Note that a locally finite Borel measure automatically satisfies μ ( C ) < ∞ for every compact set C.

Note that natural transformations can be composed: if μ ( X ): F ( X ) → G ( X ) is a natural transformation from the functor F: C → D to the functor G: C → D, and η ( X ): G ( X ) → H ( X ) is a natural transformation from the functor G to the functor H, then the collection η ( X ) μ ( X ): F ( X ) → H ( X ) defines a natural transformation from F to H. With this composition of natural transformations ( known as vertical composition, see natural transformation ), D < sup > C </ sup > satisfies the axioms of a category.

Note that τ, ( μ < sub > 1 </ sub >, Σ < sub > 1 </ sub >) and ( μ < sub > 2 </ sub >, Σ < sub > 2 </ sub >) may be all maximised independently of each other since they all appear in separate linear terms.

Note that the transition between " upper " (" contravariant ") and " lower " (" covariant ") vector or tensor components is trivial for a indices ( e. g. ), whereas for μ and ν it is nontrivial, corresponding e. g. to the usual Lorentz signature,.

Note that the probability mass function of a Poisson distribution for a count n with mean μ is given by

Note that if the measure spaces ( X, μ ) is a standard measure space ( that is X − N is a standard Borel space for some null set N and μ is a σ-finite measure ) then L < sup > 2 </ sup >< sub > μ </ sub >( X ) is separable.

Note that μ is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum.

:: Note that ν here is actually the Greek letter nu, not the Latin letter v.

Note: Call set-up time is the summation of: ( a ) call request time — the time from initiation of a calling signal to the delivery to the caller of a proceed-to-select signal ; ( b ) selection time — the time from the delivery of the proceed-to-select signal until all the selection signals have been transmitted ; and ( c ) post selection time — the time from the end of the transmission of the selection signals until the delivery of the call-connected signal to the originating terminal.

Note that summation by parts is an analogue to the integration by parts formula,

Note, however, that if the sum can be performed in twice the precision, then ε is replaced by ε < sup > 2 </ sup > and naive summation has a worst-case error comparable to the O ( nε < sup > 2 </ sup >) term in compensated summation at the original precision.

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

( Note: the Einstein summation convention is used in the above.

Note that the bounds of summation are 1 and n − 1, not 0 and n.

) Note that this is a weaker condition than Stability, because any summation method that exhibits Stability also exhibits Finite Re-indexability, but the converse is not true.

Note that it is important to assume that otherwise it would be illegitimate to change the order of summation, and the-invariance would not hold.

Note the summation over q can be resummed as a Lambert series ; that is, one has

Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.

Note that here Latin indices denote the " Lorentzian " vierbein labels while Greek indices denote manifold coordinate indices.

Note: attempt to do parallel loads into the same table ( partition ) usually causes locks — if not on the data rows, then on indices.

( Note: this has three indices, but is not a tensor ).

Note the mixture of coordinate and fiber indices in this expression.

Note that there are also rare instances where it is possible to directly work with compressed data, such as in the case of compressed bitmap indices, where it is faster to work with compression than without compression.

Note that the refractive indices of are reversed, when comparing to usual waveguides.

are indices between 1 and m. Note that, since S was assumed to uniquely decodable,

Note that in the above, the italic lower-case index i is a single index, whereas the upper-case Roman J stands for all of the remaining ( n-1 ) indices.

Note that the operators operate on elements from the domain and range, respectively, of the " one-to-one " and " onto " function ƒ.

Note the range of tones, fading toward the edges.

Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (" saturated ") states.

The path loss for the first ten kilometers may be 150 -- 190 dB ( Note: These values are very approximate and are given here only as an illustration of the range in which the numbers used to express the path loss values can eventually be, these are not definitive or binding figures -- the path loss may be very different for the same distance along two different paths and it can be different even along the same path if measured at different times.

Note that the dynamic range is much larger than fixed-point, but at a cost of a worse signal-to-noise ratio.

: Note: List of Urdu language poets provides pen names for a range of Urdu poets.

Note that the occurrence of brown recluses in a single building ( such as a warehouse ) outside of the native range is not considered a successful colonization ; such single-building populations can occur ( e. g., several such cases in Florida ), but do not spread, and can be easily eradicated.

Note that this notion of image may not correspond to the usual notion of image, or range, of a function, even assuming that the morphisms in the category are functions.

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 also that Unicode includes non-graphical language tag characters in the range U + E0000 – U + E007F for plain text language tagging.

Note that the sine function is such that there are two solutions for for a given range.

Note that for purposes of computer programming, this table should start at 0 instead of 1 and thus use all of the 7-bit range ( 0-127 ) allowed by the MIDI Program Change message.

Blue Note offered better pay and more artistic control than other labels, and his work for this organization is highly regarded and includes leadership and sideman dates with a wide range of musicians, including Donald Byrd, Sonny Clark, Lee Morgan, Ornette Coleman, Dexter Gordon, Billy Higgins, Freddie Hubbard, Grachan Moncur III, Bobby Hutcherson, Mal Waldron, and many others.

Note that this may be difficult to arrange in practice with simple linkages, and designers are advised to draw or analyze their steering systems over the full range of steering angles.

Note, however, that although temperature reconstructions from proxy data help us understand the character of natural climate variability, attribution of recent climate change relies on a broad range of methodologies of which the proxy reconstructions are only a small part.

Note that we do not count the time needed to find the largest pancake, only the number of flips ; if we wished to create a real machine to execute this algorithm in linear time, it would have to both perform prefix reversal ( flips ) and be able to find the maximum of a range of consecutive numbers in constant time.

Note that audible sound has a very wide frequency range ( from 20 to about 17000 Hz ), and thus a very wide range of wavelengths ( from about 20 mm to 17 m ).

* Info on the range ( Note: the western range separated from the rest is actually the range of Eumeces callicephalus.

Note that the exponent range for this format is only about a quarter as large as the corresponding IEEE binary format.

Note that the image of the pole ’ s top will overlay that of some terrain point which is on the same slant range arc but at a shorter horizontal range (“ ground-range ”).