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Page "Banach fixed-point theorem" ¶ 11
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Note and requirement
Note that the requirement that the maps be continuous is essential ; if X is infinite-dimensional, there exist linear maps which are not continuous, and therefore not bounded.
Note also that until well into the 20th Century, rather than an official readying the ball for scrimmage, the side entitled to the snap had complete custody of the ball and could snap it from the required spot at any time ; for instance, a tackled ball carrier might feign injury, then suddenly snap the ball while recumbent, there being no stance requirement yet.
Note that former military officers from the World War II era may be appointed prime minister despite the " civilian " requirement, Yasuhiro Nakasone being one prominent example.
Note that none of these listed characteristics are a requirement, as seen in shōnen manga like Yotsuba &!, which features a female lead, and almost no fan service or action, and that what most defines whether or not a series is shōnen are things like the magazine ( see Weekly Shōnen Jump ) it is serialized in or the time slot it airs on T. V.
Note 2: The FCC registration program contains no requirement that accepted terminal equipment be compatible with, or function with, the network.
Note: Part 68 rules provide the technical and procedural standards under which direct electrical connection of customer-provided telephone equipment, systems, and protective apparatus may be made to the nationwide network without causing harm and without a requirement for protective circuit arrangements in the service-provider networks.
Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement.
Note that there is no requirement for uniqueness over time.
Note that at least for type specimens there is no requirement for a " typical " individual to be used.
Note that both files have been sorted on the join field — this is a requirement of the program.
Note that this requirement can be rephrased by saying that binary meets preserve binary joins.
Note that using the channel numbers in an identification is not a requirement.
Note that there is no requirement of commutativity.

Note and d
Note that the sampling deviation, d, depends not only on the estimator, but on the sample.
Note that retroflex d, l and r are found not only in southern Italy and Tuscany but also in Asturias.
* The probability a set will have features different and features the same is ( Note: d = 0 all four features the same is impossible as no two cards are identical ).
Note 1: Compared to tactical communications, long-haul communications are characterized by ( a ) higher levels of users, such as the National Command Authority, ( b ) more stringent performance requirements, such as higher quality circuits, ( c ) longer distances between users, including world wide distances, ( d ) higher traffic volumes and densities, ( e ) larger switches and trunk cross sections, and ( f ) fixed and recoverable assets.
* Background Note: Cote d ' Ivoire
Note présentée par la noblesse d ' Haïti aux trois grands alliés ," an 1820 chanson written by Pierre-Jean de Béranger.
Note: Most Sabbateans during and after Sabbatai Zevi were Jews and practiced only Judaism, whereas the Dönmeh officially practice / d Islam and are not regarded as Jews.
Note that d < sup > 2 </ sup > R / dt < sup > 2 </ sup > and F / m are both equal to the gravitational acceleration g ( equivalent to the inertial acceleration, so same mathematical form, but also defined as gravitational force per unit mass ).
Note that " d " is made more distinctively different from " b " than is usual in standard typefaces ( which is possible since in the I. T. A.
* Bonaparte, Charles Lucien Jules Laurent ( 1850 ): Note sur plusieurs familles naturelles d ' Oiseaux, et descriptions d ' espèces nouvelles.
Note that result ( 28 ) here applies for a barrier of any shape ( though d < sub > F </ sub > will be different for different barriers ).
* Note: Wilde, in addition to his role listed above, played the same-named son of d ' Artagnan as the main hero in 1952's At Sword's Point ; Tobias Mehler was similarly cast in the Young Blades series, while the indicated performance there by Shaughnessy was a single guest appearance as his famous father.
( Note: The copyright reads: Réalisations des basses et chants du Traité d ' harmonie par Théodore Dubois ).
* Note d: In her early career, Lale Andersen was sometimes billed as Liselotte Wilke.
Note that this works equally well when degree ( n ) < degree ( d ); in that case the result is just the trivial ( 0, n ).
Note that using r = 6, 371, 009 metres is appropriate for calculating great-circle distances between points on the Earth's surface, in which case the result d will also be in metres.
Note that there are similar types of sponge cakes named after the same fashion, in, in, in Portuguese: Pão de Espanha, in, in, in ( Castile is a former kingdom of Spain comprising its central provinces, thus Pain d ' Espagne and other variants are quasi-synonymous to " bread from Castile ").
Note that d < sub > i </ sub > is applied on the left.
Note, as well, that this algorithm does not work when n is a prime number, since, in this case, d will be always 1.
* Note sur la forme du tombeau d ' Eschmounazar ( 1880 )
Note that the first part of the name, " Live ( d )", spelled backwards is "( D ) evil " and the second part, " dog ", spelled backwards is " God ".
Note sur quelques gymnosomes de provenances diverses et diagnose d ' un genre nouveau.

Note and T
Note that S and T need not be subgroups.
Note that this applies even if neither S nor T is normal.
Note that a system need not include source code derived in any way from AT & T Unix to meet the specification.
Note that some mathematical literature uses different definitions for the term " completely regular " and the terms involving " T ".
Note that when N = R, the map< sub > x </ sub >: T < sub > x </ sub > M → R coincides with the usual notion of the differential of the function φ.
A set T of real numbers ( red and green balls ), a subset S of T ( green balls ), and the infimum of S. Note that for finite set s the infimum and the minimum are equal.
* Note 3: Historically, if an " F " precedes the " T ", optical fiber cables are utilized at the same rates.
( Note that it is written as a relation, not as a function: T isn't written here as a function of M, L, and g .)
Note that there is a similarity between the construction of T and the set in Russell's paradox.
A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in T. Note that u is an element of P but need not be an element of T. An element m of P is called a maximal element ( or non-dominated ) if there is no element x in P for which m < x.
( Note that X < sup > T </ sup > is defined here and not X itself, and what we are calling X < sup > T </ sup > is often alternatively denoted as X itself.
Note the crucial feature: the unknown parameter p interacts with the data x only via the statistic T ( x )
Note that the assumption the v is relatively large is equivalently to the assumption that the thermal diffusivity is small compared to, where L is the acean width ( from mid-ocean ridges to continental shelf ) and T is its age.
Note that T is a function of p alone, while V is a function of q alone.

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