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.

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.

The Bernstein problem and the Plateau problem are central topics inthe theory of minimal submanifolds. This important book presents theDouglasOCoRado solution to the Plateau problem, but the main emphasisis on the Bernstein problem and its new developments in variousdirections: the value distribution of the Gauss image of a minimalsurface in Euclidean 3-space, Simons'' work for minimal graphichypersurfaces, and author''s own contributions to Bernstein typetheorems for higher codimension."

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.

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.

The articles in this volume are inspired by the Minimalist Program first outlined in Chomsky's MIT Fall term class lectures of 1991 and in his seminal paper "A Minimalist Program for Linguistic Theory." The articles seek to develop further some key idea in the Minimalist Program, sometimes in ways deviating from the course taken by Chomsky.The articles are preceded by a 40 page introduction into the minimalist framework. The introduction pays special attention to the question how the minimalist framework developed out of the Principles and Parameters (Government and Binding) framework. The introduction serves as a guide through the entire volume, presenting the issues to be discussed in the articles in detail, and offering a thematic overview over the volume as a whole.Most of the articles in this volume are concerned with issues raised in Chomsky's first two minimalist papers, namely "A Minimalist Program for Linguistic Theory" (1993, first distributed in 1992) and "Bare Phrase Structure" (1995a, first distributed 1994). In acknowledgment of this, each article starts out with a quote from Chomsky (1993, 1995a). This quote also serves to highlight the particular grammatical or theoretical issue that is primarily discussed in the relevant article.Several articles relate issues raised in Chomsky's first two minimalist papers to the basic ideas in Kayne's book, The Antisymmetry of Syntax (1994, distributed in part in manuscript form in 1993). In many respects, therefore, these articles develop alternatives to ideas proposed in chapter 4, "Categories and Transformations," of Chomsky's most recent book, The Minimalist Program (1995b). Some of the articles contain references to chapter 4, and some comments on similarities and differences between ideas developed in these papers and in chapter 4 of Chomsky 1995b can also be found in the Introduction to this volume.

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.