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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
Point a is an ordinary point when functions p 1 (x) and p 0 (x) are analytic at x = a. Point a is a regular singular point if p 1 (x) has a pole up to order 1 at x = a and p 0 has a pole of order up to 2 at x = a. Otherwise point a is an irregular singular point.
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.
Consider a smooth real-valued function of two variables, say f (x, y) where x and y are real numbers.So f is a function from the plane to the line. The space of all such smooth functions is acted upon by the group of diffeomorphisms of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the source and the target.
Protein sequence interpretation: a scheme new protein to be engineered in a yeast. It is often desirable to know the unordered amino acid composition of a protein prior to attempting to find the ordered sequence, as this knowledge can be used to facilitate the discovery of errors in the sequencing process or to distinguish between ambiguous results.
Lady Gaga is showing off quite the sparkler on Carpool Karaoke!. The singer, 38, revealed her giant-sized engagement ring while appearing in Apple TV+ and Apple Music’s Christmas special of A ...
The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like cusps. For example, the equation y 2 − x 3 = 0 defines a curve that has a cusp at the origin x = y = 0. One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at ...