Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

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, although rarely occurring, if a runner tags and advances from second base ( or, theoretically, from first base ) all the way to home and scores ( without an intervening error ) the batter is credited with a sacrifice fly.

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 that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.

Note that the validity of a conditional proof does not require that the CPA is actually true, only that if it is true it leads to the consequent.

( Note that, technically, Wisda's damages would be the lost profits only — if Wisda would have had $ 35 per hour in wages, materials and other expenses, its actual damages are only $ 15 per hour

Note that this document type declaration can only appear after the optional XML declaration, and before the document body, if the document syntax conforms to XML.

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.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

Note, however, that if the MSE is relatively low, then the arrows are likely more highly clustered ( than highly dispersed ).

Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Note that these drugs do not treat hyperthyroidism or any of its long-term effects if left untreated, but, rather, they treat or reduce only symptoms of the condition.

Note: if the product resulting from the labor process is homogeneous ( all similar in quality and traits, for example, all cups of coffee ) then the value of the period ’ s product can be divided by the total number of items ( use-values ) produced to derive the unit value of each item.

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: 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: if 19a or 19b is answered " NO " that ends the due process analysis-the totality of circumstances test is not reached )

Note that if you graph the functions the axes represent quantities.

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.

Note that the non-inverting input of the operational amplifier will need a path for DC to ground ; if the signal source might not give this, or if that source requires a given load impedance, the circuit will require another resistor — from input to ground.

* * Note: if submerged reefs are included then Velasco reef is Palau's northern-most point

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 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 we have omitted the Π < sub > j </ sub > n < sub > j </ sub > term, because each single-particle state can appear only once in a fermionic state.

* Silver ' n Brass ( Blue Note, 1975 )

* Silver ' n Wood ( Blue Note, 1976 )

* Silver ' n Voices ( Blue Note, 1976 )

* Silver ' n Percussion ( Blue Note, 1977 )

* Silver ' n Strings Play the Music of the Spheres ( Blue Note, 1978 )

Sometimes his name is turned into the Frankish name Rodolf ( us ) or Radulf ( us ) or the French Raoul, that are derived from it .< ref group =" Note "> Rou is the result of a series of French regular phonetic changes from Hrólfr > Rolf > Rouf to Rou ( see Lepelley 15-16 ) and Norman names in-ouf and-ou ( t ): I ( n ) gouf and Ygout < Old Norse Ingulfr / Ingólfr ( Old Danish Ingulf ).

Note that the trace is only defined for a square matrix ( i. e., n × n ).

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 the definition of PSPACE-completeness is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.

Note that, if the language is infinite, the enumerating algorithm provided can be chosen so that it avoids repetitions, since we can test whether the string produced for number n is " already " produced for a number which is less than n. If it already is produced, use the output for input n + 1 instead ( recursively ), but again, test whether it is " new ".

Note that for large enough n, only the first and second terms are not converging to zero, so we get an asymptotic expression:, as.

( 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 that the leading coefficient of the polynomial bx − a is the integer b. As another special case, the square root √ n of a non-negative integer n is an algebraic integer, and so is irrational unless n is a perfect square.

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 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.