![]() ![]() SeptemDxO Labs announces the immediate availability of DxO ViewPoint 2, its software dedicated to fixing problems with perspective and to correcting volume deformations. Special introductory offer through October 20, 2013 Press release: DxO ViewPoint 2 includes new tools for fixing even the most complex perspective problems, and now corrects optical distortions In particular, the geometric ideas are presented in a self-contained manner for some of the needed analytic or measure-theoretic results, references are given.DxO Labs has released version 2 of its distortion-correction software Viewpoint. Designed to correct for perspective distortions such as converging verticals, Viewpoint can now also use DxO Optics Modules to correct for the lens's barrel or pincushion distortion. It can work both as standalone software and as a plug-in, which is now compatible with Adobe Photoshop Elements and Apple Aperture (as well as Adobe Photoshop CC and Lightroom 5). A one month free trial version is available to download now, and Viewpoint 2 is on sale at reduced prices until 20th October. See below for more info and download links.Ĭlick here to download the free trial version of DxO Viewpoint 2 Also mathematicians working in other areas can profit a lot from this carefully written book. "The book can be highly recommended for graduate students as a comprehensive introduction to the field of geometric analysis. A short bibliography and an index complete this book, which is clearly written and makes an interesting link between analysis and geometry." Two appendices deal with some metrics on the collection of subsets of a Euclidean space and some basic constants associated to those spaces. The last chapter deals with some questions related to complex analysis, namely quasiconformal mappings and Weyl's theorems on the asymptotic expression of eigenvalues. Steiner symmetrization is then treated, with its applications to isoperimetric inequalities. One chapter is devoted to Sard's theorem and its application to the Whitney extension theorem, and another one to convexity and some of its generalizations. Then comes a study of the restriction, trace and extension of functions belonging to a Sobolev space. This includes the notion of defining functions for a bounded domain, techniques related to the smoothness of the boundary, some measure theory, including rectifiable sets, Minkowski content, covering lemmas, functions with bounded variation, and the area and co-area formula. "This monograph collects a number of concepts, techniques and results of geometrical nature, centered around the concept of domain, and which are widely used by analysts. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. Correspondingly, there is no longer any natural way to apply the Fourier transform. No longer can we expect there to be symmetries. In this context the tools, perforce, must be different. Much modern work in analysis takes place on a domain in space. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. The analysis of Euclidean space is well-developed. ![]()
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