

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6

CAMFIELD, CHRISTOPHER SCOTT. "Comparison of BV Norms in Weighted Euclidean Spaces and Metric Measure Spaces." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1211551579.

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7

Soneji, Parth. "Lower semicontinuity and relaxation in BV of integrals with superlinear growth." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:c7174516-588e-46ae-93dc-56d4a95f1e6f.

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8

Shillam, Laura-Lee. "Structural diversity and decomposition functions of volcanic soils at different stages of development." Thesis, University of Stirling, 2008. http://hdl.handle.net/1893/444.

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During a volcanic eruption, the extrusion of lava onto surfaces destroys biological activity creating virgin land surfaces. Through time this new land will be subject to soil formation and colonisation under relatively similar climatic conditions and parent materials. Soils formed from volcanic deposits present a unique opportunity to study microbial community development. Soils at different developmental stages and differing in vegetation cover were selected from four locations on the slopes of Mount Etna, Sicily. Three main research objectives were determined in order to test the hypothesis that the microbial communities from soils at later stages of development would have a greater biomass, be more diverse, be more efficient at utilising carbon sources and recover from an environmental disturbance at a greater rate. A field experiment was conducted to ascertain the long term in situ catabolic abilities of the microbial communities in each soil and to establish the effects of litter mixing on decomposition rate. Litter bags containing either Genista aetnensis (Etnean Broom), Pinus nigra (Corsican Pine) or a mixture of the two were buried at each of the sites and their decomposition monitored over a 2.5 year period. PLFA diversity, community composition and function was assessed for each of the soils. The soils were also subject to a disturbance and the recovery of key community parameters was monitored over a six month period in order to establish each soil community’s resistance and resilience to disturbance. A laboratory experiment was conducted in order to investigate functional diversity and decomposition functions of each soil community using a range of simple and complex substrates. The relationship between PLFA diversity and functional diversity was also investigated. No correlation was found between soil C and N contents, microbial biomass or soil respiration and soil developmental stage and there was no detectable difference in litter bag mass loss between the soil types. No non- additive effects were noted in mixed litters. The more developed soil had a greater PLFA diversity and PLFA biomass however the more developed soil was not more resistant or resilient to disturbance. Developed soils showed greater catabolic diversity compared with less developed soils broadly correlating with PLFA diversity. Despite increased PLFA diversity and functional diversity in the more developed soils, residue decomposition in situ was unaffected. Reduced PLFA diversity and community complexity did not result in reduced function. Soils at different developmental stages had similar catabolic responses and were able to degrade simple and complex substrates to a similar degree. Microbial diversity in soil has the potential to be very high thus resulting in a high rate of functional redundancy i.e. many species within the same community which have the same functional role. It is possible that only a few key functional groups present within the soil community contribute to the main decomposition function within the soil and were able to maintain function during perturbation. Both Etna soils had similar PLFA’s present in similar concentrations and these groups in general were maintained during disturbance. This suggests that total microbial community diversity may not be as important to community function as the presence of key functional groups.

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9

MENEGATTI, GIORGIO. "Sobolev classes and bounded variation functions on domains of Wiener spaces, and applications." Doctoral thesis, Università degli studi di Ferrara, 2018. http://hdl.handle.net/11392/2488305.

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The main thread of this work is the bounded variation (BV) functions in abstract Wiener spaces (a topic in infinite-dimensional analysis). In the first Part of this work, we present some known results, and we introduce the concepts of Wiener space, of Sobolev space in Wiener spaces, of BV functions (and finite perimeter sets) in Wiener spaces, and of BV functions in convex sets of Wiener spaces (by following the definition in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); moreover, we introduce the trace theory on subsets of a Wiener space (by following P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), and the concept of Mosco convergence. In the second Part we present some new results. In Chapter 6, we consider a subset O of a Wiener space which satisfies a regularity condition, and we prove that a function in W^{1,2}(O) has null trace if and only if it is the limit of a sequence of functions with support contained in O. The main chapter is Chapter 7, which is devoted to the extension in the Wiener spaces setting of a result given in the section 8 of (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): if O is a convex bounded set with regular boundary in R^{d} and L is the Laplace operator in O with null Dirichlet boundary condition, then the normalized resolvent of L is contractive in sense L^1 respect to the gradient. We extend this result to the case of L Ornstein-Uhlenbeck operator in O with null Dirichlet boundary condition, with Gaussian measure (by using the results of Chapter 6): in this case O must satisfy a condition (which we call Gaussian convexity) which takes the place of the convexity in the Gaussian setting. Moreover, we extend the result also to the case of: L Laplace operator in an open convex O with null Neumann boundary condition, with Lebesgue measure; L Ornstein-Uhlenbeck operator in an open convex O with null Neumann boundary condition, with Gaussian measure. In the last part of Chapter 7, we use the preceding results to give an alternative definition of BV function (in the case L^2(O)). In Chapter 8, let X the set of continuous functions on [0,1] with starting point 0, provided with the measure induced by the Brownian motion with starting point 0; it is a Wiener space. For every A subset of X, we define Ξ_A, set of functions in X with image in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) it is proved that, if d ≥ 2 and A is an open subset of R^d which satisfies an uniform outer ball condition then Ξ_A has finite perimeter in the sense of Gaussian measure. We present a weaker condition on A (in dimension sufficiently great) such that Ξ_A has finite perimeter: in particular, A can be the complement of a convex unbounded symmetric cone.
L’argomento principale di questo lavoro sono le funzioni a variazione limitata (BV) in spazi di Wiener astratti (un argomento di analisi infinito-dimensionale). Nella prima parte di questo lavoro, presentiamo alcuni risultati noti, e introduciamo i concetti di spazi di Wiener, di classi di Sobolev su spazi di Wiener, di funzioni BV (e insiemi di perimetro finito) in spazi di Wiener, e di funzioni BV in sottoinsiemi convessi di Spazi di Wiener (seguendo la definizione in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); inoltre, introduciamo la teoria delle tracce su sottoinsiemi di uno spazio di Wiener( seguendo P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), e il concetto di convergenza di Mosco. Nella seconda parte presentiamo alcuni risultati originali. Nel capitolo 6, consideriamo un sottoinsieme O di uno spazio di Wiener che soddisfa a una condizione di regolarità, e proviamo che una funzione in W^{1,2} (O) ha traccia nulla se e solo se è il limite di una sequenza di funzioni con supporto contenuto in O. Il capitolo principale è il 7, che è dedicato all'estensione all'ambito degli spazi di Wiener di un risultato dato nella sezione 8 di (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): se O è un insieme convesso limitato con frontiera regolare in R^{d} e L è l'operatore di Laplace in O con condizione al bordo di Dirichlet nulla, allora il risolvente normalizzato di L è contrattivo nel senso L^1 rispetto al gradiente. Estendiamo questo risultato al caso di L operatore di Ornstein-Uhlenbeck in O con condizione al bordo di Dirichlet nulla, con misura gaussiana (usando i risultati del Capitolo 6): in questo caso O deve soddisfare una condizione (che chiamiamo convessità Gaussiana) che nel caso gaussiano prende il posto della convessità. Inoltre, estendiamo il risultato anche al caso di: L operatore di Laplace in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura di Lebesgue; L operatore in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura gaussiana. Nell'ultima parte del Capitolo 7, usiamo i precedenti risultati per dare una definizione alternativa di funzione BV in O (nel caso L^2(O) ). Nel Capitolo 8, sia X l'insieme delle funzioni continue in R^d su [ 0,1 ] con punti di partenza nell’origine fornito della misura indotta dal moto browniano con punto di partenza nell’origine; è uno spazio di Wiener. Per ogni A sottoinsieme di X, definiamo Ξ_A, insieme delle funzioni in X con immagine in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) viene dimostrato che, se d ≥ 2 e A è un insieme aperto in R^d che soddisfa una condizione di uniforme palla esterna, allora Ξ_A ha perimetro finito nel senso della misura gaussiana. Presentiamo una condizione più debole su A (in dimensione sufficientemente grande) tale che Ξ_A ha perimetro finito: in particolare, A può essere il complementare di un cono convesso illimitato simmetrico.

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10

Amato, Stefano. "Some results on anisotropic mean curvature and other phase transition models." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4859.

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The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions.

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11

Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.

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Dissertation for the Degree of Doctor of Philosophy in Mathematics
Fundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA

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12

Jones, Adam. "Development of a near-wall domain decomposition method for turbulent flows." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/development-of-a-nearwall-domain-decomposition-method-for-turbulent-flows(bf7149b7-c26a-4924-9886-42a92cce4f51).html.

