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Examples ofconformal map
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In general, it is not clear how to determine theconformalmapf() from this equation.
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We have now constructed aconformalmapsatisfying all the (necessary and sufficient) conditions (ii)-(iv) for a consistent solution to the original problem.
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Theconformalmap(3.23) representing our solutions simplifies considerably in these two special cases.
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Two consecutive reflections have implied an invariance property of the function giving theconformalmap.
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Again, this can be regarded as aconformalmapof the -plane, cut along the negative real axis.
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For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is aconformalmap.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The fact that "f" is biholomorphic implies that it is aconformalmapand therefore angle-preserving.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In each case the angle of "a" is added to that of "z" giving aconformalmap.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.For this reason, any function which is defined by a potential can be transformed by aconformalmapand still remain governed by a potential.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.According to this weaker definition of conformality, aconformalmapneed not be biholomorphic even though it is locally biholomorphic.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.In this section we change the point of view: we will focus on the conformal maps instead of the sets defining the crack extension.
From theCambridge English Corpus
This is done without appeal to conformal mapping theory.
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In this paper, two classes of conformal maps generalizing (1.1) and (1.2) are studied in detail.
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Many explicit solutions involving rational and log-rational conformal maps can be written down for both problems.
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In our setting we replace the trial crack shapes by a suitable family of conformal maps.
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The result is established directly from the equations of motion without appeal to conformal mapping theory, although the result underlies the existence of exact conformal mapping solutions.
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Since the x limit h is a homeomorphism, standard results from the theory of quasi-conformal maps show that h is quasi-conformal.
From theCambridge English Corpus
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