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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 of a smooth function, and it is not necessary just to consider algebraic varieties. The definitions can be ...
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.
Branch points are generally the result of a multi-valued function, such as or (), which are defined within a certain limited domain so that the function can be made single-valued within the domain. The cut is a line or curve excluded from the domain to introduce a technical separation between discontinuous values of the function.
Singularity functions are a class of discontinuous functions that contain singularities, i.e., they are discontinuous at their singular points. Singularity functions have been heavily studied in the field of mathematics under the alternative names of generalized functions and distribution theory .
Singular point of a curve, where the curve is not given by a smooth embedding of a parameter; Singular point of an algebraic variety, a point where an algebraic variety is not locally flat; Rational singularity
Netflix's first NFL Christmas Day doubleheader ended up being successful globally. The Baltimore Ravens’ 31-2 victory over the Houston Texans averaged 31.3 million while Kansas City’s 29-10 ...
Being a celebrity can be tough. All of the adulation and constant media attention can take its toll. It’s not surprising that some celebrities take solace in the company of animals to give them ...
The Whitney umbrella x 2 = y 2 z has singular set the z axis, most of whose point are ordinary double points, but there is a more complicated pinch point singularity at the origin, so blowing up the worst singular points suggests that one should start by blowing up the origin. However blowing up the origin reproduces the same singularity on one ...