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In computational fluid dynamics (CFD), there are two widely-used methods for computing the near-wall regions of turbulent flows: high Reynolds number (HRN) models and low Reynolds number (LRN) models. HRN models do not resolve the near-wall region, but instead use wall functions to compute the required parameters over the near-wall region. In contrast, LRN models resolve the flow right down to the wall. Simulations with HRN models can take an order of magnitude less time than with LRN models, however the accuracy of the solution is reduced and certain requirements on the mesh must be met if the wall function is to be valid. It is often difficult or impossible to satisfy these requirements in industrial computations. In this thesis the near-wall domain decomposition (NDD) method of Utyuzhnikov (2006) is developed and implemented into the industrial code, Code_Saturne, for the first time. With the NDD approach, the near-wall regions of a fluid flow are removed from the main computational mesh. Instead, the mesh extends down to an interface boundary, which is located a short distance from the wall, denoted y*. A simplified boundary layer equation is used to calculate boundary conditions at the interface. When implemented with a turbulence model which can resolve down to the wall, there is no lower limit on the value of y*. There is a Reynolds number-dependent upper limit on y*, as there is with HRN models. Thus for large y*, the model functions as a HRN model and as y*→ 0 the LRN solution is recovered. NDD is implemented for the k−ε and Spalart-Allmaras turbulence models and is tested on five test cases: a channel flow at two different Reynolds numbers, an annular flow, an impinging jet flow and the flow in an asymmetric diffuser. The method is tested as a HRN and LRN model and it is found that the method behaves competitively with the scalable wall function (SWF) on simpler flows, and performs better on the asymmetric diffuser flow, where the NDD solution correctly captures the recirculation region whereas the SWF does not. The method is then tested on a ribbed channel flow. Particular focus is given to investigating how much of the rib can be excluded from the main computational mesh. It is found that it is possible to remove 90% of the rib from the mesh with less than 2% error in the friction factor compared to the LRN solution. The thesis then focuses on the industrial case of the flow in an annulus where the inner wall, referred to as the pin, has a rib on its surface that protrudes into the annulus. Comparison is made between CFD calculations, experimental data and empirical correlations. It is found that the experimental friction factors are significantly larger than those found with CFD, and that the trend in the friction factor with Reynolds number found in the experiments is different. Simulations are performed to quantify the effect that a non-smooth surface finish on the pin and rib surface has on the flow. This models the situation that occurs in an advanced gas-cooled nuclear reactor, when a carbon deposit forms on the fuel pins. The relationship between the friction factor and surface finish is plotted. It is demonstrated that surface roughness left over by the manufacturing process in the experiments is not the source of the discrepancy between the experimental and CFD results.

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13

Schmidt, John Michael. "Litter Decomposition in Created and Adjacent Forested Wetlands of the Coastal Plain of Virginia." Thesis, Virginia Tech, 2002. http://hdl.handle.net/10919/43580.

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Litter decomposition is a poorly understood function of constructed and natural forested wetlands. This study compared rates of litter mass loss, changes in litter morphology, and associated macroinvertebrate populations in constructed and natural non-tidal wetlands. Two sets of wetlands (constructed vs. natural) were studied in eastern Virginia; a 9 year-old riparian set near Fort Lee, (FL), and a 2 year-old wet flat set in Charles City County, (CC). Mixed deciduous forest litter collected from the FL natural wetland decayed more rapidly in the created wetlands than the adjacent forested wetlands. Mixed emergent marsh litter collected from the FL created wetland exhibited a similar relationship, although marsh litter decomposed slower than forest litter. Litter area and weight loss followed a similar pattern, although area loss lagged behind weight loss, consistent with an initial leaching phase of decomposition. Both the FL and CC created wetlands exhibited faster litter decomposition than their adjacent forested wetland, however, the FL created wetland had a lower weight:area ratio and higher detritivore abundance than the adjacent forested wetland, while the reverse was true for the CC wetland pair. These relationships suggest macroinvertebrates played an important role in decomposition in the FL created wetland, while other factors were more significant at CC. Faster decomposition in the created wetlands may be of concern for long-term soil organic matter accumulation, or conversely, may indicate quick recovery of the litter decomposition function. Overall, these findings point out the difficulties involved in using certain functional indicators to compare very young and mature systems.
Master of Science

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14

Morini, Massimiliano. "Free-discontinuity problems: calibration and approximation of solutions." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/3923.

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15

Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.

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In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases. The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales

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16

Nguyen, Hong Thuy. "The algebraic representation of OWA functions in the binomial decomposition framework and its applications in large-scale problems." Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/367977.

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In the context of multicriteria decision making, the ordered weighted averaging (OWA) functions play a crucial role in aggregating multiple criteria evaluations into an overall assessment to support decision makers reaching a decision. The determination of OWA weights is, therefore, an important task in this process. Solving real-life problems with a large number of OWA weights, however, can be very challenging and time consuming. In this research we recall that OWA functions correspond to the Choquet integrals associated with symmetric capacities. The problem of defining all Choquet capacities on a set of n criteria requires 2^n real coefficients. Grabisch introduced the k-additive framework to reduce the exponential computational burden. We review the binomial decomposition framework with a constraint on k-additivity whereby OWA functions can be expressed as linear combinations of the first k binomial OWA functions and the associated coefficients of the binomial decomposition framework. In particular, we investigate the role of k-additivity in two particular cases of the binomial decomposition of OWA functions, the 2-additive and 3-additive cases. We identify the relationship between OWA weights and the associated coefficients of the binomial decomposition of OWA functions. Analogously, this relationship is also studied for two well-known parametric families of OWA functions, namely the S-Gini and Lorenzen welfare functions. Finally, we propose a new approach to determine OWA weights in large-scale problems by using the binomial decomposition of OWA functions with natural constraints on k-additivity to control the complexity of the OWA weight distributions.

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17

Nguyen, Hong Thuy. "The algebraic representation of OWA functions in the binomial decomposition framework and its applications in large-scale problems." Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3485/1/Thesis-Nguyen.pdf.

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In the context of multicriteria decision making, the ordered weighted averaging (OWA) functions play a crucial role in aggregating multiple criteria evaluations into an overall assessment to support decision makers reaching a decision. The determination of OWA weights is, therefore, an important task in this process. Solving real-life problems with a large number of OWA weights, however, can be very challenging and time consuming. In this research we recall that OWA functions correspond to the Choquet integrals associated with symmetric capacities. The problem of defining all Choquet capacities on a set of n criteria requires 2^n real coefficients. Grabisch introduced the k-additive framework to reduce the exponential computational burden. We review the binomial decomposition framework with a constraint on k-additivity whereby OWA functions can be expressed as linear combinations of the first k binomial OWA functions and the associated coefficients of the binomial decomposition framework. In particular, we investigate the role of k-additivity in two particular cases of the binomial decomposition of OWA functions, the 2-additive and 3-additive cases. We identify the relationship between OWA weights and the associated coefficients of the binomial decomposition of OWA functions. Analogously, this relationship is also studied for two well-known parametric families of OWA functions, namely the S-Gini and Lorenzen welfare functions. Finally, we propose a new approach to determine OWA weights in large-scale problems by using the binomial decomposition of OWA functions with natural constraints on k-additivity to control the complexity of the OWA weight distributions.

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18

Piffet, Loïc. "Décomposition d’image par modèles variationnels : débruitage et extraction de texture." Thesis, Orléans, 2010. http://www.theses.fr/2010ORLE2053/document.

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Cette thèse est consacrée dans un premier temps à l’élaboration d’un modèle variationnel dedébruitage d’ordre deux, faisant intervenir l’espace BV 2 des fonctions à hessien borné. Nous nous inspirons ici directement du célèbre modèle de Rudin, Osher et Fatemi (ROF), remplaçant la minimisation de la variation totale de la fonction par la minimisation de la variation totale seconde, c’est à dire la variation totale de ses dérivées. Le but est ici d’obtenir un modèle aussi performant que le modèle ROF, permettant de plus de résoudre le problème de l’effet staircasing que celui-ci engendre. Le modèle que nous étudions ici semble efficace, entraînant toutefois l’apparition d’un léger effet de flou. C’est afin de réduire cet effet que nous introduisons finalement un modèle mixte, permettant d’obtenir des solutions à la fois non constantes par morceaux et sans effet de flou au niveau des détails. Dans une seconde partie, nous nous intéressons au problème d’extraction de texture. Un modèle reconnu comme étant l’un des plus performants est le modèle T V -L1, qui consiste simplement à remplacer dans le modèle ROF la norme L2 du terme d’attache aux données par la norme L1. Nous proposons ici une méthode originale permettant de résoudre ce problème utilisant des méthodes de Lagrangien augmenté. Pour les mêmes raisons que dans le cas du débruitage, nous introduisons également le modèle T V 2-L1, consistant encore une fois à remplacer la variation totale par la variation totale seconde. Un modèle d’extraction de texture mixte est enfin très brièvement introduit. Ce manuscrit est ponctué d’un vaste chapitre dédié aux tests numériques
This thesis is devoted in a first part to the elaboration of a second order variational modelfor image denoising, using the BV 2 space of bounded hessian functions. We here take a leaf out of the well known Rudin, Osher and Fatemi (ROF) model, where we replace the minimization of the total variation of the function with the minimization of the second order total variation of the function, that is to say the total variation of its partial derivatives. The goal is to get a competitive model with no staircasing effect that generates the ROF model anymore. The model we study seems to be efficient, but generates a blurry effect. In order to deal with it, we introduce a mixed model that permits to get solutions with no staircasing and without blurry effect on details. In a second part, we take an interset to the texture extraction problem. A model known as one of the most efficient is the T V -L1 model. It just consits in replacing the L2 norm of the fitting data term with the L1 norm.We propose here an original way to solve this problem by the use of augmented Lagrangian methods. For the same reason than for the denoising case, we also take an interest to the T V 2-L1 model, replacing again the total variation of the function by the second order total variation. A mixed model for texture extraction is finally briefly introduced. This manuscript ends with a huge chapter of numerical tests

