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A grey system means that a system in which part of information is known and part of information is unknown. Formally, grey systems theory describes uncertainty by interval-valued unknowns called grey numbers , with the width of the interval reflecting more or less precise knowledge. [ 3 ]
Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
In many cases a model can be converted to a function of the form: [5] [17] [18] m(f,p,q) where the vector function m gives the errors between the data p, and the model predictions. The vector q gives some variable parameters that are the model's unknown parts.
In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic continuation.It states that if an analytic function is defined on the upper half-plane, and has well-defined (non-singular) real values on the real axis, then it can be extended to the conjugate function on the lower half-plane.
A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a (not necessarily proper) subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are generally assumed to have a domain that contains a nonempty open subset of the complex plane.
That all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. [1] Holomorphic functions are also sometimes referred to as regular functions. [2] A holomorphic function whose domain is the whole complex plane is called an entire function.
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Great Picard's Theorem (meromorphic version): If M is a Riemann surface, w a point on M, P 1 (C) = C ∪ {∞} denotes the Riemann sphere and f : M\{w} → P 1 (C) is a holomorphic function with essential singularity at w, then on any open subset of M containing w, the function f(z) attains all but at most two points of P 1 (C) infinitely often.