Category: Geometry

By Victor A. Galaktionov

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations indicates how 4 forms of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities via their targeted quasilinear degenerate representations. The authors current a unified method of care for those quasilinear PDEs.

The e-book first reviews the actual self-similar singularity recommendations (patterns) of the equations. This process permits 4 diversified periods of nonlinear PDEs to be handled at the same time to set up their outstanding universal positive aspects. The e-book describes many homes of the equations and examines conventional questions of existence/nonexistence, uniqueness/nonuniqueness, worldwide asymptotics, regularizations, shock-wave concept, and diverse blow-up singularities.

Preparing readers for extra complex mathematical PDE research, the ebook demonstrates that quasilinear degenerate higher-order PDEs, even unique and awkward ones, should not as daunting as they first look. It additionally illustrates the deep positive aspects shared via various kinds of nonlinear PDEs and encourages readers to strengthen extra this unifying PDE strategy from different viewpoints.

By Tsoy-Wo Ma

This publication presents an trouble-free advent to the classical research of normed areas, paying detailed consciousness to non-linear issues akin to fastened issues, calculus and traditional differential equations. it truly is aimed toward rookies who are looking to get in the course of the uncomplicated fabric once attainable after which movement directly to do their very own examine instantly. It assumes basically normal wisdom in finite-dimensional linear algebra, easy calculus and trouble-free advanced research. because the therapy is self-contained with enough information, even an undergraduate with mathematical adulthood shouldn't have any challenge operating via it by myself. quite a few chapters should be built-in into elements of a grasp measure programme by means of direction paintings equipped by way of any local college. limited to finite-dimensional areas instead of normed areas, chosen chapters can be utilized for a direction in complex calculus. Engineers and physicists could locate this ebook a convenient reference in classical research

By Vagn Lundsgaard Hansen

1. Geometric varieties in Nature. 1. Spirals and the fantastic Snail. 2. The Helix and the Twining Vine. three. The Geometry of cleaning soap motion pictures. four. The Geometry of Tiled Surfaces. five. The common Polyhedra

2. The Topology of Surfaces. 1. a few regular Surfaces. 2. The Projective aircraft and the Klein Bottle. three. what's a Closed floor? four. Orientable and Non-Orientable Surfaces. five. hooked up Sum of Closed Surfaces. 6. category of Closed Surfaces. 7. Higher-Dimensional Manifolds and Poincare's Conjecture

three. The Topology of Catastrophes. 1. The beginning of disaster idea. 2. Singularities: Mappings of the airplane into the airplane. three. The Fold disaster. four. The Cusp disaster. five. Thom's Theorem for platforms with keep an eye on Variables and One nation Variable. 6. a few functions of the Cusp disaster. 7. the maths in the back of the versions of disaster thought. eight. The Seven basic Catastrophes in Space-Time. nine. a few basic comments relating Applications.

four. Geometry and the actual global. 1. On arithmetic and Its Greek Legacy. 2. Greek Astronomy and the Ptolemaic procedure. three. The Copernican international, Tycho Brahe and Kepler. four. The step forward of contemporary traditional technological know-how. five. Newton and Gravitation

five. Geometry and glossy Physics. 1. Maxwell and the Electromagnetic conception. 2. Einstein's thought of Relativity. three. Minkowski Space-Time and the specified conception of Relativity. four. Curvature and Gravitation: the final idea of Relativity. five. The Physics of simple debris. 6. Fiber Bundles and Parallel Displacement in Fiber Bundles. 7. Gauge Theories and String Theories.