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19

Wan, Wei. "A New Approach to the Decomposition of Incompletely Specified Functions Based on Graph Coloring and Local Transformation and Its Application to FPGA Mapping." PDXScholar, 1992. https://pdxscholar.library.pdx.edu/open_access_etds/4698.

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The thesis presents a new approach to the decomposition of incompletely specified functions and its application to FPGA (Field Programmable Gate Array) mapping. Five methods: Variable Partitioning, Graph Coloring, Bond Set Encoding, CLB Reusing and Local Transformation are developed in order to efficiently perform decomposition and FPGA (Lookup-Table based FPGA) mapping. 1) Variable Partitioning is a high quality hemistic method used to find the "best" partitions, avoiding the very time consuming testing of all possible decomposition charts, which is impractical when there are many input variables in the input function. 2) Graph Coloring is another high quality heuristic\ used to perform the quasi-optimum don't care assignment, making the program possible to accept incompletely specified function and perform a quasi-optimum assignment to the unspecified part of the function. 3) Bond Set Encoding algorithm is used to simplify the decomposed blocks during the process of decomposition. 4) CLB Reusing algorithm is used to reduce the number of CLBs used in the final mapped circuit. 5) Local Transformation concept is introduced to transform nondecomposable functions into decomposable ones, thus making it possible to apply decomposition method to FPGA mapping. All the above developed methods are incorporated into a program named TRADE, which performs global optimization over the input functions. While most of the existing methods recursively perform local optimization over some kinds of network-like graphs, and few of them can handle incompletely specified functions. Cube calculus is used in the TRADE program, the operations are global and very fast. A short description of the TRADE program and the evaluation of the results are provided at the_ end of the thesis. For many benchmarks the TRADE program gives better results than any program published in the literature.

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20

Prescott, Thomas Paul. "Large-scale layered systems and synthetic biology : model reduction and decomposition." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:205a18fb-b21f-4148-ba7d-3238f4b1f25b.

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This thesis is concerned with large-scale systems of Ordinary Differential Equations that model Biomolecular Reaction Networks (BRNs) in Systems and Synthetic Biology. It addresses the strategies of model reduction and decomposition used to overcome the challenges posed by the high dimension and stiffness typical of these models. A number of developments of these strategies are identified, and their implementation on various BRN models is demonstrated. The goal of model reduction is to construct a simplified ODE system to closely approximate a large-scale system. The error estimation problem seeks to quantify the approximation error; this is an example of the trajectory comparison problem. The first part of this thesis applies semi-definite programming (SDP) and dissipativity theory to this problem, producing a single a priori upper bound on the difference between two models in the presence of parameter uncertainty and for a range of initial conditions, for which exhaustive simulation is impractical. The second part of this thesis is concerned with the BRN decomposition problem of expressing a network as an interconnection of subnetworks. A novel framework, called layered decomposition, is introduced and compared with established modular techniques. Fundamental properties of layered decompositions are investigated, providing basic criteria for choosing an appropriate layered decomposition. Further aspects of the layering framework are considered: we illustrate the relationship between decomposition and scale separation by constructing singularly perturbed BRN models using layered decomposition; and we reveal the inter-layer signal propagation structure by decomposing the steady state response to parametric perturbations. Finally, we consider the large-scale SDP problem, where large scale SDP techniques fail to certify a system’s dissipativity. We describe the framework of Structured Storage Functions (SSF), defined where systems admit a cascaded decomposition, and demonstrate a significant resulting speed-up of large-scale dissipativity problems, with applications to the trajectory comparison technique discussed above.

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21

FORTE, T'AI GLADYS WHITTINGHAM. "Alpine tundra and climate change: effects of summer warming and reduced precipitation on ecosystem functions in a Carex curvula grassland." Doctoral thesis, Università degli studi di Ferrara, 2021. http://hdl.handle.net/11392/2487934.

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Alpine ecosystems have undergone significant modifications in recent years due to climate change. A trend towards reduced summer rainfall has been detected in various mountain regions, with warm, dry conditions predicted to intensify in some areas of the Alps by the end of the century. Together with increased frequency and magnitude of extreme events, new questions arise as to how climate change will impact ecosystem stability and functions. Although a number of studies have addressed the effects of warming on alpine ecosystems, responses to drier conditions remain poorly investigated. The main objective of the present research was to assess the effects of summer warming and reduced precipitation on key ecosystem functions of an alpine Carex curvula grassland over a 3-year period, with both field and lab experiments. The first field experiment investigated biomass production (Study 1) and litter decomposition (Study 2) in response to summer warming and chronic press drought. Increased temperatures were simulated using open top chambers, with rain-out shelters simulating historically-based, site-specific drought. Study 1 focused on the extent to which above- and belowground net primary production (ANPP and BNPP) were affected by treatments over 2 years; inter-annual ANPP differences, including the pre-treatment year, were also analysed. Results reveal that treatments do not influence ANPP, although there is wide inter-annual variation, whereas BNPP is lower under shelters. ANPP reveals a certain degree of resistance to short-term warming and extreme drought, but the difference between ANPP and BNPP underlines the need to take both compartments into account when assessing climate change effects on plant production. In Study 2, litter decomposition responses to treatments were analysed during one year (fall 2018-2019), with the influence of seasonality on litter quantity and quality also investigated to estimate the contribution of the long snow-covered season on the stability of decomposition processes under altered summer conditions. Standard litter (teabags) was employed in treatments, whereas native litter was used to assess the variability of litter quality and verify the degree to which native litter dynamics are reflected by standard litter. Despite more favourable growing season climate conditions, summer decomposition is limited by end-of-winter litter alteration, suggesting that early decomposition in alpine ecosystems remains stable even under altered summer conditions. Two further experiments (Study 3 and 4) investigated the extent to which ANPP and CO2 fluxes – ecosystem respiration (ER), gross ecosystem production (GEP) and net ecosystem exchange (NEE) – are affected by acute pulse dry spells during early- and mid-growing season. Study 3 assessed the role of drought timing on grassland monoliths in a mesocosm, with a full-season drought treatment also implemented to detect the soil moisture and temporal thresholds triggering changes in ER and GEP. Results indicate that ANPP and CO2 fluxes are negatively influenced by drought, the extent varying according to its timing and duration; thresholds for ER and GEP differ between drought timings, those during the mid-season being reached earlier and at higher moisture content, which underlies the importance of extreme event timing. Study 4 consisted of a single-season field replication of Study 3, with results showing that the grassland is resistant to pulse drought in the short-term, with stable ANPP and NEE responses. In the field, however, high soil moisture levels never reached the thresholds detected in the mesocosm study, highlighting the need for field experiments, which are carried out in more complex, natural conditions, in order to confirm findings from controlled studies. Overall, the present research reveals that key ecosystem processes in representative alpine grasslands are resistant to short-term press drought, but are vulnerable to pulse drought events.
Nelle ultime decadi, gli ecosistemi alpini hanno subito importanti alterazioni dovute ai cambiamenti climatici che, in diverse aree montuose, hanno comportato non solo un aumento delle temperature ma anche una riduzione delle precipitazioni. Inoltre, l’aumento della frequenza e intensità degli eventi estremi rende urgente la necessità di comprendere l’impatto di tali eventi sulla funzionalità degli ecosistemi. Per i sistemi alpini sono molteplici gli studi sulle risposte ecologiche al riscaldamento, mentre scarseggiano le ricerche sugli effetti di un clima più secco. In questo quadro si sviluppa la presente ricerca, basta su esperimenti in campo e in laboratorio volti a valutare le risposte ecologiche di una prateria alpina a Carex curvula a cambiamenti di temperatura e precipitazioni. Le risposte della produzione primaria (Studio 1) e della decomposizione (Studio 2) sono state valutate tramite manipolazioni sperimentali, effettuate nel periodo libero dalla neve, della temperatura, tramite Open Top Chambers, e delle precipitazioni, per mezzo di tettoie ad esclusione parziale della pioggia simulanti un estremo climatico sito-specifico. Lo Studio 1 ha valutato la risposta della produzione primaria epigea (ANPP) e ipogea (BNPP) a 2 anni di trattamento (2018-19), analizzando anche la variazione inter-annuale della ANPP. Dai risultati non è emerso alcun effetto dei trattamenti sulla ANPP, che ha invece esibito significative variazioni inter-annuali, mentre la BNPP è risultata inferiore sotto le tettoie. Complessivamente, la prateria sembra resistente al riscaldamento e alla riduzione estrema delle precipitazioni nel breve termine, sebbene le differenze nelle risposte tra ANPP e BNPP evidenzino la necessità di considerarle entrambe nelle indagini sulla produzione primaria in risposta ai cambiamenti climatici. Analogamente allo Studio 1, i processi di decomposizione analizzati nello Studio 2 utilizzando lettiera standard (teabags) non sono stati influenzati dai trattamenti estivi, probabilmente a causa dell’alterazione invernale della lettiera. L’uso della lettiera nativa nei controlli nel medesimo studio ha, inoltre, permesso di determinare il grado di variabilità naturale della qualità della lettiera e verificare quanto le dinamiche di decomposizione della lettiera standard riflettano quelle della lettiera locale. Ulteriori esperimenti sono stati condotti sia in mesocosmo (Studio 3) sia in campo (Studio 4) al fine di valutare la risposta della ANPP e dei flussi di CO2 – respirazione ecosistemica (ER), assimilazione ecosistemica lorda (GEP) e netta (NEE) – rispetto alla tempistica degli eventi siccitosi, i.e. periodi di assenza di precipitazioni acuti sperimentati in diverse fasi della stagione vegetativa. In entrambi gli studi, oltre a un trattamento di siccità applicato nella prima e seconda parte dell’estate (ED e MD), è stato imposto un ulteriore trattamento lungo l’intera stagione (FD) per stimare le soglie di umidità determinanti una brusca variazione dei tassi di ER e GEP. Nello Studio 3, sia ANPP sia i flussi di CO2 sono stati negativamente impattati dalla siccità in una misura diversa a seconda della durata e del periodo di incidenza del secco. Le soglie per ER e GEP sono inoltre risultate diverse tra MD e ED, con le soglie in MD raggiunte prima e a umidità maggiori rispetto a quelle in ED. Contrariamente a quanto osservato nel mesocosmo, nello Studio 4 la ANPP e i flussi di CO2 sono risultati stabili rispetto ai trattamenti e l’umidità del suolo non ha mai raggiunto le soglie identificate in laboratorio, evidenziando così la necessità di affiancare a studi controllati ulteriori esperimenti in condizioni naturali e più complesse. Concludendo, la presente ricerca rivela come i principali processi ecosistemici di una prateria alpina siano resistenti nel breve periodo al riscaldamento e a una riduzione cronica delle precipitazioni, ma siano potenzialmente vulnerabili a eventi acuti di secco.

