Surfaces

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

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.

Poetry. Art. Pushing writing to its limits, SURFACES is Eric Schmaltz's compelling debut collection that's situated at the intersection of language, bodies, and digital culture. Opening toward the embodied and the intersubjective, SURFACES is at turns playful and unsettling as it explores the processes, interactions, and erasures that occur on and below the surface of writing with machinery. Composed with a minimalist aesthetic and conceptual elements, the book combines found elements, graphic design, imprint, translation, and experimental typography to engage questions about writing and feeling in the 21st century: Where does the body go when we write to one another thru digital channels? How and what do we feel when information is realized through taps, clicks, and pressures? What happens to meaning within a digital economy when information is considered to be bodiless? Concerned with these questions, Surfaces begins to probe for their depths. "With SURFACES, Eric Schmaltz directs our gaze to points of contact and friction, whether crafting mandalas and coptic weavings from letters' negative space, drafting a dance between letterforms as they engage in 'touch at the limits of a long passage, ' or printing reliefs from a keyboard's disassembled parts. In doing so, he draws attention to our expectation that language resolve into meaning--that letters present themselves in a contract of legibility entitling us not only to their forms, but also to some deeper content. In materializing language's embodied 'surfaces, ' Schmaltz returns words' secrecy, reminding us that those inner meanings we seek are ultimately not inherent in them but in our own projected desires and intentions--a dangerous dynamic. The beauty of these forms arises in part from their refusal to come into focus. A surface, here, becomes not only a point of contact but of resistance."--Amaranth Borsuk "SURFACES is, as the book itself confesses, a catalogue of stimulations. It welcomes the saccade of the eyes, the gambits of a distracted neck, the swim of attention in the purr and drone of the ambient. In SURFACES, Schmaltz collects works of various humours--at turns witty, stern, deeply unsettling, and playful. I appreciate what he offers as an intervention into the documents that surround the history of writing with machines, writing as machines. In taking on the pleasures of écriture, the making of the mark--embodied and digitized--the book evokes and then transcends the often gendered binary between the mechanical imprint and the embodied impression. [...] In SURFACES, there is great pleasure in navigating an alphabetic labyrinth in a time of totalizing records of space--one derives from the dérive emotive pleasures of stark abstraction and indulgent design, the tenor of a dark line or the opulent aria of a gray-scale curve."--Divya Victor "SURFACES reminds us that the page is a 3D object, each page the enactment of Duchamp's infrathin. The language skims and streaks across the thinnest of sheens, a glistening moment, an uncanny reminder of what language could be, if only we let it."--Derek Beaulieu

This book describes the fundamental aspects of materials characterization for the ferric oxyhydroxides formed on steel surfaces. Selected examples, from both the basic science and the applied engineering points of view, are presented. Of special interest is the new structural information on ferric oxyhydroxides containing a small amount of alloying elements. The text relates this to their various states and their role in corrosion processes.

This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.

This Special Issue deals with the synthesis of nanostructured surfaces and thin films by means of physical vapor deposition techniques such as pulsed laser deposition, magnetron sputtering, HiPIMS, or e-beam evaporation, among others. The nanostructuration of the surface modifies the way a material interacts with the environment, changing its optical, mechanical, electrical, tribological, or chemical properties. This can be applied in the development of photovoltaic cells, tribological coatings, optofluidic sensors, or biotechnology to name a few. This issue includes research presenting novel or improved applications of nanostructured thin films, such as photovoltaic solar cells, thin-film transistors, antibacterial coatings or chemical and biological sensors, while also studying the nanostructuration mechanisms, from a fundamental point of view, that produce rods, columns, helixes or hexagonal grids at the nanoscale.

Contains recent ideas and results in three areas of growing importance in curve and surface design: algebraic methods, variational surface design, and some special applications. Leading researchers from throughout the world have contributed their latest work and provided several promising solutions to open issues in surface modeling.