O principal objetivo desta tese é estudar os difeomorfismos planares que satisfazem as hipóteses da Versão Modificada da Conjectura Discreta de Markus-Yamabe. Para estes difeomorfismos, definimos um conceito construtivo de número de rotação. Além disto, exibimos um contra-exemplo para a Versão Modificada da Conjectura Discreta de Markus-Yamabe que apresenta uma intersecção homoclínica transversal e implica a existência de infinitos pontos periódicos hiperbólicos / The main goal of this thesis is to study the plane diffeomorphisms satisfying the hypothesis of the Modified Version of the Discrete Conjecture of Markus-Yamabe. For these diffeomorphisms, we define a constructive concept of rotation number. Moreover, we present a counter-example to the Modified Version of the Discrete Markus-Yamabe Conjecture which exhibits a transversal homoclinic intersection, implying the existence of infinitely many hyperbolic periodic points

In this thesis, we study the population dynamics of predator-prey interactions described by mathematical models with age/stage structures. We first consider fixed development times for predators and prey and develop a stage-structured predator-prey model with Holling type II functional response. The analysis shows that the threshold dynamics holds. That is, the predator-extinction equilibrium is globally stable if the net reproductive number of the predator $\mathcal{R}_0$ is less than $1$, while the predator population persists if $\mathcal{R}_0$ is greater than $1$. Numerical simulations are carried out to demonstrate and extend our theoretical results. A general maturation function for predators is then assumed, and an age-structured predator-prey model with no age structure for prey is formulated. Conditions for the existence and local stabilities of equilibria are obtained. The global stability of the predator-extinction equilibrium is proved by constructing a Lyapunov functional. Finally, we consider a special case of the maturation function discussed before. More specifically, we assume that the development times of predators follow a shifted Gamma distribution and then transfer the previous model into a system of differential-integral equations. We consider the existence and local stabilities of equilibria. Conditions for existence of Hopf bifurcation are given when the shape parameters of Gamma distributions are $1$ and $2$.