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22

Nepomnyaschikh, Sergey V. "Optimal Multilevel Extension Operators." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500971.

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In the present paper we suggest the norm-preserving explicit operator for the extension of finite-element functions from boundaries of domains into the inside. The construction of this operator is based on the multilevel decomposition of functions on the boundaries and on the equivalent norm for this decomposition. The cost of the action of this operator is proportional to the number of nodes.

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23

Quellmalz, Michael. "Reconstructing Functions on the Sphere from Circular Means." Universitätsverlag Chemnitz, 2019. https://monarch.qucosa.de/id/qucosa%3A38406.

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The present thesis considers the problem of reconstructing a function f that is defined on the d-dimensional unit sphere from its mean values along hyperplane sections. In case of the two-dimensional sphere, these plane sections are circles. In many tomographic applications, however, only limited data is available. Therefore, one is interested in the reconstruction of the function f from its mean values with respect to only some subfamily of all hyperplane sections of the sphere. Compared with the full data case, the limited data problem is more challenging and raises several questions. The first one is the injectivity, i.e., can any function be uniquely reconstructed from the available data? Further issues are the stability of the reconstruction, which is closely connected with a description of the range, as well as the demand for actual inversion methods or algorithms. We provide a detailed coverage and answers of these questions for different families of hyperplane sections of the sphere such as vertical slices, sections with hyperplanes through a common point and also incomplete great circles. Such reconstruction problems arise in various practical applications like Compton camera imaging, magnetic resonance imaging, photoacoustic tomography, Radar imaging or seismic imaging. Furthermore, we apply our findings about spherical means to the cone-beam transform and prove its singular value decomposition.
Die vorliegende Arbeit beschäftigt sich mit dem Problem der Rekonstruktion einer Funktion f, die auf der d-dimensionalen Einheitssphäre definiert ist, anhand ihrer Mittelwerte entlang von Schnitten mit Hyperebenen. Im Fall d=2 sind diese Schnitte genau die Kreise auf der Sphäre. In vielen tomografischen Anwendungen sind aber nur eingeschränkte Daten verfügbar. Deshalb besteht das Interesse an der Rekonstruktion der Funktion f nur anhand der Mittelwerte bestimmter Familien von Hyperebenen-Schnitten der Sphäre. Verglichen mit dem Fall vollständiger Daten birgt dieses Problem mehrere Herausforderungen und Fragen. Die erste ist die Injektivität, also können alle Funktionen anhand der gegebenen Daten eindeutig rekonstruiert werden? Weitere Punkte sind die die Frage nach der Stabilität der Rekonstruktion, welche eng mit einer Beschreibung der Bildmenge verbunden ist, sowie der praktische Bedarf an Rekonstruktionsmethoden und -algorithmen. Diese Arbeit gibt einen detaillierten Überblick und Antworten auf diese Fragen für verschiedene Familien von Hyperebenen-Schnitten, angefangen von vertikalen Schnitten über Schnitte mit Hyperebenen durch einen festen Punkt sowie Kreisbögen. Solche Rekonstruktionsprobleme treten in diversen Anwendungen auf wie der Bildgebung mittels Compton-Kamera, Magnetresonanztomografie, fotoakustischen Tomografie, Radar-Bildgebung sowie der Tomografie seismischer Wellen. Weiterhin nutzen wir unsere Ergebnisse über sphärische Mittelwerte, um eine Singulärwertzerlegung für die Kegelstrahltomografie zu zeigen.

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24

Zhao, Kezhong. "A domain decomposition method for solving electrically large electromagnetic problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1189694496.

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25

Zhu, Shaoming. "Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/41693/1/Shaoming_Zhu_Thesis.pdf.

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Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

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26

Turunen, J. (Jarno). "Responses of biodiversity and ecosystem functions to land use disturbances and restoration in boreal stream ecosystems." Doctoral thesis, Oulun yliopisto, 2018. http://urn.fi/urn:isbn:9789526217826.

