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Page "Fundamental theorem of arithmetic" ¶ 10
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Note and factors
Note that as an income-based measure of poverty, this omits the effect of some other factors that may affect economic wellbeing, such as the availability of free health care and education.
Note the factors of two before ψ and χ corresponding respectively to the facts that any polarization ellipse is indistinguishable from one rotated by 180 °, or one with the semi-axis lengths swapped accompanied by a 90 ° rotation.
Note, however, that they lost most of their genetic diversity thousands of years ago ( see the beginning of this article ), and yet seem to have only been in decline in the last century or so, suggesting factors other than genetics are mainly responsible.
Note that what affects the value of for different values of is only the factors and, which both appear in the numerator, and hence the posterior probability is proportional to both.
Note that unlike the other two formulae ( the Euler product and the divisor sum ) this one does not require knowing the factors of n.
Note that ratios can be reduced ( as fractions are ) by dividing each quantity by the common factors of all the quantities.
* Scream 3 ( cameo ) ( Note: While their appearance in Scream 3 suggests that the Scream series and the View Askewniverse are on the same plane of existence, other factors may contradict this ; in the first Scream film, a VHS tape of Clerks is shown in the background ; also, in Jay and Silent Bob Strike Back, Jay and Silent Bob see the filming of the then fictional Scream 4.
( Note that the Cauchy distribution and this spectrum differ by scale factors.
( Note that other factors can restrict the places to which a boat can reach: for instance, boats with a high cabin top, or with insufficient tumblehome may not be able to fit into Standedge Tunnel at the summit of the Huddersfield Narrow Canal ).
: Note that the order of the factors reverses.
Note that all these generalizations are multiplicative only if the factors are reversed:
Note, however, that because the quaternions are not commutative, the order of the factors in the multiplication formula becomes important — if the last factor in the multiplication formula were rather than
Note: Early studies indicated the opposite effect, but these were later found to be inaccurate due to additional complicating factors.
Note that this tells us nothing about the factors of 221 ( which are 13 and 17 ).
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 definition is more stringent than simply requiring the integer to have exactly three prime factors ; e. g. 60 = 2 < sup > 2 </ sup > × 3 × 5 has exactly 3 prime factors, but is not sphenic.
Note that for any orthogonal matrix if we set and, the criteria for being factors and factor loadings still hold.
Note that the digits of the factors 21 and 60 can be found, in some scrambled order, in 1260.
( Note 33 is the 8th composite number to descend into the prime number 3, the others outside of this sequence being 30, 26, 16, 12 ) Since 33 is a semiprime with both its prime factors being Gaussian primes, 33 is a Blum integer.
Note that since is of degree 4, this conclusion could not have been established by only checking that has no rational roots ( which eliminates possible factors of degree 1 ), since a decomposition into two quadratic factors could also be possible.
Note that over the complex numbers factors as and is degenerate because reducible, while defines a non-degenerate curve, an ellipse / hyperbola ( these are not distinct over the complex numbers, because there is no sense of positive or negative ).
Note that this location adjustment applies only to the WP factor and not the OWP and OOWP factors.

Note and p
Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.
Note that we need not know the value of p, for the experiment to be binomial.
#* 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 the difference in the style of the subscripts: k and p are abbreviations of the words kinetic and potential, whereas p ( italic ) is the symbol for the physical quantity pressure rather than an abbreviation of the word " pressure ".
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 S is at least the length of the meridian from p to q:
Note that the bef2c compiler is not correct since it does not handle either ' p ' or string mode, but it would not be impossible to make it do so ( although the C language might not be well-suited for this ).
" Note " and " Part " are used to refer to footnotes and parts ( when parts are specifically designed ) within the same piece ; " p ." and " pp. " are used to refer to other pages within the same piece.
( Note that the conditions under which the cancellation law holds are quite strict, and this explains why Fermat's little theorem demands that p be a prime in order to make a general case for all n. For example, 2 × 2 ≡ 2 × 5 ( mod 6 ), but we cannot conclude that 2 ≡ 5 ( mod 6 ), since 6 is not prime.
Note the crucial feature: the unknown parameter p interacts with the data x only via the statistic T ( x )
Note that T is a function of p alone, while V is a function of q alone.
:• Note: Four of the dedicatees ( Turczyński, Gruenberg, Sirota, Closson ) were master class pupils of Busoni in Vienna, Jul 1908 ( Beaumont, 1987, p. 91 ), while Blanchet had been a pupil at a master class in Weimar, Jul-Sep, 1899 ( Dent ).
Note that both the probabilities p < sub > i </ sub > and the regression coefficients are unobserved, and the means of determining them is not part of the model itself.
Note that Aut ( p ) and are naturally isomorphic in this case ( as a group is always naturally isomorphic to its opposite through ).
Fear and Trembling Note p. 78
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 that this implies that M and N must have the same dimension at p.
" ( p. 85 ) Note that Bill Runs Above did not mention the lyrics of the songs, and while they are no doubt important, most lyrics of most songs employ vocables, syllable sounds such as " ya ", " hey ", and " loi " ( p. 86 ).

Note and <
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.
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.

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