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Several interrelated reasons account for such singularities, in particular the impact of pro-family policies accompanied by greater unmarried households and out-of-wedlock births.
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The wormhole closes off (forming future singularities) so rapidly that passage between the two universes would require faster-than-light velocity, and is therefore impossible.
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Solutions without additional matter always have either naked singularities or else two asymptotic regions of spacetime, resembling a wormhole but with no horizon.
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Roughly speaking, monodromy data is now regarded as data which glues together canonical solutions near the singularities.
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It follows that, if a curve has ("d" -1) ("d" -2) /2 different singularities, it is a rational curve and, thus, admits a rational parameterization.
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This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization.
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The monodromy theory of differential equations, in the complex domain, around singularities, does however come into relation with the geometric theory.
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Given that these examples are all highly symmetricand thus simplifiedit is tempting to conclude that the occurrence of singularities is an artifact of idealization.
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