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Abstract Streams and rivers have been extensively altered by humans. Channelization and land use have changed stream habitats and water quality with adverse effects on biota and ecosystem functions. Impacted streams have been targets for restoration, but there is considerable lack of understanding how streams should be restored in an ecologically effective way. In this doctoral thesis, I studied the impacts of channelization (for timber floating) and agricultural diffuse pollution on stream biota. I also studied the effectiveness of restorations of forestry impacted streams stressed by excessive sand sedimentation from catchment drainage. Finally, I also studied the effects of mosses, fine sediment and enhanced dispersal on stream macroinvertebrate communities and ecosystem functions. I found that channelization did not have effect on diatom, macrophyte, macroinvertebrate and fish assemblages, whereas diffuse pollution had strong effects, with no interactions between the two stressors. I showed that excessive sedimentation from forest drainage was harmful for stream biota but had no effect on leaf decomposition and algal accrual rate. Restoration with boulders reduced sand cover and was more beneficial for in-stream biodiversity, whereas restoration with wood tended to increase hydrological retention of stream channels, thereby altering riparian plant assemblages toward more natural composition. In a mesocosm experiment, I found mosses to have a strong impact on macroinvertebrate communities and ecosystem functions. Mosses increased organic matter retention and reduced algal accrual rate and leaf decomposition. The effect of mosses on macroinvertebrates was stronger than that of sand sedimentation, and mosses mitigated some of the negative effects of sand. Extensive dispersal had a distinct imprint on invertebrate community composition but did not blur the effect of mosses and sand on communities, suggesting strong local-scale environmental control of composition. My thesis emphasizes that priority in stream restoration should be in the mitigation of diffuse pollution rather than restoration of channel morphology, especially in streams where channel alteration has been fairly modest, as in the case of timber floating. Addition of both boulders and large wood likely yields the best biodiversity response in the restoration of forestry impacted streams. Mosses are a key component of boreal lotic ecosystems; therefore, the recovery of mosses may be a prerequisite for the full recovery of biodiversity and ecosystem integrity of boreal streams
Tiivistelmä Ihmisen toiminta on laajasti muokannut virtavesiä. Uomien kanavointi ja maankäyttö ovat muuttaneet virtavesien elinympäristöjä ja veden laatua, millä on ollut haitallisia vaikutuksia virtavesien luonnon monimuotoisuuteen ja ekosysteemin toimintaan. Huonokuntoisia virtavesiä on kunnostettu paljon, mutta ymmärrys siitä, kuinka virtavesiä tulisi kunnostaa parhaan ekologisen lopputuloksen saavuttamiseksi, on edelleen vajaata. Tutkin tässä väitöskirjassa uittoperkausten ja maatalouden hajakuormituksen merkitystä ja yhteisvaikutusta virtavesien eliöyhteisöihin. Tutkin myös kunnostusten vaikutusta hiekasta kärsivissä metsätalouden muokkaamissa puroissa, sekä vesisammalten, hiekan ja eliöiden levittäytymisen merkitystä purojen pohjaeläinyhteisöjen ja ekosysteemin toimintojen muovautumisessa. Havaitsin, että uoman perkauksilla ei ollut vaikutusta virtavesien eliöyhteisöihin, mutta hajakuormituksen vaikutus oli voimakas. Perkauksella ja hajakuormituksella ei ollut yhteisvaikutuksia eliöyhteisöihin. Osoitin, että metsäojituksista aiheutuva ylimääräinen hiekan sedimentaatio on haitallista virtavesien eliöille, mutta sillä ei ollut vaikutusta lehtikarikkeen hajotukseen tai päällyslevien tuotantoon. Kunnostukset joissa käytettiin kiveä vähensivät hiekan peittävyyttä ja olivat hyödyllisempiä uoman eliöstölle kuin kunnostukset, joissa tehtiin puurakennelmia. Puukunnostukset kuitenkin lisäsivät uoman vedenpidätyskykyä ja siten muokkasivat rantavyöhykkeen kasvillisuutta luonnontilaisemmaksi. Havaitsin, että vesisammalilla on voimakas vaikutus pohjaeläinyhteisöjen koostumukseen. Sammalet vaikuttivat ekosysteemin toimintoihin lisäämällä eloperäisen aineksen pidättymistä ja vähentämällä lehtikarikkeen hajotusta ja päällyslevien tuotantoa. Sammalten vaikutus pohjaeläimiin oli voimakkaampi kuin hiekan, ja sammalet kykenivät jopa lieventämään joitakin hiekan negatiivisia vaikutuksia. Eliöiden levittäytymisellä oli selvä vaikutus yhteisöjen koostumukseen, mutta se ei hävittänyt hiekan ja sammalen vaikutusta, mikä viittaa korkeaan ympäristötekijöiden merkitykseen yhteisöjen rakentumisessa. Tutkielmani korostaa, että maatalousjokien tilan parantamisessa hajakuormituksen hallinta tulisi olla ensisijainen kunnostustavoite uoman rakenteen kunnostamisen sijaan. Metsätalouden vaikutuksista kärsivissä puroissa kivi- ja puumateriaalin käyttö samanaikaisesti tuottaa luultavimmin laajimman vaikutuksen purojen monimuotoisuuteen. Sammalilla on merkittävä vaikutus muiden eliöiden yhteisökoostumukseen ja ekosysteemin toimintoihin, joten sammalten palautuminen on tärkeä kunnostustavoite virtavesissä, joissa on luonnostaan paljon sammalkasvustoa

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27

Moubandjo, Desiree V. "Polynomial containment in refinement spaces and wavelets based on local projection operators." Thesis, Stellenbosch : Stellenbosch University, 2007. http://hdl.handle.net/10019.1/16418.

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28

Rivetti, Sabrina. "Bounded variation solutions of capillarity-type equations." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10161.

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2012/2013
We investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
XXV Ciclo
1985

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29

Armstrong, Michael James. "A process for function based architecture definition and modeling." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26631.

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Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Mavris, Dimitri; Committee Member: Garcia, Elena; Committee Member: Soban, Danielle. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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30

Mendousse, Grégory. "Analyse Harmonique Quaternionique et Fonctions Spéciales Classiques." Thesis, Reims, 2017. http://www.theses.fr/2017REIMS007/document.

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Ce travail s’inscrit dans l’étude des symétries d’espaces de dimension infinie. Il répond à des questions algébriques en suivant des méthodes analytiques. Plus précisément, nous étudions certaines représentations du groupe symplectique complexe dans des espaces fonctionnels. Elles sont caractérisées par leurs décompositions isotypiques relativement à un sous-groupe compact maximal. Ce travail décrit ces décompositions dans deux modèles : un modèle classique (dit compact) et un autre plus récent (dit non-standard). Nous montrons que cela établit un lien entre deux familles de fonctions spéciales (fonctions hypergéométriques et fonctions de Bessel) ; ces familles sont associées à des équations différentielles ordinaires d’ordre 2, fuchsiennes dans un cas et non fuchsiennes dans l’autre. Nous mettons aussi en évidence, dans le modèle non-standard, un lien avec certaines équations d'Emden-Fowler, ainsi qu’un opérateur différentiel simple qui agit sur les décompositions isotypiques
The general setting of this work is the study of symmetry groups of infinite-dimensional spaces. We answer algebraic questions, using analytical methods. To be more specific, we study certain representations of the complex symplectic group in functional spaces. These representations are characterised by their isotypic decompositions with respect to a maximal compact subgroup. In this work, we describe these decompositions in two different models: a classical model (compact picture) and a more recent one (non-standard picture). We show that this establishes a connection between two families of special functions (hypergeometric functions and Bessel functions); these families correspond to second order differential equations, which are Fuchsian in one case and non-Fuchsian in the other. We also establish a link with certain Emden-Fowler equations and exhibit a simple differential operator that acts on the isotypic decompositions

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31

Lösch, Manfred. "Ungeordnete Zahlpartitionen mit k Parts, ihre 2^(k - 1) Typen und ihre typspezifischen erzeugenden Funktionen." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-95635.

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Jede ungeordnete Zahlpartition mit k Parts (k-Partiton) hat einen Typ, der mittels einer geordneten Partition von k definiert werden kann. Es können somit 2^(k - 1) Typen definiert werden. Pro Typ gibt es eine eindeutig nummerierbare erzeugende Funktion der geschlossenen Form. Mit Rekursionen können diese Funktionen in (unendlich lange) Potenzreihen expandiert werden. Mit diesen erzeugenden Funktionen lassen sich Bijektionen zwischen den Partitionsmengen verschiedener Typen aufspüren.

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32

Lucisine, Pierre. "Fonctionnement des sols contaminés." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0195/document.

