Category: Geometry

By Anton Alekseev (auth.), H. Gausterer, L. Pittner, Harald Grosse (eds.)

In glossy mathematical physics, classical including quantum, geometrical and useful analytic equipment are used concurrently. Non-commutative geometry specifically is turning into a great tool in quantum box theories. This ebook, aimed toward complex scholars and researchers, offers an advent to those rules. Researchers will profit fairly from the huge survey articles on types in terms of quantum gravity, string conception, and non-commutative geometry, in addition to Connes' method of the traditional model.

By James Eells

Harmonic maps among Riemannian manifolds are options of platforms of partial differential equations which seem in several contexts of differential geometry. They comprise holomorphic maps, minimum surfaces, delta-models in physics. lately, they've got develop into robust instruments within the examine of world houses of Riemannian and Kahlerian manifolds. general references for this topic are reviews, released in 1978 and 1988 through James Eells and Luc Lemaire. This e-book provides those experiences in one quantity with a quick complement reporting on a few contemporary advancements within the conception. it's either an advent to the topic and a resource of reference, supplying an geared up exposition of effects unfold all through greater than 800 papers.

By Dr. rer. nat. Gerd Fischer (auth.)

Buchhandelstext
Dieser Band enthält Anwendungen der linearen Algebra auf geometrische Fragen. Ausgehend von affingen Unterräumen in Vektorräumen werden allgemeine affine Räume eingeführt, und es wird gezeigt, wie sich geometrische Probleme mit algebraischen Hilfsmitteln behandeln lassen. Ein Kapitel über lineare Optimierung befaßt sich mit Systemen linearer Ungleichungen. Mit Hilfe der elementaren Theorie konvexer Mengen kann guy die Optimierung eines linearen Funktionals auf die Lösung linearer Gleichungssysteme zurückführen. Anschließend wird der für praktische Anwendungen so wichtige Simplex-Algorithmus abgeleitet. Besonderer Wert wird dabei auf einen Einblick in die geometrischen Zusammenhänge gelegt. Durch den projektiven Abschluß affiner Räume enthält guy den angemessenen Rahmen für das Studium von Sätzen aus der klassischen Geometrie. Durch viele Zeichnungen, Beispiele und Übungsaufgaben wird versucht, das Lesers Liebe zur Geometrie zu vertiefen. Affine Geometrie - Konvexe Mengen und lineare Optimierung - Projektive Geometrie

Inhalt
Inhalt: Affine Geometrie - Konvexe Mengen und lineare Optimierung - Projektive Geometrie.

By David A Kay

By Barletta E., Dragomir S., Duggal K.L.

By Claudio Bartocci, Luciano Boi, Corrado Sinigaglia

This quantity specializes in the interactions among arithmetic, physics, biology and neuroscience by means of exploring new geometrical and topological modelling in those fields. one of the highlights are the valuable roles performed by way of multilevel and scale-change techniques in those disciplines. the combination of arithmetic with physics, in addition to molecular and mobile biology and the neurosciences, will represent the hot frontier of twenty first century technology, the place breakthroughs usually tend to span throughout conventional disciplines.

By Henning F. Harmuth

The orthogonality of services has been exploited in communications in view that its very starting. wide awake and huge use was once made from it via Kotel'nikov in theoretical paintings in 1947. Ten years later a lot of humans have been operating during this box. besides the fact that, little experimental use may be made from the theoretical effects ahead of the arriving of strong country operational amplifiers and built-in circuits. the benefits of Walsh features, that are emphasised during this e-book, have been famous independently by way of numerous scientists within the early sixties. between them have been E. Gibbs, okay. Henderson, F.Ohnsorg, G. Sandy and E. Vandivere, whose paintings used to be now not released until eventually decades later. a little bit greater than part the illustrations during this moment variation weren't inside the first version and this displays the adjustments in contents. the main amazing distinction among the 2 variations is the growth towards sensible functions made within the intervening 3 years. besides the fact that, it can end up that an important switch is one who seems really theoretical at the floor and that issues shift-invariant gains strongly hooked up with sine-cosine services. those services are projections of the exponential functionality which, in flip, is the nature crew of the genuine numbers. The topology of the genuine numbers is usually approved to be similar to that of time or a one-dimensional area, and this can be the root for a number of claims that sinusoidal capabilities are designated and enhanced to all others.

By Lebl J.

By David E. Blair

This monograph offers with the Riemannian geometry of either symplectic and phone manifolds, with specific emphasis at the latter. The textual content is thoroughly awarded. themes spread systematically from bankruptcy 1, which examines the overall conception of symplectic manifolds. significant circle bundles (Chapter 2) are then mentioned as a prelude to the Boothby--Wang fibration of a compact usual touch manifold in bankruptcy three, which bargains with the overall conception of touch manifolds. bankruptcy four specializes in the final surroundings of Riemannian metrics linked to either symplectic and call constructions, and bankruptcy five is dedicated to critical submanifolds of the touch subbundle. subject matters handled within the next chapters contain Sasakian manifolds, the $64000 learn of the curvature of touch metric manifolds, submanifold concept in either the K¿hler and Sasakian settings, tangent sphere bundles, curvature functionals, advanced touch manifolds and three Sasakian manifolds. The publication serves either as a normal reference for mathematicians to the fundamental homes of symplectic and touch manifolds and as a very good source for graduate scholars and researchers within the Riemannian geometric area. The prerequisite for this article is a uncomplicated direction in Riemannian geometry.

By Nazrul Islam