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Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates.
Furthermore, this compact manifold with boundary, which is known as the Milnor fiber (of the isolated singular point of at the origin), is diffeomorphic to the intersection of the closed (+)-ball (bounded by the small (+)-sphere) with the (non-singular) hypersurface where = and is any sufficiently small non-zero complex number.
In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and . The equation is also known as the Papperitz equation. [1]
Repeatedly blowing up the singular points of a curve will eventually resolve the singularities. The main task with this method is to find a way to measure the complexity of a singularity and to show that blowing up improves this measure. There are many ways to do this. For example, one can use the arithmetic genus of the curve.
Hence, it is technically more correct to discuss singular points of a smooth mapping here rather than a singular point of a curve. The above definitions can be extended to cover implicit curves which are defined as the zero set f − 1 ( 0 ) {\displaystyle f^{-1}(0)} of a smooth function , and it is not necessary just to consider ...
Peptide Mass Fingerprint search Identifies proteins from an uploaded peak list using a technique known as peptide mass fingerprinting. Sequence query Combines peptide mass data with amino acid sequence and composition information usually obtained from MS/MS tandem mass spectrometry data. Based on the peptide sequence tag approach. MS/MS Ion Search
inflections. If the cubic degenerates and gets a double point, then 6 points converge to the singular point and only 3 inflection remain along the singular curve. If the cubic degenerates and gets a cusp then only one inflection remains. Note that the first two Plücker equations have dual versions:
A peptide library is a tool for studying proteins.Peptide libraries typically contain a large number of peptides that have a systematic combination of amino acids.Usually, solid phase synthesis, e.g. resin as a flat surface or beads, is used for peptide library generation.