By Prof. Dr. techn. Martin P. Bendsøe, Prof. Dr. techn. Ole Sigmund (auth.)
The topology optimization process solves the elemental engineering challenge of allotting a restricted quantity of fabric in a layout house. the 1st version of this publication has turn into the traditional textual content on optimum layout that's fascinated with the optimization of structural topology, form and fabric. This version has been considerably revised and up-to-date to mirror growth made in modelling and computational strategies. It additionally incorporates a accomplished and unified description of the state of the art of the so-called fabric distribution process, in keeping with using mathematical programming and finite parts. functions handled comprise not just constructions but additionally MEMS and materials.
This ebook is meant as an ordinary advent to differential manifolds. The authors be aware of the intuitive geometric points and clarify not just the fundamental homes but additionally educate tips on how to do the elemental geometrical buildings. a vital part of the paintings are the numerous diagrams which illustrate the proofs. The textual content is liberally provided with routines and may be welcomed through scholars with a few easy wisdom of research and topology.
By Daniel A. Klain
Here's the 1st sleek creation to geometric chance, sometimes called essential geometry, awarded at an basic point, requiring little greater than first-year graduate arithmetic. Klein and Rota current the idea of intrinsic volumes as a result of Hadwiger, McMullen, Santaló and others, besides a whole and trouble-free facts of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They strengthen the idea of the Euler attribute from an integral-geometric perspective. The authors then turn out the basic theorem of crucial geometry, particularly, the kinematic formulation. eventually, the analogies among invariant measures on polyconvex units and measures on order beliefs of finite in part ordered units are investigated. the connection among convex geometry and enumerative combinatorics motivates a lot of the presentation. each bankruptcy concludes with an inventory of unsolved difficulties.
``Lusternik-Schnirelmann type is sort of a Picasso portray. taking a look at class from varied views produces different impressions of category's good looks and applicability.'' --from the creation Lusternik-Schnirelmann classification is a topic with ties to either algebraic topology and dynamical platforms. The authors take LS-category because the imperative subject matter, after which strengthen issues in topology and dynamics round it. incorporated are routines and plenty of examples. The e-book offers the cloth in a wealthy, expository kind. The e-book offers a unified method of LS-category, together with foundational fabric on homotopy theoretic points, the Lusternik-Schnirelmann theorem on serious issues, and extra complicated issues equivalent to Hopf invariants, the development of capabilities with few serious issues, connections with symplectic geometry, the complexity of algorithms, and classification of $3$-manifolds. this can be the 1st ebook to synthesize those issues. It takes readers from the very fundamentals of the topic to the state-of-the-art. necessities are few: semesters of algebraic topology and, probably, differential topology. it really is appropriate for graduate scholars and researchers attracted to algebraic topology and dynamical structures.
By Sergei P. Novikov (auth.), S. P. Novikov (eds.)
This e-book constitutes not anything below an updated survey of the total box of topology (with the exception of "general (set-theoretic) topology"), or, within the phrases of Novikov himself, of what was once termed on the finish of the nineteenth century "Analysis Situs", and accordingly varied into some of the subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The ebook offers an summary of those subfields, starting with the weather and continuing correct as much as the current frontiers of analysis. therefore one reveals right here the entire variety of topological innovations from fibre areas (Chap.2), CW-complexes, homology and homotopy, via bordism conception and K-theory to the Adams-Novikov spectral series (Chap.3), and in bankruptcy four an exhaustive (but inevitably centred) survey of the speculation of manifolds. An appendix sketching the new amazing advancements within the thought of knots and hyperlinks and low-dimensional topology typically, brings the survey correct as much as the current. This paintings represents the flagship, because it have been, in whose wake keep on with extra certain surveys of a number of the subfields, by means of a variety of authors.
By John W. Morgan
The contemporary creation of the Seiberg-Witten invariants of gentle four-manifolds has revolutionized the examine of these manifolds. The invariants are gauge-theoretic in nature and are shut cousins of the much-studied SU(2)-invariants outlined over fifteen years in the past through Donaldson. On a realistic point, the hot invariants have proved to be extra strong and feature ended in an enormous generalization of past effects. This ebook is an creation to the Seiberg-Witten invariants.
The paintings starts with a overview of the classical fabric on Spin c constructions and their linked Dirac operators. subsequent comes a dialogue of the Seiberg-Witten equations, that is set within the context of nonlinear elliptic operators on a suitable limitless dimensional house of configurations. it's validated that the gap of options to those equations, referred to as the Seiberg-Witten moduli house, is finite dimensional, and its measurement is then computed. unlike the SU(2)-case, the Seiberg-Witten moduli areas are proven to be compact. The Seiberg-Witten invariant is then primarily the homology type within the area of configurations represented by way of the Seiberg-Witten moduli house. The final bankruptcy provides a taste for the purposes of those new invariants through computing the invariants for many Kahler surfaces after which deriving a few uncomplicated toological results for those surfaces.