By C. Davis, B. Grünbaum, F.A. Sherk

Geometry has been outlined as that a part of arithmetic which makes entice the feel of sight; yet this definition is thrown doubtful by means of the life of significant geometers who have been blind or approximately so, equivalent to Leonhard Euler. occasionally it sounds as if geometric tools in research, so-called, consist in having recourse to notions outdoors these it sounds as if proper, in order that geometry needs to be the becoming a member of of in contrast to strands; yet then what let's imagine of the significance of axiomatic programmes in geometry, the place connection with notions outdoor a limited reper­ tory is banned? no matter what its definition, geometry in actual fact has been greater than the sum of its effects, greater than the implications of a few few axiom units. it's been a huge present in arithmetic, with a particular procedure and a distinc­ ti v e spirit. A present, additionally, which has no longer been consistent. within the Thirties, after a interval of pervasive prominence, it seemed to be in decline, even passe. those related years have been these within which H. S. M. Coxeter used to be starting his clinical paintings. Undeterred via the unfashionability of geometry, Coxeter pursued it with devotion and notion. via the Fifties he looked as if it would the wider mathematical global as a consummate practitioner of a weird, out-of-the-way artwork. at the present time there isn't any longer whatever that out-of-the-way approximately it. Coxeter has contributed to, exemplified, lets nearly say presided over an unanticipated and dra­ matic revival of geometry.

By Schreier O., Sperner E.

By Stephen Smale, Felipe Cucker, Roderick S. C. Wong

Stephen smale is without doubt one of the nice mathematicians of the twentieth century. His paintings includes a wide array of matters: differential topology, dynamical platforms, calculus of diversifications, idea of computation, mechanics and mathematical economic system. In these kinds of matters he has left the imprint of choice of basic effects. He has receive numerous differences, together with the Fields Medal, he Veblen Prize, the Chauvenet Prize, the von Neumann Award and the nationwide Medal of Science.

This worthwhile publication includes the accrued papers of Stephen Smale. those are divided into 8 teams: topology; calculus of diversifications; dynamics; mechanics; economics; biology, electrical circuits and mathematical programming; thought of computation; miscellaneous. furthermore, every one staff comprises one or articles through global leaders on its topic which touch upon the impact of Smale's paintings, and one other article by way of Smale together with his one retrospective perspectives.

By Benno Artmann

This e-book is for all fanatics ofmathematics. it really is an try to less than­ stand the character of arithmetic from the perspective of its most vital early resource. whether the cloth coated by way of Euclid will be thought of ele­ mentary for the main half, the best way he offers it has set the normal for greater than thousand years. understanding Euclid's parts should be ofthe related significance for a mathematician this day as figuring out Greek structure is for an architect. sincerely, no con­ transitority architect will build a Doric temple, not to mention set up a building website within the method the ancients did. yet for the educational ofan architect's aesthetic judgment, a data ofthe Greek her­ itage is necessary. I trust Peter Hilton while he says that real arithmetic constitutesone ofthe best expressions ofthe human spirit, and that i may well upload that right here as in such a lot of different situations, now we have realized that language ofexpression from the Greeks. whereas offering geometry and mathematics Euclid teaches us es­ sential positive aspects of arithmetic in a way more basic feel. He monitors the axiomatic beginning of a mathematical conception and its awake improvement in the direction of the answer of a particular challenge. We see how abstraction works and enforces the strictly deductive presentation ofa idea. We study what inventive definitions are and v VI ----=P:. . :re:. ::::fa=ce how a conceptual clutch results in toe category ofthe proper ob­ jects.

By Krupka D., et al. (eds.)

This booklet is a suite of survey articles in a extensive box of the geometrical concept of the calculus of adaptations and its functions in research, geometry and physics. it's a commemorative quantity to rejoice the sixty-fifth birthday of Professor Krupa, one of many founders of recent geometric variational concept, and a huge contributor to this subject and its purposes during the last thirty-five years. the entire authors invited to give a contribution to this quantity have confirmed excessive reputations of their box. The booklet will completely offer a number of very important effects, ideas and functions which are frequently on hand in simple terms via consulting unique papers in lots of various journals. will probably be of curiosity to researchers in variational calculus, mathematical physics and the opposite comparable components of differential equations, usual operators and geometric constructions. additionally, it's going to develop into an enormous resource of present examine for doctoral scholars and postdoctorals in those fields.

By A. Pfister

By Nicholas D. Kazarinoff

Anyone who loved his first geometry direction will benefit from the easily said geometric difficulties approximately greatest and minimal lenghs and components during this e-book. lots of those already involved the greeks, for instance the matter of of enclosing the most important attainable zone by means of a fence of given size, and a few have been solved in the past; yet others stay unsolved even this day. a number of the suggestions of the issues posed during this ebook, for instance the matter of inscribing a triangle of smallest perimeter right into a given triangle, have been provided by way of international recognized mathemaicians, others by way of highschool scholars.