By Vladimir I. Arnold (auth.), Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev, Oleg Ya. Viro (eds.)
Vladimir Arnold was once one of many nice mathematical scientists of our time. he's well-known for either the breadth and the intensity of his paintings. while he's some of the most prolific and extraordinary mathematical authors. This moment quantity of his gathered Works makes a speciality of hydrodynamics, bifurcation idea, and algebraic geometry.
By Luis J. Alías, Paolo Mastrolia, Marco Rigoli
This monograph provides an creation to a few geometric and analytic elements of the utmost precept. In doing so, it analyses with nice aspect the mathematical instruments and geometric foundations had to advance many of the new types which are offered within the first chapters of the ebook. particularly, a generalization of the Omori-Yau greatest precept to a large type of differential operators is given, in addition to a corresponding vulnerable greatest precept and its similar open shape and parabolicity as a different more suitable formula of the latter.
In the second one half, the eye makes a speciality of quite a lot of functions, in general to geometric difficulties, but in addition on a few analytic (especially PDEs) questions together with: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian goals, Ricci solitons, Liouville theorems, specialty of options of Lichnerowicz-type PDEs and so on.
Maximum ideas and Geometric Applications is written in a simple variety making it available to newbies. The reader is guided with a close presentation of a few themes of Riemannian geometry which are frequently no longer coated in textbooks. moreover, some of the effects or even proofs of identified effects are new and bring about the frontiers of a latest and energetic box of research.
By V.V. Volchkov
Integral geometry bargains with the matter of choosing services via their integrals over given households of units. those integrals de?ne the corresponding integraltransformandoneofthemainquestionsinintegralgeometryaskswhen this rework is injective. nevertheless, after we paintings with complicated measures or kinds, operators seem whose kernels are non-trivial yet which describe very important periods of features. lots of the questions bobbing up right here relate, in a single approach or one other, to the convolution equations. a number of the popular courses during this ?eld comprise the works by way of J. Radon, F. John, J. Delsarte, L. Zalcman, C. A. Berenstein, M. L. Agranovsky and up to date monographs by way of L. H¨ ormander and S. Helgason. till lately learn during this sector used to be performed commonly utilizing the means of the Fourier remodel and corresponding equipment of advanced research. lately the current writer has labored out an primarily di?erent technique in accordance with the outline of assorted functionality areas when it comes to - pansions in distinctive capabilities, which has enabled him to set up absolute best ends up in numerous renowned problems.
By P. Deligne (auth.), Roger Howe (eds.)
By Jesús Angulo (auth.), Frank Nielsen, Rajendra Bhatia (eds.)
This booklet provides advances in matrix and tensor information processing within the area of sign, picture and data processing. The theoretical mathematical methods are discusses within the context of capability functions in sensor and cognitive platforms engineering.
The themes and alertness contain info Geometry, Differential Geometry of dependent Matrix, confident convinced Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and functions in Cognitive structures, specifically info Mining.
By Robert C. Penner
There's an basically “tinker-toy” version of a trivial package deal over the classical Teichmüller house of a punctured floor, referred to as the embellished Teichmüller area, the place the fiber over some degree is the distance of all tuples of horocycles, one approximately every one puncture. This version ends up in an extension of the classical mapping category teams referred to as the Ptolemy groupoids and to convinced matrix versions fixing similar enumerative difficulties, every one of which has proved beneficial either in arithmetic and in theoretical physics. those areas take pleasure in a number of comparable parametrizations resulting in a wealthy and complicated algebro-geometric constitution tied to the already tricky combinatorial constitution of the tinker-toy version. certainly, the normal coordinates supply the prototypical examples not just of cluster algebras but in addition of tropicalization. This interaction of combinatorics and coordinates admits extra manifestations, for instance, in a Lie conception for homeomorphisms of the circle, within the geometry underlying the Gauss product, in profinite and pronilpotent geometry, within the combinatorics underlying conformal and topological quantum box theories, and within the geometry and combinatorics of macromolecules.
This quantity provides the tale and wider context of those adorned Teichmüller areas as constructed by way of the writer over the past twenty years in a chain of papers, a few of them in collaboration. occasionally correcting error or typos, occasionally simplifying proofs and occasionally articulating extra common formulations than the unique study papers, this quantity is self-contained and calls for little formal historical past. in response to a master’s direction at Aarhus collage, it provides the 1st therapy of those works in monographic shape.
By Lennart Berggren
Pi is among the few options in arithmetic whose point out conjures up a reaction of popularity and curiosity in these no longer involved professionally with the topic. but, regardless of this, no resource booklet on Pi has ever been released. Mathematicians and historians of arithmetic will locate this ebook vital. academics from the 7th grade onward will locate plentiful assets for whatever from distinctive subject classes to person talks and detailed scholar initiatives.
By Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman
Type thought has turn into the common language of recent arithmetic. This booklet is a set of articles employing equipment of classification thought to the components of algebra, geometry, and mathematical physics. between others, this ebook includes articles on better different types and their functions and on homotopy theoretic equipment. The reader can know about the fascinating new interactions of type concept with very conventional mathematical disciplines
By K. Leichtweiß (auth.), Dirk Ferus, Wolfgang Kühnel, Udo Simon, Bernd Wegner (eds.)
By Steven Rosenberg
This article on research on Riemannian manifolds is an intensive creation to subject matters coated in complex study monographs on Atiyah-Singer index idea. the most topic is the research of warmth move linked to the Laplacians on differential kinds. this gives a unified remedy of Hodge concept and the supersymmetric facts of the Chern-Gauss-Bonnet theorem. specifically, there's a cautious therapy of the warmth kernel for the Laplacian on services. the writer develops the Atiyah-Singer index theorem and its functions (without whole proofs) through the warmth equation strategy. Rosenberg additionally treats zeta services for Laplacians and analytic torsion, and lays out the lately exposed relation among index idea and analytic torsion. The textual content is aimed toward scholars who've had a primary direction in differentiable manifolds, and the writer develops the Riemannian geometry used from the start. There are over a hundred workouts with tricks.