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Les sols des friches industrielles sont souvent multi-polluées et représentent des surfaces toujours plus importantes présentant de forts enjeux sociaux-économiques. Leur réhabilitation passe par une bonne compréhension du fonctionnement écologique des sols, qui, en plus d’être pollués, présentent des structures et des teneurs en nutriments souvent inhabituelles. Malgré cela, une recolonisation par la faune, la flore et les microorganismes est généralement observée. La capacité de ces nouvelles communautés à restaurer et maintenir les fonctions clés des sols reste à évaluer, et cela semble indissociable de la mesure d’une ou plusieurs fonctions écosystémiques. La décomposition de la litière est un processus écosystémique clef permettant la réalisation des cycles biogéochimiques du carbone et des nutriments. Les processus de la décomposition dépendent à la fois de ses acteurs (faune et microorganismes) et de la qualité de la litière végétale. De ce fait, la réponse de cette fonction écosystémique à la pollution du sol intègre les effets de cette pollution sur les communautés de plantes, d’animaux, et de microorganismes, ce qui en fait un indicateur potentiellement pertinent pour évaluer les effets de la pollution sur le fonctionnement des écosystèmes du sol. L’objectif central de cette thèse a donc été d’étudier le fonctionnement des friches industrielles en se focalisant sur les effets délétères de la pollution des sols sur la décomposition de la litière de feuilles. L’hypothèse centrale découlant de cet objectif a été que la pollution des sols pouvait impacter la décomposition par deux voies d’action. (1) La première voie, directe, est constituée de l’ensemble des effets délétères que pourraient provoquer les polluants sur les acteurs de la décomposition dont dépend la bonne réalisation de cette fonction. (2) Concernant la deuxième voie d’action, nous avons supposé que la pollution, en entraînant des modifications de la physiologie des plantes, pouvait modifier les paramètres physico-chimiques de la litière et ainsi impacter de façon indirecte la décomposition des litières. Nos résultats ont permis de montrer l’absence de l’effet direct pour huit friches industrielles fortement polluées, et ce malgré des perturbations des communautés d’acteurs, avec notamment une augmentation de l’abondance des détritivores et une modification de la colonisation microbienne des litières sur les sites pollués. Ces résultats plaident en faveur d’une redondance fonctionnelle suffisante au sein de ces communautés, permettant de maintenir le processus de décomposition. Nous avons également montré un effet indirect positif de la pollution sur la décomposition. Cet effet résulte de l’amélioration systématique de la qualité de la litière, entraînant dans certains cas une augmentation de l’activité des acteurs de la décomposition. Par ailleurs, nous avons également montré une accumulation des polluants dans ces mêmes litières, en particulier le Zn et le Cd, polluants pouvant potentiellement produire des effets délétères sur les acteurs de la décomposition. Toutefois, la présence de ces ETM n’a pas semblé influencer la consommation des litières par certains acteurs de la décomposition de la litière. Cependant, ce résultat reste à valider in situ en présence de l’ensemble des communautés de détritivores. De nombreuses perspectives s’ouvrent à la suite de ces travaux. Parmi elles, il reste notamment à déterminer 1) quels sont les mécanismes (physiologiques) qui entrainent une augmentation de la qualité des litières produites sur les sols contaminés ? 2) comment des communautés différentes permettent d’assurer des taux de décomposition similaires ? et 3) quels sont les impacts de la consommation des litières provenant des sites contaminés sur le fonctionnement et la physiologie des détritivores ?
Brownfield soils are multi-polluted areas, which cover an increasing surface and thus present serious socio-economical challenges. A better understanding of the ecological functioning of these sites is mandatory for their restoration. In addition to the high pollution found at these sites, brownfields are characterized by a specific soil structure and occasionally also by particular nutrient contents. Despite these constraints, several brownfield are well colonized by plants, fauna and microorganisms. The capacity of these new communities to uphold main ecosystem function remains to be evaluated based on the measurement of one or several ecosystem functions. Leaf litter decomposition is critically important in driving carbon and nutrient biogeochemical cycles. This function depends on decomposition actors (fauna and microorganisms) but also on leaf litter quality. By that, leaf litter decomposition integrates effects of soil pollution on plant, animal and microorganism communities. Thus, leaf litter decomposition is a relevant indicator to evaluate pollution effects on the functioning of soil ecosystems. The main objective of this thesis was to study brownfields soil function by focusing on the impairment of soil pollution on the leaf litter decomposition. The main hypothesis was that soil pollution could negatively affect leaf litter decomposition by two different ways. (1) By direct effects, resulting from adverse effects of soil pollution on decomposition actors, and (2) by indirect effects, assuming that soil pollution will induce modifications of the plant’s physiology, resulting in changes in leaf litter quality and subsequent effects on the decomposition. Our results revealed the absence of direct negative effects for eight highly polluted sites, despite a disturbance of decomposer actors, specifically the increase in abundance of detritivores and a modified microbial colonization of the leaf litter at the polluted sites. These results are in favor of a sufficient functional redundancy of decomposer actors in the local communities, which allowed the maintenance of the decomposition process. We also showed a positive indirect effect of soil pollution on the decomposition. This effect resulted from the improvement of litter quality produced at the polluted sites. This induced, at least for some sites, an increase of the decomposition rate, possibly due to a higher activity of decomposer actors. Furthermore, we also observed pollutants accumulation in these litter, especially Cd and Zn. These pollutants could potentially impair decomposition actors. Whatever, presence of these pollutants in litter did not impair litter consumption by some detritivores. Numerous perspectives can be developed from this study. Among them it seems specifically important to evaluate: 1) which are the (physiological) mechanisms behind the increase in leaf litter quality at polluted sites? 2) How can different communities assure the same decomposition rates at polluted sites? and 3) Are there negative effects observed on the performance and physiology of detritivores when consuming leaf litter from polluted sites ?

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33

Papafitsoros, Konstantinos. "Novel higher order regularisation methods for image reconstruction." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/246692.

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In this thesis we study novel higher order total variation-based variational methods for digital image reconstruction. These methods are formulated in the context of Tikhonov regularisation. We focus on regularisation techniques in which the regulariser incorporates second order derivatives or a sophisticated combination of first and second order derivatives. The introduction of higher order derivatives in the regularisation process has been shown to be an advantage over the classical first order case, i.e., total variation regularisation, as classical artifacts such as the staircasing effect are significantly reduced or totally eliminated. Also in image inpainting the introduction of higher order derivatives in the regulariser turns out to be crucial to achieve interpolation across large gaps. First, we introduce, analyse and implement a combined first and second order regularisation method with applications in image denoising, deblurring and inpainting. The method, numerically realised by the split Bregman algorithm, is computationally efficient and capable of giving comparable results with total generalised variation (TGV), a state of the art higher order method. An additional experimental analysis is performed for image inpainting and an online demo is provided on the IPOL website (Image Processing Online). We also compute and study properties of exact solutions of the one dimensional total generalised variation problem with L^{2} data fitting term, for simple piecewise affine data functions, with or without jumps . This gives an insight on how this type of regularisation behaves and unravels the role of the TGV parameters. Finally, we introduce, study and analyse a novel non-local Hessian functional. We prove localisations of the non-local Hessian to the local analogue in several topologies and our analysis results in derivative-free characterisations of higher order Sobolev and BV spaces. An alternative formulation of a non-local Hessian functional is also introduced which is able to produce piecewise affine reconstructions in image denoising, outperforming TGV.

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34

Costa, Éder Rítis Aragão. "Sistemas gradientes, decomposição de Morse e funções de Lyapunov sob perturbação." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042012-162303/.

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Neste trabalho investigamos a existência de uma função de Lyapunov associada a um sistema de tipo gradiente, semigrupos ou processos de evolução. Para isso, um estudo detalhado da teoria de Morse desempenha um papel decisivo. Como principal consequência deste estudo obtemos a estabilidade dos sistemas gradientes sob perturbação (autônoma ou não). A aplicabilidade dos resultados abstratos que aqui discutimos é exemplificada estudando-se sistemas de equações diferenciais em espaços de Banach com acoplamento unilateral
In this work we investigated the existence of a Lyapunov function associated to a gradient-like system, semigroups or evolution processes. For that, a detailed study of Morse theory plays a central role. As the main consequence of this study we obtain the stability of gradient systems under perturbation (autonomous or not). The applicability of the abstract results discussed here is exemplified by studying systems of differential equations in Banach spaces with unilateral coupling

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35

Le, Thu Hoai. "Hyperholomorphic structures and corresponding explicit orthogonal function systems in 3D and 4D." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-150508.

