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

Note that the parameter t ( called the eccentric anomaly in astronomy ) is not the angle of with the X-axis.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

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 ).

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 for LZ77 compression such as gzip, this is much easier, as the problem reduces to " Is t in s ?".

Note for completeness that condition ( 1 ) fails: any map t: B → A must map every two-cycle to the identity because the map has to be a group homomorphism, while the order of a two-cycle is 2 which can not be divided by the order of the elements in A other than the identity element, which is 3 as A is the alternating subgroup of, or namely the cyclic group of order 3.

Note, that the right hand side only contains Ramsey numbers for c − 1 colours and 2 colours, and therefore exists and is a finite number t, by the inductive hypothesis.

Note the payoff of the latter portfolio is also S ( T )-K at time T, since our share bought for S ( t ) will be worth S ( T ) and the borrowed bonds will be worth K.

Note that when there are only two groups for the one-way ANOVA F-test, F = t < sup > 2 </ sup >

Note also that a factor consisting of a sum where both types of variables are involved ( e. g. a factor of the form ) cannot be factorized in this fashion ( except in some cases where occurring directly in an exponent ); this is why, for example, the Cauchy distribution and Student's t distribution are not exponential families.

Note: A ( t ) is the amount function and a ( t ) is the accumulation function.

:: Note: Mathew B. Brady's name contains a single " t ".

Note: t

Note that such s ( t ) is uniformly continuous, this together with the decay assumption on s, show that the series defining s < sub > P </ sub > converges uniformly to a continuous function.

From the up-tempo Latin groove of “ Evanly ” with its vocal out chorus ; the mid tempo swing of “ No Way LA ” & “ Ten Minutes To Twelve ”; the Lunceford-like band vocals on “ Stompin ’ @ The Savoy ” & “ It Don ’ t Mean a Thing ( If It Ain ’ t Got that Swing )”; to Hamilton ’ s vocalizing on “ Every Time I Smile ”; the pastoral melodic beauty of “ You ’ re Note Alone ”; the up-tempo funk of “ Black Eyed Peas ”; and the bossa funkiness of “ Foot Prints in the Sand ” with its starkly beautiful vocal out chorus-every track is like turning a page in a book that ’ s holding you on the edge of your seat, your rapt attention dying to know what ’ s next to be revealed.

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-is a long syllable, u a short syllable, and U either one long or two shorts:

Note the intersection of the two circles — the distinction between short a, i and u is made by both speakers, but Arabic lacks the mid articulation of short vowels, while Hebrew lacks the distinction of vowel length.

Note that u can only be given if linear, nondispersive and uniform materials are involved, i. e., if the constitutive relations can be written as

Note that some of these verbs share a kanji reading ( i, u, and ha ), and okurigana are conventionally picked to maximize these sharings.

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 such forms should logically keep the capital for the " genus " name — i. e., < u > H </ u > omo economicus rather than < u > h </ u > omo economicus.

">< u > Note :</ u > the spelling according to modern orthography could not be found and the meaning seems uncertain or lost .</ ref > a peak beyond La Plata Mountains.

Note that if the u < sup > 2 </ sup > term were replaced with u, the problem would be linear ( the exponential decay problem ).

Note that on the right-hand side, u is differentiated and v is integrated ; consequently it is useful to choose u as a function that simplifies when differentiated, and / or to choose v as a function that simplifies when integrated.

Note that the ( trivial ) copy function ' c ' is necessary because though the universal constructor ' u '

Note that there were no integral boundaries to transform, but in the last step we had to revert the original substitution u

Note that in this last sentence, the plurality of it (-) is obscured ; the meaning can be either I give < u > it </ u > to you all or I give < u > them </ u > to you all.