The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces PDF Download
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Author: Karl-Theodor Sturm
Publisher: American Mathematical Society
ISBN: 1470466961
Category : Mathematics
Languages : en
Pages : 124
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Book Description
View the abstract.
Author: Karl-Theodor Sturm
Publisher: American Mathematical Society
ISBN: 1470466961
Category : Mathematics
Languages : en
Pages : 124
Get Book Here
Book Description
View the abstract.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333
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Book Description
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Author: Larry Ford
Publisher: JHU Press
ISBN: 9780801863318
Category : Architecture
Languages : en
Pages : 248
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Book Description
Three photographic essays offer a study of the neglected "nooks and crannies" between structures, from gates and fences to sidewalks, alleys, and parking lots. In his exploration of how spaces become places, geographer Ford invites readers to see anew the spaces they encounter every day and often take for granted. 52 halftones.
Author: Peter Gardenfors
Publisher: MIT Press
ISBN: 9780262572194
Category : Psychology
Languages : en
Pages : 324
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Book Description
Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3764373091
Category : Mathematics
Languages : en
Pages : 330
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Book Description
This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.
Author: Martin R. Bridson
Publisher: Springer Science & Business Media
ISBN: 3662124947
Category : Mathematics
Languages : en
Pages : 665
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Book Description
A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.
Author: James J Yeh
Publisher: World Scientific
ISBN: 9813200421
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.
Author: Debbie Diller
Publisher: Taylor & Francis
ISBN: 1003843409
Category : Education
Languages : en
Pages : 429
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Book Description
From Debbie Diller, author of numerous best-selling books and videos on literacy work stations and small group reading instruction, comes another practical resource filled with ideas you can use immediately to better manage your classroom and support student learning and independence. In Spaces & Places: Designing Classrooms for Literacy' you' ll find a wealth of full-color photos from all sorts of classroom spaces in PreK-5th grade, including well-organized areas for whole group and small group reading instruction, classroom libraries, literacy work stations, teacher desks, and storage areas. You' ll love the before and after pictures and the step-by-step processes outlined for organizing your furniture and cabinets, setting up your room space by space, and using your walls thoughtfully. Diller' has even documented how to pack your room at the end of the year to save time next fall (so you can focus on thinking about instruction) and what to do if you must move all your belongings. Through pictures and text, this unique visual reference answers tough questions educators ask, such as: What do I really need in my room and what' s the best way to set it up? How does my physical classroom impact student learning? How can I find the space I need to teach more effectively? What can I get rid of and how? Where do I put all my stuff?Charts, reproducible forms, motivating quotes, a list of shopping sources, and reflection questions are included, along with a section outlining ten specific suggestions for on-going staff development. Whether or not you implement literacy work stations in your classroom, Spaces & Placesincludes everything you need to look deeply at classroom space and how it supports instruction.
Author: Juha Heinonen
Publisher: Springer Science & Business Media
ISBN: 1461301319
Category : Mathematics
Languages : en
Pages : 149
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Book Description
The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.
Author: Rebecca Tanqueray
Publisher:
ISBN: 9781845978211
Category : Architecture
Languages : en
Pages : 0
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Book Description
Living space is a precious commodity. Few of us have as much space as we'd like, whether we live in a studio or have a key room that's just too small. Rebecca Tangueray starts with Making the Most of Your Space. She presents compact homes that show how clever use of color, lighting, or other elements makes for a spacious feel. In "The Zones", Rebecca explores the organization of space, including the areas for living, cooking, working, bathing, and sleeping, and how to make your home multi-functional. Solutions tackles elements crucial to the compact home--including dividing space, using color, lighting and texture, and clever storage and furniture.*Make every inch of your home, from tiny kitchen to compact bedroom, work for you.*Inspirational ideas for everyone, whether your style is pared-down modern, eclectic bohemian or classic with a twist.*Includes helpful details such as where to hide the kitchen utensils or trailing electrical leads.
