Note: Every permutation over a set with k elements is a cyclic permutation of definition type 2 if and only if it is a cyclic permutation of definition type 1 with gcd ( k, offset )

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

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 this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.

Note that Q ( x, y ) is simply replaced by.

Note that the bilinearity and alternating properties imply anticommutativity, i. e., for all elements x, y in, while anticommutativity only implies the alternating property if the field's characteristic is not 2.

Note that the terms < tt > x </ tt > and < tt > y </ tt > aren't alpha-equivalent, because they are not bound in a lambda abstraction.

Note that the example net given above on the neighborhood system of a point x does indeed converge to x according to this definition.

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.

The tree is rotated on the edge joining p with its parent g, then rotated on the edge joining x with p. Note that zig-zig steps are the only thing that differentiate splay trees from the rotate to root method introduced by Allen and Munro prior to the introduction of splay trees.

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.

Note that in any font the glyph of " x " is not exactly the same as one of the multiplication sign.

Note: 2. x / 3. x ( for Series 600 / 800 ) were developed in parallel with 5. x / 6. x ( for Series 200 / 300 / 400 ), so, for example, 3. x was really contemporary with 6. x.

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 there are N independent eigenvectors ; a unitary matrix is never defective.

Note that we have to restrict the sum to ordered values of m < sub > 1 </ sub >, ..., m < sub > N </ sub > to ensure that we do not count each multi-particle state more than once.

Note how sib is displaced by the recombination event from the N extended P < sub > L </ sub > promoter open reading frame.

: Note: The label N will be used to denote the current node ( colored red ).

Note that s < sub > 0 </ sub > is now the sum of the weights and not the number of samples N.

Note that if N is itself prime, i. e., there is no such prime F ≠ N, then some event will prevent the execution of step 3 that receives the value F from the future.

Note, however, that the DCT-I is not defined for N less than 2.

Note that although s and S are infinite, this works for finite matrices by only considering Stirling numbers up to some number N.

Note that R might not be a subgroup, let alone a normal subgroup of F < sub > S </ sub >, so we cannot take a quotient by R. The solution is to take the normal closure N of R in F < sub > S </ sub >.

Note that N < sub > 2 </ sub >' s East output VC will specify that it is reserved by the North input VC.

Note that N = R at the equator:

* Application Note Application Note ( in engineering ) most often seen as A. N.

Note that this cube would contain no such subgraph if, for example, the bottom edge in the present subgraph were replaced by a blue edge – thus proving by counterexample that N * > 3.

Note, however, that PFA can be combined with mixed-radix Cooley – Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors.

Note that this is a Belgian law and is different from the International Criminal Court, which is a treaty body to try war crimes, and also different from the International Court of Justice, which is a U. N. body to settle disputes between countries.

Note that this implies that M and N must have the same dimension at p.

The structure of the ring can be analysed by considering all ways of embedding both K and L in some field extension of N. Note that the construction here assumes the common subfield N ; but does not assume a priori that K and L are subfields of some field M ( thus getting round the caveats about constructing a compositum field ).

Note that X is also a Kaprekar number for base b < sup > n </ sup >, for this specific choice of n. More narrowly, we can define the set K ( N ) for a given integer N as the set of integers X for which

Note the very strong and crucial hypothesis that f maps the fundamental class of M to the fundamental class of N. Naturality does not hold for an arbitrary continuous map f, since in general f < sup >∗</ sup > is not an injection on cohomology.

Note that if f is already unstable ( with respect to D ), then r ( f, D )= 0 ( as long as C contains zero ).

path from vertex A to vertex i. Note that d ( A )=

Note that it prohibits referrals under either condition ( 1 ) or condition ( 2 ).

Quite other feelings are evidenced by this style: Af Note the drop to pitch 1 ( the lowest ) on mother with no rise at the end of the sentence ; ;

( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

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

1. 975 million ( 2008 ) Note: Excluding Nicaraguans living in the country

An empirical or an a posteriori concept is a general representation ( Vorstellung ) or non-specific thought of that which is common to several specific perceived objects ( Logic, I, 1., § 1, Note 1 )

Note: Version 1. 6 effectively coincided with the release of Valve Software's Steam content delivery system on September 12, 2003.

Note also that even in validating SGML or XML 1. 0 or XML 1. 1 parsers, the external entities referenced by an FPI and / or URI in declared notations are not retrieved automatically by the parsers themselves.

Note that if the operations are performed in a colour space where γ is not equal to 1 then the operation will lead to non-linear effects which can potentially be seen as aliasing artifacts ( or ' jaggies ') along sharp edges in the matte.

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

Cultured skin and prostate cancer cells showed significant mortality ( compared to nonmalignant cells ) when treated with a combination of quercetin and ultrasound Note that ultrasound also promotes topical absorption by up to 1, 000 times, making the use of topical quercetin and ultrasound wands an interesting proposition.

By Rule 1. 04, Note ( a ), all parks built after 1958 have been required to have foul lines at least long and a center-field fence at least from home plate.

Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i. e..

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: 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 Karachentsev divides this group into two subgroups centered around IC 342 and Maffei 1.