Search results
Results from the WOW.Com Content Network
Testing whether a differentiable map is a diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: [1] If , are connected open subsets of such that is simply connected, a differentiable map : is a diffeomorphism if it is proper and if the differential: is bijective (and hence a linear isomorphism) at each point in .
The first algorithm for dense image mapping via diffeomorphic metric mapping was Beg's LDDMM [1] [2] for volumes and Joshi's landmark matching for point sets with correspondence, [3] [4] with LDDMM algorithms now available for computing diffeomorphic metric maps between non-corresponding landmarks [5] and landmark matching intrinsic to ...
In mathematics, an exotic is a differentiable manifold that is homeomorphic (i.e. shape preserving) but not diffeomorphic (i.e. non smooth) to the Euclidean space. The first examples were found in 1982 by Michael Freedman and others, by using the contrast between Freedman's theorems about topological 4-manifolds, and Simon Donaldson's theorems about smooth 4-manifolds.
[2] It follows that a map f : X → Y {\displaystyle f:X\to Y} between two manifolds of equal dimension ( dim X = dim Y {\displaystyle \operatorname {dim} X=\operatorname {dim} Y} ) is a local diffeomorphism if and only if it is a smooth immersion (smooth local embedding), or equivalently, if and only if it is a smooth submersion .
For example, Milnor showed that two 7-cells can be glued along their boundary so that the result is an exotic sphere homeomorphic but not diffeomorphic to a 7-sphere. However, there is a canonical way to choose the gluing of M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} which gives a unique well-defined connected sum. [ 1 ]
Twosday is the name given to Tuesday, February 22, 2022, and an unofficial one-time secular observance held on that day, characterized as a fad. [1] [2] The name is a portmanteau of two and Tuesday, deriving from the fact that the digits of the date form a numeral palindrome marked by exclusivity or prevalence of the digit 2—when written in different numerical date formats, such as: 22/02 ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Morse Code Aptitude - The last test of Day 1 had the recruits listening to a song with a hidden message in morse code. DAY 2. Obstacle Course - On Day 2, the Recruits were put through a rigorous obstacle course with points awarded for every obstacle completed. Recruits must score a total of 50 points out of a possible 90 to pass the course.