| 21. | Conversely, the metric tensor itself is the derivative of the distance function ( taken in a suitable manner ).
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| 22. | This is given in terms of a distance function, giving how much an injective correspondence differs from an isomorphism.
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| 23. | The sine top / sine bottom method may be called the vertical distance function or a two-point method.
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| 24. | Using these resources they could evaluate the 4095-bit edit distance function, whose circuit comprises almost 6 billion gates.
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| 25. | Another limitation of the algorithm is that it cannot be used with arbitrary distance functions or on non-numerical data.
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| 26. | In general, when we define metric space the distance function is taken to be a real-valued order complete.
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| 27. | For real numbers, the arithmetic mean is a Fr�chet mean, using the usual Euclidean distance as the distance function.
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| 28. | This distance function ( which makes a metric space ) is sufficient to define all Euclidean geometry, including the dot product.
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| 29. | In particular, the Hessian of the signed distance function on the boundary of " ? " gives the Weingarten map.
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| 30. | If the family of affine distance functions can be shown to be a certain kind of family then the local structure is known.
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