Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Historical demography of Lantana camara L. reveals clues about the influence of land use and weather in the management of this widespread invasive species

Weather is a general stochastic influence on the life history of weeds. In contrast, anthropogenic disturbance (e.g. land use) is an important deterministic influence on weed demography. Our aim with this study was to investigate the relative contributions of land use and weather on the demography of Lantana camara (lantana), a weed of agricultural and natural habitats, based on the intensive monitoring of lantana populations under three land uses (viz. farm[pasture], and burnt and grazed forests) in subtropical Australia. Lantana populations were growing vigorously across all land uses (asymptotic population growth rate, λ > 3). Examination of historical demography using retrospective perturbation analyses showed that weather was a strong influence on lantana demography with the transition from an El Niño (2008–09) to a La Niña (2009–10) year having a strong positive effect on population growth rate. This effect was most marked at the grazed site, and to a lesser extent at the burnt site, with seedling-to-juvenile and juvenile-to-adult transitions contributing most to these effects. This is likely the result of burning and grazing having eliminated/reduced interspecific competition at these sites. Prospective perturbation analyses revealed that λ was most sensitive to proportionate changes in growth transitions, followed by fecundity and survival transitions. Examination of context-specific patterns in elasticity revealed that growth and fecundity transitions are likely to be the more critical vital rates to reduce λ in wet years at the burnt and grazed forest sites, compared to the farm/pasture site. Management of lantana may need to limit the transition of juveniles into the adult stages, especially in sites where lantana is free from competition (e.g. in the presence of fire or grazing), and this particularly needs to be achieved in wet years. Collectively, these results shed light on aspects of spatial and temporal variation in the demography of lantana, and offer insights on its context-specific management.

Intermolecular interactions in the formation of aromatic hydrocarbon dimers

Both short-range and long-range intermolecular interaction energies between two aromatic hydrocarbon molecules, both in their ground state, separated by a range of interplanar distances of 3 ∼ 4 Aring, are estimated using the standard perturbation theory. The results show that aromatic hydrocarbons can form weak sandwich dimers with larger separation between them than is normally believed in their excimers. The non-sandwich form of dimer in which the long in-plane axes of the monomers are parallel and their short in-plane axes inclined, represents an unstable orientation because this form can pass to the perfect sandwich form without an energy barrier.

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

Effect of ionic temperature on propagation of ion-acoustic solitary waves in a collisionless plasma of warm-ion fluid and non-isothermal electrons

Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).

Power and Authority. Birgitta of Sweden and her Revelations

In the High Middle Ages female saints were customarily noble virgins. Thus, as a wife and a mother of eight children, the Swedish noble lady Birgitta (1302/3 1373) was an atypical candidate for sanctity. However, in 1391 she was canonized only 18 years after her death and became a role model for many late medieval women, who were mothers and widows. The dissertation Power and Authority Birgitta of Sweden and Her Revelations investigates how Birgitta went about establishing her power and authority during the first ten years of her career as a living saint, in 1340 1349. It is written from the perspectives of gender, authority, and power. The sources consist of approximately seven hundred revelations, hagiographical texts and other medieval documents. This work concentrates on the interaction between Birgitta and her audience. During her lifetime Birgitta was already regarded as a holy woman, as a living saint. A living saint could be given no formal papal or other recognition, for one could never be certain about his or her future activities. Thus, the living saint needed an audience for whom to perform signs of sanctity. In this study particular attention is paid to situations within which the power relations between the living saint and her audience can be traced and are open to critical analysis. Situations of conflict that arose in Birgitta s life are especially fruitful for this purpose. During the Middle Ages, institutional power and authority were exclusively in the hands of secular male leaders and churchmen. In this work it is argued, however, that Birgitta used different kinds of power than men. It is evident that she exercized influence on lay people as well as on secular and clerical authorities. The second, third, and fourth chapter of this study examine the beginning of Birgitta s career as a visionary, what factors and influences lay behind it, and what kind of roles they played in establishing her religious authority. The fifth, sixth, and seventh chapter concentrate on Birgitta s exercising of power in specific situations during her time in Sweden until she left on a pilgrimage to Rome in 1349. The central question is how she exercised power with different people. As a result, this book will offer a narrative of Birgitta s social interactions in Sweden seen from the perspectives of power and authority. Along with the concept of power, authority is a key issue. By definition, one who has power also has authority but a person who does not have official power can, nevertheless, have authority. Authority in action is defined here as meaning that a person was listened to. Birgitta acted both in situations of open conflict and where no conflict was evident. Her strategies included, for example, inducement, encouragement and flattery. In order to make people do as she felt was right she also threatened them openly with divine wrath. Sometimes she even used both positive persuasion and threats. Birgitta s power seems very similar to that of priests and ascetics. Common to all of them was that their power demanded interaction with other people and audiences. Because Birgitta did not have power and authority ex officio she had to persuade people to believe in her powers. She did this because she was convinced of her mission and sought to make people change their lives. In so doing, she moved from the domestic field to the public fields of religion and politics.