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Die Reichhaltigkeit und breite Anwendbarkeit der Theorie der holomorphen Funktionen in der komplexen Ebene ist stark motivierend eine ähnliche Theorie für höhere Dimensionen zu entwickeln. Viele Forscher waren und sind in diese Aufgaben involviert, insbesondere in der Entwicklung der Quaternionenanalysis. In den letzten Jahren wurde die Quaternionenanalysis bereits erfolgreich auf eine Vielzahl von Problemen der mathematischen Physik angewandt. Das Ziel der Dissertation besteht darin, holomorphe Strukturen in höheren Dimensionen zu studieren. Zunächst wird ein neues Holomorphiekonzept vorgelegt, was auf der Theorie rechtsinvertierbarer Operatoren basiert und nicht auf Verallgemeinerungen des Cauchy-Riemann-Systems wie üblich. Dieser Begriff umfasst die meisten der gut bekannten holomorphen Strukturen in höheren Dimensionen. Unter anderem sind die üblichen Modelle für reelle und komplexe quaternionenwertige Funktionen sowie Clifford-algebra-wertige Funktionen enthalten. Außerdem werden holomorphe Funktionen mittels einer geeignete Formel vom Taylor-Typ durch spezielle Funktionen lokal approximiert. Um globale Approximationen für holomorphe Funktionen zu erhalten, werden im zweiten Teil der Arbeit verschiedene Systeme holomorpher Basisfunktionen in drei und vier Dimensionen mittels geeigneter Fourier-Entwicklungen explizit konstruiert. Das Konzept der Holomorphie ist verbunden mit der Lösung verallgemeinerter Cauchy-Riemann Systeme, deren Funktionswerte reellen Quaternionen bzw. reduzierte Quaternionen sind. In expliziter Form werden orthogonale holomorphe Funktionensysteme konstruiert, die Lösungen des Riesz-Systems bzw. des Moisil-Teodorescu Systems über zylindrischen Gebieten im R3, sowie Lösungen des Riesz-Systems in Kugeln des R4 sind. Um konkrete Anwendungen auf Randwertprobleme realisieren zu können wird eine orthogonale Zerlegung eines Rechts-Quasi-Hilbert-Moduls komplex-quaternionischer Funktionen unter gegebenen Bedingungen studiert. Die Ergebnisse werden auf die Behandlung von Maxwell-Gleichungen mit zeitvariabler elektrischer Dielektrizitätskonstante und magnetischer Permeabilität angewandt
The richness and widely applicability of the theory of holomorphic functions in complex analysis requires to perform a similar theory in higher dimensions. It has been developed by many researchers so far, especially in quaternionic analysis. Over the last years, it has been successfully applied to a vast array of problems in mathematical physics. The aim of this thesis is to study the structure of holomorphy in higher dimensions. First, a new concept of holomorphy is introduced based on the theory of right invertible operators, and not by means of an analogue of the Cauchy-Riemann operator as usual. This notion covers most of the well-known holomorphic structures in higher dimensions including real, complex, quaternionic, Clifford analysis, among others. In addition, from our operators a local approximation of a holomorphic function is attained by the Taylor type formula. In order to obtain the global approximation for holomorphic functions, the second part of the thesis deals with the construction of different systems of basis holomorphic functions in three and four dimensions by means of Fourier analysis. The concept of holomorphy is related to the null-solutions of generalized Cauchy-Riemann systems, which take either values in the reduced quaternions or real quaternions. We obtain several explicit orthogonal holomorphic function systems: solutions to the Riesz and Moisil-Teodorescu systems over cylindrical domains in R3, and solutions to the Riesz system over spherical domains in R4. Having in mind concrete applications to boundary value problems, we investigate an orthogonal decomposition of complex-quaternionic functions over a right quasi-Hilbert module under given conditions. It is then applied to the treatment of Maxwell’s equations with electric permittivity and magnetic permeability depending on the time variable

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36

Singh, Shiu Raj. "Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis." Diss., Lincoln University, 2008. http://hdl.handle.net/10182/774.

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Abstract of thesis submitted in partial fulfilment of the requirements for the Degree of Master of Commerce and Management Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis By Shiu Raj Singh The objective of this study is to examine how macroeconomic variables of Fiji inter-relate with aggregate demand and co-determine one another using a vector autoregression (VAR) approach. This study did not use a prior theoretical framework but instead used economic justification for selection of variables. It was found that fiscal policy, which is generally used as a stabilisation tool, did not have a positive effect on real Gross Domestic Product (GDP) growth in the short term. Effects on GDP growth were positive over the long term but not statistically significant. Furthermore, expansionary fiscal policy caused inflationary pressures. Fiji has a fixed exchange rate regime, therefore, it was expected that the focus of monetary policy would be the maintenance of foreign reserves. It was, however, found that monetary expansion in the short term resulted in positive effects on real GDP growth and resulted in inflation. The long term effects of monetary policy on real GDP growth were negative, which are explained by the fixed exchange rate regime, endogenous determination of money supply by the central bank, an unsophisticated financial market and, perhaps, an incomplete transmission of the policy. Both merchandise trade and visitor arrivals growth were found to positively contribute to short term and long term economic growth. Political instability was found not to have significant direct effects on real GDP growth but caused a significant decline in visitor arrivals which then negatively affected economic growth in the short term.

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37

Chou, Fu-I., and 周阜毅. "A New Stoppage Criterion for Searching Intrinsic Mode Functions of Empirical Mode Decomposition." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/p66zj7.

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碩士
國立東華大學
電機工程學系
100
Empirical Mode Decomposition (EMD) is one of new methods for doing signal processing. By EMD, inputted signal will be separated into several set of independent components which are called Intrinsic Mode Functions (IMF). Each of them can be thought as an independent part of source signal or one of the sources from mixed signal. IMF has it definition hardly to satisfy in real experiments, and therefore defining an appropriate IMF searching rule before running EMD process becomes an important work. This thesis proposes a new way for searching IMF without setting any value as threshold. Not only avoiding from complicated testing of threshold value but also keeping the analysis efficacy in different situation make it becomes a strong method for searching IMF, especially in doing blind source separation. In this field of research, scientists are assumed under a condition that any information of inputted signals is unknown. By the reason, finding suitable threshold value becomes a hard work. The only way to solve the problem is defining a self-adaptive method for substituting traditional IMF searching rule. Problems mentioned above also inspire the purpose of this thesis for finding a new IMF searching way.

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38

Uliczka, Jan. "Graded Rings and Hilbert Functions." Doctoral thesis, 2010. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201007066381.

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Die Arbeit basiert auf zwei Veröffentlichungen zur graduierten kommutativen Algebra: Thema des ersten Artikels ist die Übertragung eines klassischen Ergebnisses zur Höhe von Primidealen in Polynomringen auf allgemeine multigraduierte Ringe; einige Anwendungen für die multigraduierte Dimensionstheorie werden vorgestellt. Der zweite Artikel behandelt Hilbertreihen von Moduln über einem standard-graduierten Polynomring über einem Körper. Ausgehend von einem grundlegenden Ergebnis über gewisse formale Laurentreihen werden unter anderem die möglichen Hilbertreihen und h-Vektoren solcher Moduln charakterisiert.

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39

Calbeck, William Stanley. "L[superscript p] decomposition of functions defined on C[infinity] totally real sub-manifolds of C[superscript n] into boundary values of functions holomorphic in wedges." 1990. http://catalog.hathitrust.org/api/volumes/oclc/24122445.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1990.
Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 44).

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40

Goldstein, Hilton. "The investigation into an algorithm based on wavelet basis functions for the spatial and frequency decomposition of arbitrary signals." Thesis, 1994. http://hdl.handle.net/10413/7347.

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The research was directed toward the viability of an O(n) algorithm which could decompose an arbitrary signal (sound, vibration etc.) into its time-frequency space. The well known Fourier Transform uses sine and cosine functions (having infinite support on t) as orthonormal basis functions to decompose a signal i(t) in the time domain to F(w) in the frequency . domain, where the Fourier coefficients F(w) are the contributions of each frequency in the original signal. Due to the non-local support of these basis functions, a signal containing a sharp localised transient does not have localised coefficients, but rather coefficients that decay slowly. Another problem is that the coefficients F(w) do not convey any time information. The windowed Fourier Transform, or short-time Fourier Transform, does attempt to resolve the latter, but has had limited success. Wavelets are basis functions, usually mutually orthonormal, having finite support in t and are therefore spatially local. Using non-orthogonal wavelets, the Dominant Scale Transform (DST) designed by the author, decomposes a signal into its approximate time-frequency space. The associated Dominant Scale Algorithm (DSA) has O(n) complexity and is integer-based. These two characteristics make the DSA extremely efficient. The thesis also investigates the problem of converting a music signal into it's equivalent music score. The old problem of speech recognition is also examined. The results obtained from the DST are shown to be consistent with those of other authors who have utilised other methods. The resulting DST coefficients are shown to render the DST particularly useful in speech segmentation (silence regions, voiced speech regions, and frication). Moreover, the Spectrogram Dominant Scale Transform (SDST), formulated from the DST, was shown to approximate the Fourier coefficients over fixed time intervals within vowel regions of human speech.
Thesis (Ph.D.)-University of Natal, Durban, 1994.

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41

Ncube, Mahluli Naisbitt. "The natural transform decomposition method for solving fractional differential equations." Diss., 2018. http://hdl.handle.net/10500/25348.

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In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense.
Mathematical Sciences
M. Sc. (Applied Mathematics)

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42

(6852506), Gowtham Manikanta Reddy Tamanampudi. "REDUCED FIDELITY ANALYSIS OF COMBUSTION INSTABILITIES USING FLAME TRANSFER FUNCTIONS IN A NONLINEAR EULER SOLVER." Thesis, 2019.

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Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.

To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.

In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.

The main objectives of this thesis are:

1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver

2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).

3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.

The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.

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Silverman, Shawn F. "On the simulation of overhead transmission lines." Thesis, 2005. http://hdl.handle.net/1993/180.

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This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page.
October 2005

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Gonçalves, Daniel Fernandes. "Business cycle dynamics across Europe: a cluster analysis." Master's thesis, 2016. http://hdl.handle.net/10071/13216.

