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Applied nonlinear functional analysis : an introduction
The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.
Contents
Basic Topology
Measure Theory
Basic Functional Analysis
Banach Spaces of Functions and Measures
Convex Functions – Nonsmooth Analysis
Nonlinear Analysis
eBook
The spatiality of emotion in early modern China : from dreamscapes to theatricality
\"Emotion takes place. Rather than an interior state of mind in response to the outside world, emotion per se is spatial, at turns embedding us from without, transporting us somewhere else, or putting us ahead of ourselves. In this book, Ling Hon Lam gives a deeply original account of the history of emotions in Chinese literature and culture centered on the idea of emotion as space, which the Chinese call \"emotion-realm\" (qingjing). Lam traces how the emotion-realm underwent significant transformations from the dreamscape to theatricality in sixteenth- to eighteenth-century China. Whereas medieval dreamscapes delivered the subject into one illusory mood after another, early modern theatricality turned the dreamer into a spectator who is no longer falling through endless oneiric layers but pausing in front of the dream. Through the lens of this genealogy of emotion-realms, Lam remaps the Chinese histories of morals, theater, and knowledge production, which converge at the emergence of sympathy, redefined as the dissonance among the dimensions of the emotion-realm pertaining to theatricality.The book challenges the conventional reading of Chinese literature as premised on interior subjectivity, examines historical changes in the spatial logic of performance through media and theater archaeologies, and ultimately uncovers the different trajectories that brought China and the West to the convergence point of theatricality marked by self-deception and mutual misreading. A major rethinking of key terms in Chinese culture from a comparative perspective, The Spatiality of Emotion in Early Modern China develops a new critical vocabulary to conceptualize history and existence.\"-- Provided by publisher.
Book
On the differential structure of metric measure spaces and applications
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the
duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of
analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To
employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a
meaning to an expression like
eBook
Composition operators on Hardy-Orlicz spaces
The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function \\Psi grows rapidly: compactness, weak compactness, to be p-summing, order bounded, \\ldots, and show how these notions behave according to the growth of \\Psi. They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces.
eBook
Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems approach
This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on \\mathbf{R}^n to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.
eBook
Atlas of the Irish rural landscape
\"The second edition of Atlas of the Irish Rural Landscape is a magnificently illustrated, beautifully written, and thoroughly updated introduction to the hidden riches of the Irish landscape. Topics include archaeology, field and settlement patterns, houses, demesnes, villages and small towns, monuments, woodland, bogs, roads, canals, and a host of other features. The Atlas combines superbly chosen illustrations and cartography with a text amenable to a general reader. Hundreds of maps, diagrams, photographs, and paintings present accessible information suitable for any school, college, or home. New content in the contemporary section takes into account the Celtic Tiger and explores six fresh case studies - Tory Island (Donegal), the Wicklow Uplands, Inistiogue (County Kilkenny), Aughris (County Sligo), Clonfert (County Galway), and Point Lance in Newfoundland. This second edition of the award-winning Atlas of the Irish Rural Landscape continues to increase the visibility of the landscape within national heritage while establishing a proper basis for conservation and planning\"--Publisher description.
Book
Challenges encountered by teachers in improving essay writing skills in rural schools of O.R. Tambo Inland District Eastern Cape Province
The essay is a typical task provided in schools to evaluate learner’s writing abilities and newly acquired knowledge. Because of how text-oriented the world has become, writing has been regarded as one of the most important abilities. As a result, teachers are in tremendous need of efficient methods to boost writing abilities in their classrooms. Yet, most learners lack the ability to write an English essay, particularly in remote areas. The aim of the study is to investigate the underlying reasons for the difficulties teachers encounter while attempting to teach English writing skills in rural schools of OR Tambo Inland District, Eastern Cape Province. The Zone of Proximal Development is highlighted as the issue of collaboration in the education system in order to develop children’s creative writing. Therefore, the study adopted socio-cultural theory as the theoretical framework. The study also adopted a quantitative research method. The participants of the study included six language teachers that were purposefully selected as information-rich participants. The findings of the study revealed that (i) teachers were lacking inappropriate methods, (II) the time spent in teaching essay writing was grossly inadequate, and finally (III) teachers experienced many challenges in reading and writing skills, which included, difficulty in motivating their learners, learners of diverse levels, difficult materials and time constraints to teach the learners. Therefore, the study recommended the use of pre-taught vocabulary, various teacher influences and the implementation of positive literacy practices.
Journal Article