In Sweden as well as other countries the trend of building higher is more and more popular. The global stability of tall buildings is a very important aspect that has to be taken into account while designing. Foundation on piles, that is common in Sweden, reduces the global stability compared to foundation directly on bedrock. Using inclined piles in the foundation is inevitable for high-rise buildings, because they are essential for transferring the horizontal loads into the bedrock. The aim of this paper is to look into the influence that foundation on piles has on global stability and investigate two simple methods to asses global stability. In this thesis the influence of the stiffness of the substructure (foundation), length and inclination of the piles on the global stability were investigated. It was also looked into how does the pile center affect the rotation and thus global stability. One method that was presented was based on the equivalent stiffness. Displacement at the top of the wall is used in order to calculate the bending stiffness that is reduced due to foundation on piles and further calculate buckling load on the basis of Euler buckling. In the other method that was proposed rotation at the foundation level was taken into account so as to calculate rotational spring stiffness and later buckling load due to combined flexural and rotational buckling. The analysis was conducted on a simple two dimensional problem, namely stabilizing wall as well as a building stabilized by two towers. Three different configurations of piles were investigated for single wall as well as for the structure. The investigation showed that the position of pile center has its effect on the global stability. The closer the pile center is to the foundation on piles the better the global stability of a  structure. The length of the piles plays a role in stability as well. The longer the piles are the worse the stability is. With longer piles the overall stiffness of a structure decreases and thus the global stability. The analysis showed that the foundation of piles significantly lowers the stability of high rise building. The investigated methods showed that the one based on rotation at the base gave better results compared to the method based on the equivalent bending stiffness. But to use this first method, the position of the pile center is required to be known in order to get correct results which in a complex structure is hard to estimate. In an analysis of a building stabilized by two towers it was seen that when the inclined piles that are inclined opposite to each other in a pile group and are positioned far from rotation center of a structure it increases the global safety and rotational stiffness as well. It is recommended to use such configuration of piles that the pile center is at the foundation level in order to increase global stability. / I Sverige och andra länder är trenden att bygga högre alltmer populärt. Den globala stabiliteten hos höga byggnader är en viktig aspekt som måste beaktas vid byggnadens utformning. Den vanligaste grundläggningsmetoden i Sverige är grundläggning med pålar. Denna typ av grundläggning minskar den globala stabiliteten jämfört med grundläggning direkt på berggrunden. Att använda sneda pålar i grundläggningen är oundviklig för höghus, eftersom de är nödvändiga för att överföra horisontella laster till berggrunden. Syftet med detta examensarbete är att se hur grundläggning på pålar påverkar den globala stabiliteten och undersöka två enkla metoder för global stabilitet. I detta examensarbete undersöktes hur styvheten påverkar grundläggning med pålar med olika längder och lutningar, med hänseende på den globala stabiliteten. Pålcentrumets påverkan av rotation och den globala stabiliteten har även studerats. En metod som presenterades i examensarbetet är baserades på ekvivalent styvhet. Där utböjning på toppen av väggen togs för att beräkna böjstyvheten som reduceras på grund av grundläggning med pålar och ytterligare beräknades knäcklasten baserat på Eulers knäckning. I den andra metoden som föreslogs togs rotationen vid grundläggningsnivån med i beräkningen för att beräkna rotationsfjäderns styvhet och senare knäckningslasten på grund av kombinerad böjnings- och rotationsknäckning. Analysen genomfördes på en enkel tvådimensionell vägg och en tredimensionell byggnad som är stabiliserad av två torn. Tre olika konfigurationer av pålar undersöktes för enkel vägg och även för byggnaden Utredningen av examensarbetet visade att positionen av pålcentrum har en stor påverkan på den globala stabiliteten. Ju närmare pålcentrumet är till grundläggningsnivån desto bättre är den globala stabiliteten hos en konstruktion. Längden på pålarna har även en betydelse när det gäller stabiliteten. Ju längre pålarna är desto värre blir stabiliteten. Med längre pålar minskar den totala styvheten hos hela konstruktionen och därmed minskar även den globala stabiliteten. Utredningen visade även att metoden med rotation vid grundläggningsnivån gav mer noggrannare resultat än metoden för ekvivalent styvhet. Men för att kunna använda den förstnämnda metoden behöver man ha kännedom om vart pålcentrum ligger för konstruktionen och detta kan vara svårt att uppskatta. I en analys av en byggnad stabiliserad av två torn visades det att när pålarna är placerade långt från rotationscentrum av en konstruktion ökar den globala säkerheten och rotationsstyvheten. Det rekommenderas att använda sådan konfiguration av pålar att pålcentrum ligger på grundnivå för att öka den globala stabiliteten.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23873号 / 工博第4960号 / 新制||工||1775(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 大崎 純, 教授 池田 芳樹, 准教授 藤田 皓平 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and different means of transition control of such flows which are of great interest in aeronautical applications. Acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coefficient defined as the relative amplitude of acoustic disturbances and TS wave. The existing results in the literature for this flow case plot a scattered image and are inconclusive. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods. Our results have shown that the generally-accepted level of acoustic receptivity coefficient for this flow case is one order of magnitude too high. The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. A swept flat plate of FSC type boundary layer with surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed. The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed roughness elements in the presence of acoustic waves have been studied. Moreover, ring-type plasma actuators are employed as virtual roughness elements to delay laminar-turbulent transition. / <p>QC 20161124</p>

