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Singularity (statistics)
Singularity or singular point may refer to: Science, technology, and mathematics Mathematics * Mathematical singularity, a point at which a given mathematical object is not defined or not "well-behaved", for example infinite or not differentiable Geometry * 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 Complex analysis * Essential singularity, a singularity near which a function exhibits extreme behaviour * Isolated singularity, a mathematical singularity that has no other singularities close to it * Movable singularity, a concept in singularity theory * Removable singularity, a point at which a function is not defined but at which it can be so defined that it is continuous at the singularity Natural sciences * Singularity (system theory), in dynamical and social systems, a context in which a small change c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the real function : f(x) = \frac has a singularity at x = 0, where the numerical value of the function approaches \pm\infty so the function is not defined. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory. Real analysis In real analysis, singularities are either discontinuities, or discontinuities of the derivative (sometimes also discontinuities of higher order derivatives). There are four kinds of discon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
