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 on numbering: Pope Benedict X is now considered an antipope.

Note that only two sequences of moves by O ( both starting with center, top-right, left-mid ) lead to a draw, with the remaining sequences leading to wins from X.

Note: In the Defense Data Network ( DDN ), a packet-switching node is usually configured to support up to thirty-two X. 25 56 kbit / s host connections, as many as six 56 kbit / s interswitch trunk ( IST ) lines to other packet-switching nodes, and at least one Terminal Access Controller ( TAC ).

( Note, however, that Norwegian både, for example, though cognate with English both, can be used with more than two things, as in X sparer både tid, penger, og arbeid, literally " X saves both time, money, and labour ".

Note that X. 25 provides for virtual calls, so appears to be a circuit switched network, even though in fact the data itself is packet switched internally, similar to the way TCP provides connections even though the underlying data is packet switched.

Note also that the X < sub > i </ sub > are in general not independent ; they can be seen as the result of applying the matrix A to a collection of independent Gaussian variables z.

Note that the corresponding Mac OS X release may have been released on a different date ; refer to the Mac OS X pages for those dates.

( Note that the contact X on the second rung serves no useful purpose, as X is already defined in the ' AND ' function of S from the 1st rung.

Note: As of Mac OS X version 10. 4. 9, the system will sometimes incorrectly display the AIFC icon for files with the. aif extension, whether or not the actual file format is AIFF or AIFF-C.

Note that latest versions of Mac OS X, v10. 5 " Leopard " and newer, eliminated Classic support, even for PowerPC-based Macs.

In radar applications, it ranges from 12-18 GHz according to the formal definition of radar frequency band nomenclature in IEEE Standard 521-2002 .< ref > Note that in the band 11. 2 – 12 GHz the working definitions of K < sub > u </ sub > band and X band overlap ; satellite communications engineers would generally regard frequencies above 11. 2 GHz as being part of the K < sub > u </ sub > band .</ ref >

Note that Si and Ge are indirect with minima at X and L, while GaAs and InAs are direct band gap materials.

Note that to include a constant in the model above, one can choose to include the variable X < sub > K </ sub > all of whose observed values are unity: X < sub > iK </ sub > = 1 for all i.

Note that the number of monochromatic r-subgraphs is the sum of X ( S ) over all possible subsets.

Note that P will itself be a relational predicate involving both X and Y.

** Vol X: The Inspirations of Historians ; A Note on Chronology ( Oxford University Press 1954 )

Note that chemists often write H < sup >+</ sup >( aq ) and refer to the hydrogen ion when describing acid-base reactions but the free hydrogen nucleus, a proton, does not exist alone in water, it exists as the hydronium ion, H < sub > 3 </ sub > O < sup >+</ sup >.

Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.

Note that the beryllium scale is inverted, so increases on this scale indicate lower < sup > 10 </ sup > Be levels

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

Note that t < sup > 0 </ sup > = 1, ( 1 − t )< sup > 0 </ sup > = 1, and that the binomial coefficient,, also expressed as or is:

Note that at ocean pH most of the CO < sub > 2 </ sub > produced in this reaction is immediately converted back into.

Note the position of the hydroxyl group ( red or green ) on the anomeric carbon relative to the CH < sub > 2 </ sub > OH group bound to carbon 5: they are either on the opposite sides ( α ), or the same side ( β ).

Note that in other fields, a lower division between high and ultra-high vacuum is common, often 10 < sup >− 7 </ sup > Pa.

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note that when this routine is called by < tt > jsr </ tt >, AC3 holds the return address.

< cite id =" demographics "> Note I </ cite >-There were around 300, 000 people () working as electrical engineers in the US ; in Australia, there were around 17, 000 () and in Canada, there were around 37, 000 (), constituting about 0. 2 % of the labour force in each of the three countries.

Note that the Bernoulli numbers are defined as B < sub > n </ sub > = B < sub > n </ sub >( 0 ), and that these vanish for odd n greater than 1.

Note that by reversing the equation, we can swap < math > < </ math > and, for example:

Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products.

Note that factors p < sup > 0 </ sup > =

Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.

Note that if n < sub > 1 </ sub > and n < sub > 2 </ sub > are the same, the antisymmetric expression gives zero, which cannot be a state vector as it cannot be normalized.

( Note: ∇< sup > 2 </ sup > F represents, in this case, the vector formed by the individual Laplacian of each component of the vector in question )

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

Note that if the preorder is R < sup >+=</ sup >, S / ~ is the set of R-cycle equivalence classes: x ∈ if and only if x = y or x is in an R-cycle with y.

Note that S and T need not be subgroups.

Note that this applies even if neither S nor T is normal.

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 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 dφ < 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 the requirement d ( T ( x ), T ( y )) < d ( x, y ) for all unequal x and y is in general not enough to ensure the existence of a fixed point, as is shown by the map T: < nowiki >

( 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 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 " d " is made more distinctively different from " b " than is usual in standard typefaces ( which is possible since in the I. T. A.

Note that T is a function of p alone, while V is a function of q alone.