Yhteisön ja yhteiskunnan ehdoilla : Seurakuntien ja kuntien yhteistyö vuorovaikutuksen näkökulmasta

In this research, the cooperation between Finnish municipalities and Evangelical Lutheran parishes is studied from the standpoint of institutional interaction. The most essential theoretical background for the study is the differentiation thesis of the secularization theory. Cooperation from the viewpoints of both organizations is examined using the functional approach. Furthermore, the market theory and other theories are applied in order to place the studied phenomenon in the wider context of the theories of the sociology of religion. Sacralization in modern society and its relationship with the differentiation thesis of the secularization theory are in the theoretical foci. In addition, along with a descriptive examination of cooperation, the normative sides of the phenomenon are discussed. The survey was conducted among all municipalities and parishes in continental Finland. The questionnaires were sent to all municipal managers of youth work and afternoon activities and to all managers of child, youth and social work in the parishes. The response rate for the municipalities was 73.9 % and for the parishes 69.5 %. In addition, two qualitative data were utilized. The aim of the study is to scrutinize what kind of limitations of differentiation can be caused by the interaction between the secular and the religious. In order to solve the problem, an empirical study of sacralization in the modern context is required. For this purpose, the survey was carried out to determine the effects of the religious on the secular and the impact of the secular on the religious. In the articles of the study the following relationships are discussed: the positions of municipalities and parishes in relation to the state and civil society; cooperation in relation to differentiation; sacralization in relation to the differentiation thesis and cooperation in relation to pluralism. The results of the study highlighted the significance of the cooperation, which was contrary to the secularization theory connected to religious sacralization. The acceptance of the appearance of religion in cooperation and parishes support for municipal function was high in municipalities. Religious cooperation was more active than secular cooperation within all fields. This was also true between fields: religiously orientated child work was more active than the societally orientated social work of the church. Religious cooperation in modern fields of activity underlined sacralization. However, the acceptance of sacralization was weaker in cities than rural areas. Positive relationships between the welfare function of municipalities and the religious function of parishes emphasized the incompleteness of differentiation and the importance of sacralization. The relationship of the function of municipalities with parishes was neither negative nor neutral. Thus, in the most active fields, that is, child work and the traditional social work of the church, the orientation of parishes in cooperation supported the functions of both organizations. In more passive fields, that is, youth work and the societal social work of the church, parishes were orientated towards supporting the municipal function. The orientation of municipalities to religion underlined the perception that religious function is necessary for cooperation. However, the official character of cooperation supported accommodation to the requirements of societal pluralism. According to the results, sacralization can be effective also at the institutional level. The religious effect of voluntary cooperation means that religious sacralization can also readjust to modern society. At the same time, the results of the study stressed the importance of institutional autonomy. Thus, the public sector has a central role in successful cooperation. The conditions of cooperation are weakened if there is no official support of cooperation or adjustment to the individual rights of modern society. The results called into question the one-directional assumptions in the secularization paradigm and the modernization theory in the background. In these assumptions, religion that represents the traditional is seen to give way to the modern, especially at the institutional level. Lack of an interactional view was identified as a central weakness of the secularization paradigm. In the theoretical approach created in the study, an interactional view between religious and secular institutions was made possible by limiting the core of the differentiation thesis to autonomy. The counter forces of differentiation are despecialization and sacralization. These changes in the secularization theory bring about new interactivity on the institutional level. In addition to the interactional approach, that is, the secularization and sacralization theory created as a synthesis of the study, interaction between the religious and the secular is discussed from the standpoint of multiple modernities. The spiritual welfare role of religion is seen as a potential supporter of secular institutions. Religion is set theoretically amongst other ideologies and agents, which can create communal bonds in modern society. Key words: cooperation, municipalities, parishes, sacralization, secularization, modernization, multiple modernities, differentiation, interaction, democracy, secularism, pluralism, civil society

