isolated singularity उदाहरण वाक्य

Formally, and within the general scope of functional analysis, an isolated singularity for a function f is any " topologically isolated " point within an open set where the function is defined.
Then " g " has an isolated singularity at " x " 0, and maps the boundary of some deleted neighborhood of " x " 0 to the unit sphere.
W Pardon and M Stern, Pure hodge structure on the L2-cohomology of varieties with isolated singularities, Journal fur die Reine und Angewandte Mathematik, vol . 533 ( 2001 ), pp . 55 80
Wall's work since the mid-1970s has mostly been in singularity theory as developed by R . Thom, J . Milnor and V . Arnold, and especially concerns the classification of isolated singularities of differentiable maps and of algebraic varieties.
Bers proved an extension of Riemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950 International Congress of Mathematicians and published it in " Annals of Mathematics ".

The series you have calculated is the Laurent expansion of sin ( 1 / z ) about the origin, and there is a theorem that says that the principal part of the Laurent expansion ( the part with the negative powers ) about an isolated singularity is an infinite sum if and only if the singularity is essential.
A " measured foliation " ( \ mathcal F, \ mu ) on S is a foliation \ mathcal F on S which may admit isolated singularities, together with a " transverse measure " \ mu, i . e . a function which to each each arc \ alpha transverse to the foliation \ mathcal F associates a positive real number \ mu ( \ alpha ).