A. Browder, Topology in the complex plane, Amer. Math. Monthly 107 (2000), 393-401.A. Browder, "Topology in the Complex Plane," The American Mathematical Monthly, Vol. 107 No. 10, 2006, pp. 393-401. https://getinfo.de/app/Topology-in-the-Complex-Plane/id/BLSE%3ARN079983226...
If for each value of ρ we remove the trace of H (i.e., replace H(ρ) with H(ρ)−Itr(H(ρ)) where I is the identity matrix), this amounts to translating (in the complex plane) the eigenvalue spectrum as a whole. Even if this translation is different for each value of ρ...
a In the conventional NHSE, all bulk eigenstates localize at a boundary (left panel). This corresponds to the single-loop winding of the complex energy spectrum in the complex plane (right panel). The winding direction is characterized by the winding number (v = +1 in the illustration...
This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows, which is developed based on the exact relation between skin friction and surface pressure through the boundary enstrophy flux (BEF). The key of this method is that a skin friction...
This Application runs in Maple.Don't have Maple? No problem! Try Maple free for 15 days! In this section we investigate some basic ideas concerning sets of points in the plane. Application Details Publish Date:October 01, 2003 Created In:Maple V ...
4.MathematicsA topological space in which each point has a neighborhood that is equivalent to a neighborhood in Euclidean space. The surface of a sphere is a two-dimensional manifold because the neighborhood of each point is equivalent to a part of the plane. ...
At best, x could be defined as an unsigned infinity (¥) like the "infinite circle" at the horizon of the complex plane (¥+¥ is undetermined). This could be a hint that a proper extension of c would have complex values... ...
In this definition, C is the complex plane, “the closure of the upper half-plane” is the set {z∈C:Im(z)≥0},“second-countable” is a topological space T in which there exists some countable collection U={Ui}i=1∞ of open sets such that any open set in T can be written as...
was the German mathematicianJohann Listing, who publishedVorstudien zur Topologie(1847; “Introductory Studies in Topology”), which is often cited as the first print occurrence of the termtopology. In 1851 the German mathematicianBernhard Riemannconsidered surfaces related tocomplex numbertheory and, he...
The following article is fromThe Great Soviet Encyclopedia(1979). It might be outdated or ideologically biased. Complete Metric Space a metric space in which the Cauchy convergence criterion is satisfied. A sequence of pointsx1,x2, …,xn, … on a line, in a plane, or in space is said ...