Note that with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

Note that the rules to move-up or pull-down the a, b, or c indexes are trivial, (+......+), so that f < sup > abc </ sup >

Note: Call set-up time is the summation of: ( a ) call request time — the time from initiation of a calling signal to the delivery to the caller of a proceed-to-select signal ; ( b ) selection time — the time from the delivery of the proceed-to-select signal until all the selection signals have been transmitted ; and ( c ) post selection time — the time from the end of the transmission of the selection signals until the delivery of the call-connected signal to the originating terminal.

Note 2: A data transmission circuit may transfer information in ( a ) one direction only, ( b ) either direction but one way at a time, or ( c ) both directions simultaneously.

Note 1: Compared to tactical communications, long-haul communications are characterized by ( a ) higher levels of users, such as the National Command Authority, ( b ) more stringent performance requirements, such as higher quality circuits, ( c ) longer distances between users, including world wide distances, ( d ) higher traffic volumes and densities, ( e ) larger switches and trunk cross sections, and ( f ) fixed and recoverable assets.

Note: Net operations ( a ) allow participants to conduct ordered conferences among participants who usually have common information needs or related functions to perform, ( b ) are characterized by adherence to standard formats and procedures, and ( c ) are responsive to a common supervisory station, called the " net control station ", which permits access to the net and maintains net operational discipline.

: Note: If a = b, then a / b = 1 and b / a = 1

Note that the constants a, b, IP have different values under each of these conditions.

:: See Committee Note to Interim Rule 8001 ( f ) (" Given the short time limit to file the petition with the circuit clerk, subdivision ( f )( 1 ) provides that entry of a certification on the docket does not occur until an effective appeal is taken under Rule 8003 ( a ) or ( b ).

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 when P < sub > a </ sub > was blocked by P < sub > b </ sub >, the upstream node could not transmit any more packets downstream.

Note that can be of a varying number of bits, and is specifically only b bits for Rice code,

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: symmetry is not the exact opposite of antisymmetry ( aRb and bRa implies b = a ).

Note that quadratic functions, such as in the one variable case, are not quadratic forms, as they are typically not homogeneous ( unless b and c are both 0 ).

* Note b: Lehe at the time of her birth was an independent municipality.

*< cite id =" fn_b "> Note b :</ cite > Satter ( 2007 ) " note that it tends to turn their feces reddish in color "

Note: in the code above, an immediate predecessor of node n is any node from which control is transferred to node n, and doms ( b ) is the node that immediately dominates node b ( a singleton set ).

Pointer a pointing to the memory address associated with variable b. Note that in this particular diagram, the computing architecture uses the same address space and # Formal_description | data primitive for both pointers and non-pointers ; this need not be the case.

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 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 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.

( 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 that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.

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 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: Some older operating systems may handle such values incorrectly ( i. e., signed instead of unsigned ), which would make it impossible to access files larger than 2 GB in size.

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 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.

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.

Note that a sample of random variables ( i. e. a set of measurable functions ) must not be confused with the realizations of these variables ( which are the values that these random variables take, formally called random variates ).

Note, however, that the converse is not true in general, i. e. zero skewness does not imply that the mean is equal to the median.

Note that ω < sup > 2 </ sup > = 0 ( i. e., ω is nilpotent of order 2 ), and moreover, for all.

Note that the fronted variant caused by umlaut was originally allophonic ( i. e. a variant sound automatically predictable due to the context ), but later became phonemic ( a separate sound in its own right ) when the context was lost but the variant sound remained.

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 that the gain of momentum of a rocket ( including fuel ) per unit time is not equal to the thrust, because the momentum that the fuel has while in the rocket has to be subtracted to the extent that it is used, i. e., the gain of momentum of a rocket per unit time is equal to the thrust, minus the velocity of the rocket multiplied by the amount of fuel used per unit time.

Note: In DSB-RC transmission, the carrier is usually transmitted at a level suitable for use as a reference by the receiver, except for the case in which it is reduced to the minimum practical level, i. e. the carrier is suppressed.

Note: off-hook originally referred to the condition that prevailed when telephones had a separate earpiece ( i. e., receiver ), which hung from its switchhook until the user wished to activate it.

Note: on-hook originally referred to the storage of an idle telephone receiver, i. e., separate earpiece, on a switchhook.

Note that with this definition, unlike SNR, a SINAD reading can never be less than 1 ( i. e. it is always positive when quoted in dB ).

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

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 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 how the equation above reduces to that of the univariate normal distribution if is a matrix ( i. e. a real number ).