Note that the maximally extended Schwarzschild metric describes an idealized black hole / white hole that exists eternally from the perspective of external observers ; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.

Note the conventions being used here are the metric signature of (− + + +) and the natural units where c = 1 ( although the gravitational constant G will be kept explicit, and M will denote the characteristic mass of the Schwarzschild geometry ).

Note GM is the gravitational constant multiplied with the Schwarzschild mass parameter, and this article is using units where c = 1.

Note that, in a metric space, every compact subset is closed and bounded.

Note that completeness is a property of the metric and not of the topology, meaning that a complete metric space can be homeomorphic to a non-complete one.

Note that this is also true if the boundary is the empty set, e. g. in the metric space of rational numbers, for the set of numbers of which the square is less than 2.

Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).

Note: The listed measurements of this system range from the lowest to highest acceptable halachic value, in terms of conversion to either metric or Imperial units.

Note that in general, no such relation exists in spaces not endowed with a metric tensor.

In particular, given a point p in a Riemannian manifold, it is always possible to find metrics conformal to the given metric g for which the Ricci tensor vanishes at p. Note, however, that this is only pointwise assertion ; it is usually impossible to make the Ricci curvature vanish identically on the entire manifold by a conformal rescaling.

Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no effect at all.

Note that this is a sphere in the sense that it is a collection of points at constant metric distance from the origin, but visually it is a hyperboloid, as in the image shown.

Note that an isometry is never strictly metric, except in the degenerate case of the empty space or a single-point space.

Note the summation that is a representation of the metric due to.

( Note: The < tt >+---</ tt > metric signature is used in this article so that will always be positive definite for timelike paths.

Note that minimizing the difference ( usually the squared difference ) between euclidean and ideal distances between nodes is then equivalent to a metric multidimensional scaling problem.

Note that the symmetric difference of two distinct sets can have measure zero ; hence the pseudometric as defined above need not to be a true metric.

* Note that the above space is not homeomorphic to the same set of equivalence classes endowed with the obvious metric: i. e. regular Euclidean distance for two points in the same interval, and the sum of the distances to the left hand point for points not in the same interval.

Note that the hyperbolic area of E is exactly 1, when computed using the canonical Poincaré metric.

Note that if or is equal to zero at some point, the metric would be singular at that point.

Note that the spacetime represented by the above metric is asymptotically flat, i. e. as, the metric approaches that of the Minkowski metric and the spacetime manifold resembles that of Minkowski space.

Internet Experiment Note ( IEN ) 96 ( 1979 ) describes an early RF cable modem system.

Note that the above density operator describes the full ensemble after measurement.

Note that the above equation describes the Earth's gravitational potential, not the geoid itself, at location the co-ordinate being the geocentric radius, i. e., distance from the Earth's centre.

Note: the WDO describes how to proceed on offenses that are not ( yet ) covered by the military penal code but clearly against a military regulation.

Note that Bergmann's rule describes a tendency of body mass variation within groups ; it does not suggest that large-bodied animals do not occur in warm climates.

Note: The Encyclopedia of Saskatchewan describes the terrain and initial encounter somewhat differently but in many respects shows Fine Day to be an even more brilliant tactician than here described.

( Note that this explanation assumes that the atmosphere starts in a geostrophically unbalanced state and describes how such a state would evolve into a balanced flow.

Note that neither one sequentialisation according to pre -, in-or postorder describes the underlying tree uniquely ; any combination of < em > two </ em > different sequentialisations enables full reconstruction, though.

Note that this parable describes three yana " vehicles ; carts " drawn by goats, deer, and oxen, which is a Mahayanist wordplay upon classifying the Sutrayana Schools of Buddhism into the Hearer's Vehicle ( Sravakayana ), Solitary Conqueror's Vehicle ( Pratyekabuddhayana ), and the Bodhisattva's Vehicle ( Mahayana ).

Note: the series, published in 1916, describes a fictional German invasion of the USA, dated in 1920-21.

( Note: This does not work on iOS, but the activation talk page describes some unofficial workarounds.

Note: Pointillism merely describes the technique of painting used during this period.

Note that the address given for the designation of 7 Crescent Road, differs from the TTC address, but more accurately describes the location.

Note: The Systema article describes history common to these arts.

Philips Technical Note 083 describes how to interface the 2651 PCI to various other microprocessors, such as the 8080, 8085, Z80, 8048 and 6800

Note that the image itself describes colors using sRGB, and colors outside the sRGB gamut cannot be displayed properly.

: Note: English language sources show ranging moves along all four diagonals ( BrlRfbR5 ), but Japanese Wikipedia only describes the piece this way for taikyoku shogi.

: Note: English language sources show ranging moves along all four diagonals ( BfbRrlR5 ), but Japanese Wikipedia only describes the piece this way for taikyoku shogi.

: Note: Since Japanese Wikipedia also describes the piece this way for taikyoku shogi, which often has unique movements for its pieces, this may be an error.

: Note: The following synopsis describes the original version.