A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Perceiving and pursuing novelty : a grounded theory of adolescent creativity

Creativity plays an increasingly important role in our personal, social, educational, and community lives. For adolescents, creativity can enable self-expression, be a means of pushing boundaries, and assist learning, achievement, and completion of everyday tasks. Moreover, adolescents who demonstrate creativity can potentially enhance their capacity to face unknown future challenges, address mounting social and ecological issues in our global society, and improve their career opportunities and contribution to the economy. For these reasons, creativity is an essential capacity for young people in their present and future, and is highlighted as a priority in current educational policy nationally and internationally. Despite growing recognition of creativity’s importance and attention to creativity in research, the creative experience from the perspectives of the creators themselves and the creativity of adolescents are neglected fields of study. Hence, this research investigated adolescents’ self-reported experiences of creativity to improve understandings of their creative processes and manifestations, and how these can be supported or inhibited. Although some aspects of creativity have been extensively researched, there were no comprehensive, multidisciplinary theoretical frameworks of adolescent creativity to provide a foundation for this study. Therefore, a grounded theory methodology was adopted for the purpose of constructing a new theory to describe and explain adolescents’ creativity in a range of domains. The study’s constructivist-interpretivist perspective viewed the data and findings as interpretations of adolescents’ creative experiences, co-constructed by the participants and the researcher. The research was conducted in two academically selective high schools in Australia: one arts school, and one science, mathematics, and technology school. Twenty adolescent participants (10 from each school) were selected using theoretical sampling. Data were collected via focus groups, individual interviews, an online discussion forum, and email communications. Grounded theory methods informed a process of concurrent data collection and analysis; each iteration of analysis informed subsequent data collection. Findings portray creativity as it was perceived and experienced by participants, presented in a Grounded Theory of Adolescent Creativity. The Grounded Theory of Adolescent Creativity comprises a core category, Perceiving and Pursuing Novelty: Not the Norm, which linked all findings in the study. This core category explains how creativity involved adolescents perceiving stimuli and experiences differently, approaching tasks or life unconventionally, and pursuing novel ideas to create outcomes that are not the norm when compared with outcomes by peers. Elaboration of the core category is provided by the major categories of findings. That is, adolescent creativity entailed utilising a network of Sub-Processes of Creativity, using strategies for Managing Constraints and Challenges, and drawing on different Approaches to Creativity – adaptation, transfer, synthesis, and genesis – to apply the sub-processes and produce creative outcomes. Potentially, there were Effects of Creativity on Creators and Audiences, depending on the adolescent and the task. Three Types of Creativity were identified as the manifestations of the creative process: creative personal expression, creative boundary pushing, and creative task achievement. Interactions among adolescents’ dispositions and environments were influential in their creativity. Patterns and variations of these interactions revealed a framework of four Contexts for Creativity that offered different levels of support for creativity: high creative disposition–supportive environment; high creative disposition–inhibiting environment; low creative disposition–supportive environment; and low creative disposition–inhibiting environment. These contexts represent dimensional ranges of how dispositions and environments supported or inhibited creativity, and reveal that the optimal context for creativity differed depending on the adolescent, task, domain, and environment. This study makes four main contributions, which have methodological and theoretical implications for researchers, as well as practical implications for adolescents, parents, teachers, policy and curriculum developers, and other interested stakeholders who aim to foster the creativity of adolescents. First, this study contributes methodologically through its constructivist-interpretivist grounded theory methodology combining the grounded theory approaches of Corbin and Strauss (2008) and Charmaz (2006). Innovative data collection was also demonstrated through integration of data from online and face-to-face interactions with adolescents, within the grounded theory design. These methodological contributions have broad applicability to researchers examining complex constructs and processes, and with populations who integrate multimedia as a natural form of communication. Second, applicable to creativity in diverse domains, the Grounded Theory of Adolescent Creativity supports a hybrid view of creativity as both domain-general and domain-specific. A third major contribution was identification of a new form of creativity, educational creativity (ed-c), which categorises creativity for learning or achievement within the constraints of formal educational contexts. These theoretical contributions inform further research about creativity in different domains or multidisciplinary areas, and with populations engaged in formal education. However, the key contribution of this research is that it presents an original Theory and Model of Adolescent Creativity to explain the complex, multifaceted phenomenon of adolescents’ creative experiences.

Velocity and acceleration analysis of complex mechanisms by graphical iteration

A simple graphical method is presented for velocity and acceleration analysis of complex mechanisms possessing low or high degree of complexity. The method is iterative in character and generally yields the solution within a few iterations. Several examples have been worked out to illustrate the method.

Bifurcation theory of nonlinear boundary value problems

The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.

The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.