Inculcating character education through EFL teaching in Indonesian state schools

This paper describes how English as foreign language (EFL) teachers in Indonesia have implemented the recent character education policy within an era of school-based curriculum reform. The character education policy required all teachers, EFL teachers included, to instill certain values in every lesson whilst the school-based curriculum reform permitted teachers to develop locally responsive curriculum content. The design behind the reform seeks to sharpen education’s role as a site of moral inculcation in the face of growing social diversity that threatens social cohesion and the prolonged social problem of massive corruption. Drawing on Durkheim’s (1925) distinction between secular and religious morality, this paper considers how the Indonesian curriculum promoted rational or secular moral education and how the EFL teachers enacted religious moral education given religiosity is salient in both the community and schools of Indonesia. Bernstein’s concepts of pedagogic discourse, instructional and regulative discourses were adopted to analyse how EFL teachers have re-contextualized both curricular reforms in their micro pedagogic settings. The conclusion suggests that teachers’ implementation of moral education in their classes was dominated by their school communities’ and the teachers’ own preferred value of religiosity. Such values played out in their classes through both the regulative discourse and the instructional discourse.

Intermolecular potentials in the dimer, the excimers, and the dimer ions of ethylene

Calculations are reported on the interaction energies in the dimer, the excimers, and the dimer ions of ethylene. The various a- and u-electron terms for different conformations of the dimeric species are determined by using the exchange perturbation method. The results predict that the singlet excimer and the dimer cation are stable primarily because of the large magnitude of the exciton-resonance and charge-resonance terms, respectively, while the neutral dimer, the triplet excimer, and the dimer anion are weakly stable. The variations of the various energy terms with conformations suggest that these dimeric species cannot have identifical structure.

A Soul for Europe? : Contributions of European Churches to the Forum of the Convention on the Future of Europe

The aim of this research was to study how European churches contributed to the shaping of the Constitutional Treaty during the work of the Convention on the future of Europe through the public discussion forum, established by the Convention for this specific purpose in the years 2002 2003. In particular, this study sought to uncover the areas of interest brought up by the churches in their contributions, the objectives they pursued, and the approaches and arguments they employed to reach those objectives. The data for this study comprised all official submissions by European churches and church alliances to the Forum, totalling 21 contributions. A central criterion for inclusion of the data was that the organization can reasonably be assumed to represent the official position of one or more Christian churches within the European Union before the 2004 expansion. The contributing churches and organizations represent the vast majority of Christians in Europe. The data was analyzed using primarily qualitative content analysis. The research approach was a combination of abductive and inductive inference. Based on the analysis a two-fold theoretical framework was adopted, focusing on theories of public religion, secularization and deprivatization of religion, and of legitimation and collective identity. The main areas of interest found in the contributions of the churches were the value foundation of the European Union, which is demanded to coherently permeate all policies and actions of the EU, and the social dimension of Europe, which must be given equal status to the political and economic dimensions. In both areas the churches claim significant experience and expertise, which they want to see recognized in the Constituional Treaty through a formally guaranteed status for churches and religious communities in the EU. In their contributions the churches show a strong determination to secure a significant role for both religion and religious communities in the public life of Europe. As for the role of religion, they point out to its potential as a motivating and cohesive force in society and as a building block for a collective European identity, which is still missing. Churches also pursue a substantial public role for themselves beyond the spiritual dimension, permeating the secular areas of the social, political and economic dimensions. The arguments in suppport of such role are embedded in their interest and expertise in spiritual and other fundamental values and their broad involvement in providing social services. In this context churches use expressions inclusive of all religions and convictions, albeit clearly advocating the primacy of Europe's Christian heritage. Based on their historical role, their social involvement and their spiritual mission they use the public debate on the Constitutional Treaty to gain formal legitimacy for the public status of religion and religious communities, both nationally and on a European level, through appropriate provisions in the constitutional text. In return they offer the European Union ways of improving its own legitimacy by reducing the democratic and ideological deficit of the EU and advancing the development a collective European identity.

Positional Consensus in Multi-Agent Systems using a Broadcast Control Mechanism

In this paper a strategy for controlling a group of agents to achieve positional consensus is presented. The proposed technique is based on the constraint that every agents must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming formulation that is computationally less intensive than earlier proposed methods. Moreover, we introduce a random perturbation input in the control command that helps us to achieve perfect consensus even for a large number of agents, which was not possible with the existing strategy in the literature. Moreover, we extend the method to achieve positional consensus at a pre-specified location. The effectiveness of the approach is illustrated through simulation results.

Mossbauer lineshape in the presence of NMR transitions

The general expression for the Mössbauer lineshape in the presence of radio frequency perturbation derived earlier has been further extended. This involves the calculation of the off-diagonal matrix elements of the correlation function. The results show that there are additional transition lines owing to the nuclear magnetic resonance induced transition in the resonance region. These lines do not show any broadening or splitting. As an example the effect of the rf field on 57Fe nuclei is discussed.