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Motion picture music --- History and criticism

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The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.

Statistical science --- Algebraic geometry --- Differential geometry. Global analysis --- Operator theory --- Functional analysis --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- grafieken --- analyse (wiskunde) --- topologie (wiskunde) --- waarschijnlijkheidstheorie --- functies (wiskunde) --- statistiek --- wiskunde --- geometrie

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Statistical science --- Algebraic geometry --- Differential geometry. Global analysis --- Operator theory --- Functional analysis --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- grafieken --- analyse (wiskunde) --- topologie (wiskunde) --- waarschijnlijkheidstheorie --- functies (wiskunde) --- statistiek --- wiskunde --- geometrie

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The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

Geometric analysis --- Graph theory --- Manifolds (Mathematics)

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I4.0 has become a leading topic within manufacturing and digital policy in Germany. Through published policy, the German federal government seeks to control the direction of the digital transformation of the manufacturing sector of the economy. Challenges and successes within the adoption and transformation process have been realized and either support or limit the speed at which the transformation occurs. Through investigating the heart of the German economy, which are machine tool SMEs, this dissertation attempt to provide an isolated evaluation of the challenges and successes within the IT and application landscape, which are landscapes faced within supporting I4.0 transformation. As these landscapes are responsible for supporting the entirety of I4.0, it is crucial that a sound application system is implemented. Conduction of a policy analysis was performed to determine what are the current objectives of the federal government regarding I4.0 and what is required of the IT and application landscape to support these objectives. Additionally, a literature review was performed to identify already determined successes and challenges, which will indicate whether they have been replicated or overcome since publication. The SIMMI4.0 maturity model is utilized to evaluate and determine the level of adoption which case studies have achieved and in which dimensions successes and challenges can be identified. The to-be maturity level was exchanged for the current level of desired government attainment and the average level of SME adoption, which were concluded from expert interviews, to allow for the ability to conduct a gap analysis between the desired state and the current as-is state of the case studies. The results were obtained from semi-structured interviews with experts in the field of I4.0, the machine and tool industry, and the IT and application landscape. The results of the gap analysis would serve to support the findings that there are significant limitations within the IT and application landscape of German SMEs, which hamper the ability for successful digital transformation and I4.0 standards. The findings were then compiled into policy recommendations for the federal government, designed to support recommend changes within policy to support the innovation of the IT and application landscapes of SMEs with the aims to support the attainment of federal policy objectives.