The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Perturbation theory for spectral subspaces

In der vorliegenden Arbeit wird die Variation abgeschlossener Unterräume eines Hilbertraumes untersucht, die mit isolierten Komponenten der Spektren von selbstadjungierten Operatoren unter beschränkten additiven Störungen assoziiert sind. Von besonderem Interesse ist hierbei die am wenigsten restriktive Bedingung an die Norm der Störung, die sicherstellt, dass die Differenz der zugehörigen orthogonalen Projektionen eine strikte Normkontraktion darstellt. Es wird ein Überblick über die bisher erzielten Resultate gegeben. Basierend auf einem Iterationsansatz wird eine allgemeine Schranke an die Variation der Unterräume für Störungen erzielt, die glatt von einem reellen Parameter abhängen. Durch Einführung eines Kopplungsparameters wird das Ergebnis auf den Fall additiver Störungen angewendet. Auf diese Weise werden zuvor bekannte Ergebnisse verbessert. Im Falle von additiven Störungen werden die Schranken an die Variation der Unterräume durch ein Optimierungsverfahren für die Stützstellen im Iterationsansatz weiter verschärft. Die zugehörigen Ergebnisse sind die besten, die bis zum jetzigen Zeitpunkt erzielt wurden.

Leadership in American Evangelical churches:an explanatory theory

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT This study is about leadership in American Evangelical Churches, which as a sub-set of American Christianity, are growing, while American Christianity as a whole is in decline. As a result evangelicalism is quickly becoming the dominate iteration of American Christianity. It is anecdotal that well led churches grow while poorly led churches do not, yet no one has identified what leadership, in the evangelical church context, is. Researchers have investigated a number of aspects of church leadership (much of it without identifying whether or not the churches under investigation were evangelical or not) but no one has put forth a unified theory linking these aspects together. The purpose of this research is to address that gap and develop a theory that explains how evangelicals view leadership in their local churches. In this study of three churches, dissimilar in size and governance, a purely qualitative approach to data collection and analysis was employed. The study involved 60 interviews that sought points-of-view from top and mid-level leadership along with congregant followers. The study borrowed heavily from Glaser and Strauss (1967) Grounded Theory approach to data analysis. The results developed a theory which provides a unified explanation of how leadership actually works in the three evangelical churches. Several implications for practice are discussed as to the theory's usefulness as a method of leadership education and evaluation. An original discovery was found that an individual's incumbency within the organization was identified as a social power. Limitations to this research are the limitations generally imputed to purely qualitative research in that questions are raised about the theory's applicability to evangelical churches beyond the three studied. The suggestions for further research involve addressing those limitations

Matching theory based travel plan aware charging algorithms in V2G smart grid networks

The frequency, time and places of charging have large impact on the Quality of Experience (QoE) of EV drivers. It is critical to design effective EV charging scheduling system to improve the QoE of EV drivers. In order to improve EV charging QoE and utilization of CSs, we develop an innovative travel plan aware charging scheduling scheme for moving EVs to be charged at Charging Stations (CS). In the design of the proposed charging scheduling scheme for moving EVs, the travel routes of EVs and the utility of CSs are taken into consideration. The assignment of EVs to CSs is modeled as a two-sided many-to-one matching game with the objective of maximizing the system utility which reflects the satisfactory degrees of EVs and the profits of CSs. A Stable Matching Algorithm (SMA) is proposed to seek stable matching between charging EVs and CSs. Furthermore, an improved Learning based On-LiNe scheduling Algorithm (LONA) is proposed to be executed by each CS in a distributed manner. The performance gain of the average system utility by the SMA is up to 38.2% comparing to the Random Charging Scheduling (RCS) algorithm, and 4.67% comparing to Only utility of Electric Vehicle Concerned (OEVC) scheme. The effectiveness of the proposed SMA and LONA is also demonstrated by simulations in terms of the satisfactory ratio of charging EVs and the the convergence speed of iteration.

Feminist Disability Theory: Domestic Violence Against Women with a Disability

Women with a disability continue to experience social oppression and domestic violence as a consequence of gender and disability dimensions. Current explanations of domestic violence and disability inadequately explain several features that lead women who have a disability to experience violent situations. This article incorporates both disability and material feminist theory as an alternative explanation to the dominant approaches (psychological and sociological traditions) of conceptualising domestic violence. This paper is informed by a study which was concerned with examining the nature and perceptions of violence against women with a physical impairment. The emerging analytical framework integrating material feminist interpretations and disability theory provided a basis for exploring gender and disability dimensions. Insight was also provided by the women who identified as having a disability in the study and who explained domestic violence in terms of a gendered and disabling experience. The article argues that material feminist interpretations and disability theory, with their emphasis on gender relations, disablism and poverty, should be used as an alternative tool for exploring the nature and consequences of violence against women with a disability.