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Extensions of MSD to highly constrained design problems of higher dimension is also described.
This resulted in a significant pattern in the scales of higher dimension.
These algorithms can be used for systems of higher dimension and on longer time horizons than the existing methods.
The natural problem was to see how far Riemann's ideas could be applied to the study of spaces of higher dimension.
In principle, the design method of the control pulse sequence proposed can be generalized to use in the quantum systems of higher dimension.
This paper focuses on the design of a dedicated P1 function space to model elliptic boundary value problem on a manifold embedded in a space of higher dimension.
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J ingeniously generalizes this scheme to arrays of higher dimensions.
Others have come up with ideas about new physics that modify special relativity by taking the unexpected effects of higher dimensions into account.
As for Horgan's bête noire of physics -- higher dimensions, or what he refers to as "hyperspace theories" -- he writes: "But pursuers of this 'theory of everything' have wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality".
Hence, the next steps will be to develop appropriate compensation schemes, to test quantum states of higher dimensions, for example with pure OAM encoding, and distribute high-dimensionally entangled photons for large quantum networks.
In this context it is shown, that, particularly for problems of higher dimensions, approximation techniques utilizing linearization may be prone to considerable errors.
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