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JEL Classification: E32, E37
This dissertation aims to analyze the dynamics of business cycles across European countries between 1960Q1 and 2016Q1. For such purpose we identify country-groups of national deviation cycles through Hierarchical Agglomerative Clustering with the Ward’s method. The clustering technique suggests the existence of three country-groups, which include, aside from other countries, France and Spain in Cluster 1, United Kingdom and Denmark in Cluster 2 and Germany and Italy in Cluster 3. We execute an extensive analysis on business cycle stylized facts, synchronization and turning points detection over the clusters’ deviation cycles. Further on, we analyze the propagation of economic shocks through a VAR model, over which we study Granger-causalities, Impulse Response Functions and Forecast Error Variance Decomposition. Our results show that both Cluster 1 and Cluster 2 share similar cyclical characteristics when compared to Cluster 3. Nevertheless, Cluster 1 and Cluster 3 appear to be the most synchronous pair, and simultaneously verify the largest proportion of time spent in the same cyclical phase. We show that there has been an increasing business cycle synchronization in Europe since the beginning of the 90’s. The structural analysis shows that Cluster 1 and Cluster 2 have the strongest permanent cumulative shocks, whereas Cluster 3 induces not only the weakest impulses but also explains the smallest fraction of the counterparts’ forecast error variance decomposition. These conclusions question the "German Dominance" hypothesis and allow the identification of alternative major economic propellers in Europe.
A presente tese pretende analisar as dinâmicas dos ciclos económicos na Europa no período compreendido entre 1960Q1 e 2016Q1. Como tal, procedemos à identificação de grupos de ciclos económicos nacionais através de Clusterização Hierárquica Aglomerativa com o método de Ward. A Clusterização sugere a existência de três grupos que incluem, além de outros países, França e Espanha no Cluster 1, Reino Unido e Dinamarca no Cluster 2, e Alemanha e Itália no Cluster 3. Analisamos as principais características, sincronização e cronologia de pontos de inflexão dos ciclos económicos dos clusters. Estudamos ainda a propagação de choques económicos com um modelo VAR, sobre o qual concluímos sobre causalidade à Granger, funções de impulso-resposta e decomposição de variância. Os resultados mostram que o Cluster 1 e Cluster 2 apresentam maiores semelhanças nas características dos seus ciclos quando comparados ao Cluster 3. Simultaneamente, o Cluster 1 e Cluster 3 apresentam quer o maior nível de sincronização quer a maior fração de tempo partilhada na mesma fase cíclica. Concluímos também que o nível de sincronização dos ciclos económicos na Europa apresenta uma tendência crescente, especialmente após os anos 90. A análise estrutural conclui que o Cluster 1 e Cluster 2 produzem os choques permanentes mais fortes, enquanto que o Cluster 3 induz os impulsos mais fracos, além de explicar a menor parte da decomposição de variância do erro de previsão dos restantes. As presentes conclusões questionam a hipótese de "Domínio Alemão" e permitem a identificação de outros propulsores económicos na Europa.

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45

Fontaine, Paul. "Croisements de lignes de flot entre fonctions de Morse et décomposition en cône itéré." Thesis, 2020. http://hdl.handle.net/1866/24343.

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Ce mémoire présente une nouvelle méthode d’étudier des fonctions de Morse sur une variété compacte. Plus précisément, les croisements entre les lignes de flot de pseudo-gradients associés à des fonctions de Morse permettent de définir géométriquement des morphismes entre les complexes de Morse, morphismes qui ne peuvent généralement pas être obtenus par une homotopie. Cette nouvelle classe de morphismes mène à la définition d’une catégorie triangulée. La question centrale est de savoir si tout objet de cette catégorie est décomposable en cône itéré de fonctions de Morse parfaites. En effet, une telle décomposition simplifierait l’étude de la dynamique d’une fonction de Morse en l’interprétant plutôt comme plusieurs fonctions parfaites. Une seconde question d’importance porte sur une condition de généricité globale à laquelle est soumise cette catégorie triangulée. Nous étudions la possibilité de s’en soustraire en proposant une méthode de déformations des fonctions de Morse.
This master’s thesis introduces a new way to sudy Morse functions on a compact manifold. More specifically, crossings between flows of pseudo-gradients associated to Morse functions allow one to define geometric realisations of morphisms between the Morse complexes. This new class of morphisms leads to the definition of a triangulated category. The main question is to determine if every object of this category admits an iterated cone decomposition. Such a decomposition would greatly simplify the study of the dynamic of a Morse function by interpreting it as many perfect Morse functions. A second topic concerns the global genericity condition to which this category is subject. We study a way, through deformation of Morse functions, to avoid such a constraint.

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46

Pereira, Gonçalo Filipe Faustino. "Indicadores de confiança e a realidade económica e financeira." Master's thesis, 2010. http://hdl.handle.net/10071/6563.

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Classificação: C32; C51; E23
No presente estudo é feito o exame da relação existente entre os indicadores de confiança dos Consumidores e dos Empresários com a realidade Económica e Financeira observada em Portugal entre Janeiro de 1999 e Dezembro de 2009. Para representar a realidade económica foi utilizado o Produto Interno Bruto a Preços Constantes e, por sua vez, o índice PSI-20 foi utilizado como indicador representativo da realidade Financeira. Para proceder a esta averiguação foi utilizada uma metodologia de vectores auto regressivos (VAR). De entre as várias conclusões retiradas, é necessário realçar que a variação dos indicadores de confiança é bastante relevante para explicar a evolução económica e financeira de Portugal. Destaque especial para o Indicador de confiança dos consumidores em termos de ajuda na explicação da variação do PIB e na previsão do mesmo. Por sua vez a variação do PSI-20 ajuda a prever a variação da Confiança dos Empresários.Já esta última consegue explicar mais de 17% da variabilidade do principal Índice Bolsista Português. O que é importante reter, neste estudo, é que sendo os indicadores de confiança apresentados com uma maior antecedência em relação à maioria dos indicadores de conjuntura económica e financeira e com uma periodicidade mensal, é necessário que estes sejam alvo frequente de atenção por parte dos vários governos e instituições com responsabilidade económica e financeira (por exemplo a União Europeia o BCE e o FMI) para análise das várias políticas e estratégias de crescimento económico implementadas.
The present study was done by examining the relationship between Consumer and Business confidence indicators and the Economic and Financial reality observed in Portugal between January 1999 and December 2009. To represent the economic reality, we used Gross Domestic Product at Constant Prices, and in turn the PSI-20 was used as a proxy indicator of financial reality. To carry out this investigation we used vector auto regressive methodology (VAR). Among the many conclusions drawn, it must be stressed that the range of confidence indicators is very important to explain the economic and financial developments in Portugal. Of particular note is the indicator of consumer confidence as a help in explaining the variation and also the anticipation of GDP. The variation of the PSI-20 helps predict the variation of the Business Confidence, since it can explain more than 17% of the variability of the main Portuguese stock index. Based on this study, we can point out that the confidence indicators being presented, with a major advance in relation to most indicators of economic and financial environment and on a monthly basis, should be a frequent target of attention from various governments and institutions with responsibility for economy and finances (e.g. the European Union, the ECB and the IMF) for the analysis of various policies and implemented strategies for economic growth.

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Sunde, Tafirenyika. "A small macro-econometric model for Namibia emphasising the dynamic modelling of the wage-price, productivity and unemployment relationship." Thesis, 2015. http://hdl.handle.net/10500/21721.

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The contribution of this thesis is to build a small macro-econometric model of the Namibian economy, which demonstrates that there is significant statistical support for the hypothesis that there is a contemporaneous relationship between real wage, productivity, unemployment and interest rates in Namibia. This phenomenon has not yet been exploited using macro-econometric modelling, and thus, represents a significant contribution to modelling literature in Namibia. The determination of the sources of unemployment also receives special attention given that high unemployment is a chronic problem in Namibia. All models specified and estimated in the study use the SVAR methodology for the period 1980 to 2013. The study develops a small macro-econometric model using three modular experiments, which include, a basic model, models that separately append demand and exchange rate channels variables to the basic model, and the specification of a small macro-econometric model. The ultimate aim is to find out if monetary policy plays a role in influencing labour market and nominal variables. The hypothesis that the basic real wage, productivity, unemployment rate and interest rate system can be estimated simultaneously is validated. Further, demand and exchange rate channels variables are found to have important additional information, which explains the monetary transmission process, and that shocks to labour market variables affect monetary policy in Namibia. The results also show that the demand channel (import prices and bank credit to the private sector) and the exchange rate channel (nominal exchange rate) variables have important additional information, which affects monetary transmission process in Namibia, which justifies their inclusion in the small macro-econometric model. In addition, shocks to the import price and exchange rate in the macro-econometric model significantly affect labour market variables. However, shocks to bank credit only partially perform as expected, implying that its results need to be considered cautiously. The study further finds that tight monetary policy shocks significantly affect real and nominal variables in Namibia. The results also show that shocks to all variables in the unemployment model significantly affect unemployment, suggesting that the hysteresis assumption is corroborated. This implies that long run aggregate demand is non-neutral in Namibia.
Economics
D. Litt. et Phil. (Economics)

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