{"title":"Tibor Rado","description":null,"products":[{"product_id":"on-the-problem-of-plateau-book-tibor-rad-9783642983078","title":"On the Problem of Plateau","description":"The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter- points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52666304332049,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52666305249553,"sku":"NLS9783642983078","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642983078.jpg?v=1762279614"},{"product_id":"continuous-transformations-in-analysis-book-tibor-rado-9783642859915","title":"Continuous Transformations in Analysis","description":"The general objective of this treatise is to give a systematic presenta­ tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought initiated by BANACH, GEOCZE, LEBESGUE, TONELLI, and VITALI. To indicate a basic feature in this line of thought, let us consider a real-valued continuous function I(u) of the single real variable tt. Such a function may be thought of as defining a continuous translormation T under which x = 1 (u) is the image of u. About thirty years ago, BANACH and VITALI observed that the fundamental concepts of bounded variation, absolute continuity, and derivative admit of fruitful geometrical descriptions in terms of the transformation T: x = 1 (u) associated with the function 1 (u). They further noticed that these geometrical descriptions remain meaningful for a continuous transformation T in Euclidean n-space Rff, where T is given by a system of equations of the form 1-\/(1 ff) X-I U, . . . ,tt ,. \", and n is an arbitrary positive integer. Accordingly, these geometrical descriptions can be used to define, for continuous transformations in Euclidean n-space Rff, n-dimensional concepts 01 bounded variation and absolute continuity, and to introduce a generalized Jacobian without reference to partial derivatives. These ideas were further developed, generalized, and modified by many mathematicians, and significant applications were made in Calculus of Variations and related fields along the lines initiated by GEOCZE, LEBESGUE, and TONELLI.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52667013267729,"sku":"NLS9783642859915","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642859915.jpg?v=1786700524"},{"product_id":"on-the-problem-of-plateau-book-tibor-rado-9781013998614","title":"On The Problem Of Plateau","description":"\u003cp\u003eThis work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.\u003c\/p\u003e\u003cp\u003eThis work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.\u003c\/p\u003e\u003cp\u003eScholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.\u003c\/p\u003e\u003cp\u003eWe appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":52741776441617,"sku":"NIN9781013998614","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781013998614.jpg?v=1786128780"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-tibor-rado.oembed","provider":"World of Books ","version":"1.0","type":"link"}