Este trabalho tem o objetivo de transmitir aos Engenheiros de Estruturas o conhecimento teórico necessário para o dimensionamento e detalhamento de pilares usuais de edifícios em concreto armado. A definição das posições dos pilares em uma estrutura, bem como uma estimativa da seção transversal dos mesmos são abordadas neste trabalho. O estudo da estabilidade global, realizado no Capítulo 3, nos permite avaliar se os deslocamentos ocorridos na estrutura em função das ações horizontais e verticais, geram esforços de segunda ordem consideráveis ou não. A instabilidade de pilares será comentada no Capítulo 5, bem como os Métodos desenvolvidos para avaliar se um determinado pilar é estável ou instável. O detalhamento de pilares segundo as prescrições do Texto Base para a revisão da NBR - 6118/78, bem como o desenvolvimento de exemplos de dimensionamento de pilares estão contidos neste trabalho nos Capítulos 7 e 8, respectivamente. / The objective of this work is to transrnit to the structural engineers the necessary theoretical knowledge for the design and detail of usual columns in reinforced concrete buildings. The definition of the columns positions in the structure, as well as an estimate of their cross section will be explained in this work. The global stability study, described in chapter 3, allows us to evaluate whether the deformations ocurred in the structure due to horizontal and vertical actions, cause considerable second order strength or not. The columns instability will be commented in chapter 5, as well as the methods developed to evaluate whether a specific column is stable or instable. The columns detail as prescribed in the Basic Text for the Revision of NBR - 6118/78, and also the development of examples for columns design are in chapter 7 and 8, respectively.

ix, 111 p. / This dissertation contains the results obtained from a study of two subjects in mathematical general relativity. The first part of this dissertation is about the existence of Killing symmetries in spacetimes containing a compact Cauchy horizon. We prove the existence of a nontrivial Killing symmetry in a large class of analytic cosmological spacetimes with a compact Cauchy horizon for any spacetime dimension. In doing so, we also remove the restrictive analyticity condition and obtain a generalization to the smooth case. The second part of the dissertation presents our results on the global stability problem for a class of cosmological models. We investigate the power law inflating cosmological models in the presence of electromagnetic fields. A stability result for such cosmological spacetimes is proved. This dissertation includes unpublished co-authored material. / Committee in charge: James Brau, Chair; James Isenberg, Advisor; Paul Csonka, Member; John Toner, Member; Peng Lu, Outside Member

Este trabalho tem o objetivo de transmitir aos Engenheiros de Estruturas o conhecimento teórico necessário para o dimensionamento e detalhamento de pilares usuais de edifícios em concreto armado. A definição das posições dos pilares em uma estrutura, bem como uma estimativa da seção transversal dos mesmos são abordadas neste trabalho. O estudo da estabilidade global, realizado no Capítulo 3, nos permite avaliar se os deslocamentos ocorridos na estrutura em função das ações horizontais e verticais, geram esforços de segunda ordem consideráveis ou não. A instabilidade de pilares será comentada no Capítulo 5, bem como os Métodos desenvolvidos para avaliar se um determinado pilar é estável ou instável. O detalhamento de pilares segundo as prescrições do Texto Base para a revisão da NBR - 6118/78, bem como o desenvolvimento de exemplos de dimensionamento de pilares estão contidos neste trabalho nos Capítulos 7 e 8, respectivamente. / The objective of this work is to transrnit to the structural engineers the necessary theoretical knowledge for the design and detail of usual columns in reinforced concrete buildings. The definition of the columns positions in the structure, as well as an estimate of their cross section will be explained in this work. The global stability study, described in chapter 3, allows us to evaluate whether the deformations ocurred in the structure due to horizontal and vertical actions, cause considerable second order strength or not. The columns instability will be commented in chapter 5, as well as the methods developed to evaluate whether a specific column is stable or instable. The columns detail as prescribed in the Basic Text for the Revision of NBR - 6118/78, and also the development of examples for columns design are in chapter 7 and 8, respectively.

