§ 2.1 differentiation of complex valued functions A function f defined on an open setG⊆Cis differentiable atz∈Giflimh→0f(z+h)−f(z)h=f′(z)exists. Comments: h is a complex number f′(z)is a complex number which is independent from the direction off(z+h)that approachesf(z)...
{1}{2} ({m z} + \\\frac{1}{m z})$Elementary Transcendental FunctionsThe exponential functionezTrigonometric functionscos z,sin z, andtan zElementary Multiple-Valued FunctionsThe origin of multiple-valuedness:arg z$w = \\\sqrt[n]{z} (n \\\geq 2)$and its Riemann surface (etc.)w...
We considered that the cause was nonboundedness of the complex function [Eq.(3)] and decided to adopt bounded functions. Actually, Eq.(3) has the periodic poles at the imaginary axis. The complex function defined in Eq.(2) is valid as an activation function of complex-valued neurons for...
Stationary complex-valued functionals are discussed and seen to have unique stationary points if they are analytic, which corresponds to analyticity of functions in complex-valued function theory. As an application, the problem of wave propagation in a circular waveguide with an impedance boundary and...
Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras. 展开 ...
On the range of one complex-valued functionalOn the range of one complex-valued functionalfunctionalrangevariational methodboundary functionunivalent functionWe solve the problem of finding the range 惟 of one functional on the class of pairs of normalized univalent functions. Using the method of int...
Open in MATLAB Online The Curve Fitting Toolbox does not accept complex valued functions. To carry out the fit, use the LSQNONLIN function or the FMINSEARCH function. The objective function passed to LSQNONLIN or FMINSEARCH should take the real and complex parts of the parameters separate...
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Optimizing Real-Valued Functions(优选) 热度: Pleasecitethisarticleinpressas:M.Sivachitra,S.Vijayachitra,Ametacognitivefullycomplexvaluedfunctionallinknetworkforsolving realvaluedclassificationproblems,Appl.SoftComput.J.(2015),http://dx.doi/10.1016/j.asoc.2015.04.022 ...
The differentiation of functions of conjugate complex variables: application to power network analysis. IEEE Trans Educ 1988;31:286–91. https://doi.org/10.1109/13.9757.Search in Google Scholar 11. Pires, RC. Complex-valued steady-state models as applied to power flow analysis and power system ...