| 21. | Although less used, the separability assumption is considered more general because every stochastic process has a separable version.
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| 22. | The separability of " S " depends both on the Hamiltonian and on the choice of generalized coordinates.
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| 23. | In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian.
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| 24. | Thus every positive, but not completely positive, map ? gives rise to a necessary condition for separability in this way.
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| 25. | Extending the definition of separability from the pure case, we say that a mixed state is separable if it can be written as
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| 26. | This follows from the fact that for every normed space " Y ", separability of the continuous dual implies separability.
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| 27. | This follows from the fact that for every normed space " Y ", separability of the continuous dual implies separability.
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| 28. | A number of indicators of approximate separability can be used, see Golyandina et al . ( 2001, Ch . 1 ).
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| 29. | The two kinds of information have to be extracted on different occasions, because of the non-separability of the wave function representation.
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| 30. | For the and cases, a necessary and sufficient criterion for separability is given by the famous Positive Partial Transpose ( PPT ) condition.
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