Apresenta-se uma metodologia para análise de interação solo-estrutura aplicada ao estudo da estabilidade global de estruturas de concreto armado sobre fundações profundas. A metodologia de análise de interação solo-estrutura consiste num processo iterativo no qual, inicialmente, determinam-se as reações da superestrutura, considerando os apoios indeslocáveis. Com estas reações, por meio do programa EDRR, calculam-se os deslocamentos dos blocos de fundação. Com as reações e estes deslocamentos calcula-se os coeficientes das molas que substituirão os apoios fixos da superestrutura, cujas reações são recalculadas. Repete-se o processo até que as reações de duas iterações consecutivas sejam aproximadamente iguais. O programa EDRR (estaqueamento, deslocamento horizontal, recalque, rotação), elaborado em linguagem FORTRAN, determina os esforços no estaqueamento através de análise matricial considerando a reação horizontal do solo. Os deslocamentos horizontais e rotações são calculados através da teoria de viga sobre apoio elástico, enquanto os recalques no maciço de solos são calculados considerando o efeito de grupo através da continuidade do meio. Através de exemplos de casos reais, com medida de recalques, demonstra-se a eficiência da metodologia na previsão dos recalques. Além disso, procura-se mostrar que os recalques influenciam na estabilidade global da superestrutura. / This work presents a methodology for the analysis of soil-structure interaction applied to the study of the global stability of reinforced concrete structures on deep foundations. The soil-structure interaction methodology consists of an iterative process in which, at the beginning, the superstructure support reactions are computed, assuming fixed supports. Using the computed reactions, with aid of the EDRR program, foundation cap displacements are computed. Then, with the computed support reactions and displacements, spring coefficients, which will replace the fixed supports, are calculated. The process is repeated until reactions determined in two consecutive iterations are close to each other. The EDRR program, written in FORTRAN language, computes the forces at the top of piles by means of matrix analysis, taking into account the horizontal soil reaction. Horizontal linear displacements and rotations are computed using the elastic foundation beam theory, and soil mass settlements are computed taking into account the group effect considering the mass continuity. Thro ugh real case examples, with settlement monitoring, the proposed methodology efficiency is demonstrated. Furthermore, the influence of settlements on the structure global stability is shown.

>Magister Scientiae - MSc / HIV/AIDS is nowadays considered as the greatest public health disaster of modern time. Its progression has challenged the global population for decades. Through mathematical modelling, researchers have studied different interventions on the HIV pandemic, such as treatment, education, condom use, etc. Our research focuses on different compartmental models with emphasis on the effect of public health education. From the point of view of statistics, it is well known how the public health educational programs contribute towards the reduction of the spread of HIV/AIDS epidemic. Many models have been studied towards understanding the dynamics of the HIV/AIDS epidemic. The impact of ARV treatment have been observed and analysed by many researchers. Our research studies and investigates a compartmental model of HIV with treatment and education campaign. We study the existence of equilibrium points and their stability. Original contributions of this dissertation are the modifications on the model of Cai et al. [1], which enables us to use optimal control theory to identify optimal roll-out of strategies to control the HIV/AIDS. Furthermore, we introduce randomness into the model and we study the almost sure exponential stability of the disease free equilibrium. The randomness is regarded as environmental perturbations in the system. Another contribution is the global stability analysis on the model of Nyabadza et al. in [3]. The stability thresholds are compared for the HIV/AIDS in the absence of any intervention to assess the possible community benefit of public health educational campaigns. We illustrate the results by way simulation The following papers form the basis of much of the content of this dissertation, [1 ] L. Cai, Xuezhi Li, Mini Ghosh, Boazhu Guo. Stability analysis of an HIV/AIDS epidemic model with treatment, 229 (2009) 313-323. [2 ] C.P. Bhunu, S. Mushayabasa, H. Kojouharov, J.M. Tchuenche. Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa. J Math Model Algor 10 (2011),31-55. [3 ] F. Nyabadza, C. Chiyaka, Z. Mukandavire, S.D. Hove-Musekwa. Analysis of an HIV/AIDS model with public-health information campaigns and individual with-drawal. Journal of Biological Systems, 18, 2 (2010) 357-375. Through this dissertation the author has contributed to two manuscripts [4] and [5], which are currently under review towards publication in journals, [4 ] G. Abiodun, S. Maku Vyambwera, N. Marcus, K. Okosun, P. Witbooi. Control and sensitivity of an HIV model with public health education (under submission). [5 ] P.Witbooi, M. Nsuami, S. Maku Vyambwera. Stability of a stochastic model of HIV population dynamics (under submission).