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A stylish and inspiring guide to living a happier life in balance with the natural world Minimal offers readers inspiration and tools to embrace simple living and create meaningful, lasting change in their lives. From advice on home decorating and decluttering, and easy-to-follow recipes for making your own cosmetics and cleaning products, to tips for shopping sustainably, composting, and restoring old furniture, Minimal provides a host of small but powerful ways to live a more balanced life while being good to the planet.
Complete and Compact Minimal Surfaces by Kichoon Yang Pdf
'Et moi, ... , si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem by A. T. Fomenko Pdf
Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applied problems in chemistry, physics, and also in nature. In applications, one finds not only two-dimensional but also multidimensional minimal surfaces that span fixed closed ``contours'' in some multidimensional Riemannian space. An exact mathematical statement of the problem of finding a surface of least area or volume requires the formulation of definitions of such fundamental concepts as a surface, its boundary, minimality of a surface, and so on. It turns out that there are several natural definitions of these concepts, which permit the study of minimal surfaces by different, and complementary, methods. In the framework of this comparatively small book it would be almost impossible to cover all aspects of the modern problem of Plateau, to which a vast literature has been devoted. However, this book makes a unique contribution to this literature, for the authors' guiding principle was to present the material with a maximum of clarity and a minimum of formalization. Chapter 1 contains historical background on Plateau's problem, referring to the period preceding the 1930s, and a description of its connections with the natural sciences. This part is intended for a very wide circle of readers and is accessible, for example, to first-year graduate students. The next part of the book, comprising Chapters 2-5, gives a fairly complete survey of various modern trends in Plateau's problem. This section is accessible to second- and third-year students specializing in physics and mathematics. The remaining chapters present a detailed exposition of one of these trends (the homotopic version of Plateau's problem in terms of stratified multivarifolds) and the Plateau problem in homogeneous symplectic spaces. This last part is intended for specialists interested in the modern theory of minimal surfaces and can be used for special courses; a command of the concepts of functional analysis is assumed.
The Global Theory of Minimal Surfaces in Flat Spaces by William Meeks,A. Ros,H. Rosenberg Pdf
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
In Minimal Rationality, Christopher Cherniak boldly challenges the myth of Man the the Rational Animal and the central role that the "perfectly rational agent" has had in philosophy, psychology, and other cognitive sciences, as well as in economics. His book presents a more realistic theory based on the limits to rationality which can play a similar generative role in the human sciences, and it seeks to determine the minimal rationality an actual agent must possess.
Minimal NetworksThe Steiner Problem and Its Generalizations by Alexander O. Ivanov,Alexei A. Tuzhilin Pdf
This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.
Minimal Surfaces II by Ulrich Dierkes,Stefan Hildebrandt,Albrecht Küster,Ortwin Wohlrab Pdf
Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
A Survey on Classical Minimal Surface Theory by William Meeks,Joaquín Pérez Pdf
Meeks and Perez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject. This book includes an updated tour through some of the recent advances in the theory, such as Colding-Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi-Yau problem, local pictures on the scale of curvature and topology, the local removable singularity theorem, embedded minimal surfaces of finite genus, topological classification of minimal surfaces, uniqueness of Scherk singly periodic minimal surfaces, and outstanding problems and conjectures.
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees by Rodney G. Downey,Keng Meng Ng,Reed Solomon Pdf
First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
A Course in Minimal Surfaces by Tobias Holck Colding,William P. Minicozzi II Pdf
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
The Minimal Cell by Pier Luigi Luisi,Pasquale Stano Pdf
In the last ten years there has been a considerable increase of interest on the notion of the minimal cell. With this term we usually mean a cell-like structure containing the minimal and sufficient number of components to be defined as alive, or at least capable of displaying some of the fundamental functions of a living cell. In fact, when we look at extant living cells we realize that thousands of molecules are organized spatially and functionally in order to realize what we call cellular life. This fact elicits the question whether such huge complexity is a necessary condition for life, or a simpler molecular system can also be defined as alive. Obviously, the concept of minimal cell encompasses entire families of cells, from totally synthetic cells, to semi-synthetic ones, to primitive cell models, to simple biomimetic cellular systems. Typically, in the experimental approach to the construction of minimal the main ingredient is the compartment. Lipid vesicles (liposomes) are used to host simple and complex molecular transformations, from single or multiple enzymic reactions, to polymerase chain reactions, to gene expression. Today this research is seen as part of the broader scenario of synthetic biology but it is rooted in origins of life studies, because the construction of a minimal cell might provide biophysical insights into the origins of primitive cells, and the emergence of life on earth. The volume provides an overview of physical, biochemical and functional studies on minimal cells, with emphasis to experimental approaches. 15 International experts report on their innovative contributions to the construction of minimal cells.
A 52 illustration two-part book on the exploration of minimal surfaces. Part 1 explores the surface from an artistic perspective, and part 2 visually reproduces the equations that stand in their own right as a beautiful expression of pure geometry. Each book includes notes from an informal work-in-progress diary and references directing the reader to the images’ original mathematical source. Both sides complement each other in helping us appreciate better these unrivaled expressions of our environment found in nature, from butterflies to black holes, and studied in statistics, material sciences, and architecture.
Minimal Neoplasia by Ekkehard Grundmann,Lutwin Beck Pdf
Minimal neoplasia may be defined as a small cancer that has progressed beyond its site of primary origin into the surrounding tissue, but that has not yet reached the stage of deeper invasion or metastasization. The basic principles of this minimal cancer are presented in chapters on molecular, biological and experimental aspects, and, in particular, on the clinical manifestations in various organs: preleukemia, incipient lymphoma, and minimal carcinomas of the uterine cervix, breast, thyroid, larynx, lung, prostate, stomach and colon. A separate chapter is devoted to cryptic gliomas. The latest morphological methods including cytology, early clinical diagnostics and, in particular, radiodiagnostics, are considered. The reader can expect up-to-date information about prompt diagnosis of the very early manifestations of cancer, together with inferences on therapy, which, especially in tumors of the uterine cervix, breast and thyroid, differs considerably from the treatment of advanced neoplasia.
The Mechanisms Underlying the Human Minimal Self by Verena V. Hafner,Bernhard Hommel,Ezgi Kayhan,Dongheui Lee,Markus Paulus,Stephan Alexander Verschoor Pdf