§ 2.1 differentiation of complex valued functionsA function f defined on an open set G⊆ C is differentiable at z∈G if limh→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 of f(z+h) tha...
This chapter discusses complex-valued functions of a real variable. The complex-valued function f(x) = φ (x) + iψ(x) of the real variable x will be called measurable (integrable) provided its real part φ and its imaginary part ψ are measurable (integrable). By virtue of this ...
A metric for quantifying nonlinearity in k-dimensional complex-valued functions In this paper, we introduce a metric for quantifying NL in multi-dimensional complex-valued functions. The metric is an extension of a real-valued NL ... LC Llewellyn,MR Grimaila,DD Hodson,......
🐛 Describe the bug Compiling fails for even very simple functions when tensors are complex-valued. See e.g. import torch @torch.compile def foo(X, Y): Z = X + Y return Z X = torch.zeros(10, dtype=torch.complex128) Y = torch.zeros(10, dty...
I found an excellent project on GitHub (https://github.com/artmenlope/complex-plotting-tools) which I decided to use as a starting point, and potentially contribute to in the future. The repo provided a very easy interface for plotting complex-valued functions in a variety of ...
As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer's Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their ...
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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...
doi:10.29229/uzmj.2020-4-6KORTEWEG-de Vries equationIn this paper, the integration of the loaded Korteweg-de Vries equation in the class of rapidly decreasing complex-valued functions is studied via the inverse scattering method.Uzbek Mathematical JournalU. A., Hoitmetov...
One typical example is the problem of best restricted range approximations in C(Q), the space of all continuous complex-valued functions defined on a compact metric space Q; see =-=[21, 33, 34, 35, 36, 37]-=-; this problem can be reformulated as an approximation problem with ...