( Note on numbering: Pope Benedict X is now considered an antipope.

( Note on numbering: Pope Boniface VII is now considered an antipope.

Note the reverse numbering order.

Note that some sources switch the numbering of the second and third theorems.

Note on numbering of popes: There has never been a Pope Martin II or Pope Martin III.

Note also that the male children within a single nuclear family need not bear sequential numbers, as all members of the larger family use a common numbering system.

Note: Exits numbers increase from north to south, the opposite of the standard Interstate numbering scheme.

Note the numbering ; these units were intended to be shared with the 1350 system.

Note: As of February 2006 new letter classes will be used in conjunction with the new horsepower based numbering system ( The Z on the end of some class letters refers to locomotives fitted with ZTR ).

Note that it is often rational to improve a system in an order that is " non-optimal " in this sense, given that some improvements are more difficult or consuming of development time than others.

Note that this is before the effects of round-off error are taken into account ; conditioning is a property of the matrix, not the algorithm or floating point accuracy of the computer used to solve the corresponding system.

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

Note that positions on a surface in navigation use latitude and longitude in a similar two dimensional system.

Note however that working with the current two form itself and the exterior derivative is usually easier than working with the vector field and divergence, because unlike the divergence, the exterior derivative commutes with a change of ( curvilinear ) coordinate system.

Note that HDLC operates as a statistical multiplexing system.

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

Methods PUT and DELETE are defined to be idempotent, meaning that multiple identical requests should have the same effect as a single request ( Note that idempotence refers to the state of the system after the request has completed, so while the action the server takes ( e. g. deleting a record ) or the response code it returns may be different on subsequent requests, the system state will be the same every time ).

Note: The head of state in a " presidential " system may not actually hold the title of " president "-the name of the system refers to any head of state who actually governs and is independent of the legislature.

Note that is positive while is negative ; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot ( high-entropy ) system to a cold ( low-entropy one ), decreasing the entropy of the heat source and increasing that of the heat sink.

Note that round trip latency excludes the amount of time that a destination system spends processing the packet.

Note that from the perspective of the smaller-mass object — from the moon, in the preceding example — a spacecraft might appear to orbit in an irregular path about the or point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass ( or more precisely, all of the objects are in orbit around the barycenter of the system ); they simply have overlapping orbital paths.

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 a measurement of a qubit state entangled with another quantum system transforms a pure state into a mixed state.

Note also that the oar can be used to provide a drag force ( a force acting against the forward motion ) when the system is brought to rest.

Note that using a hierarchical system like this ( assuming it is done carefully ) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence.

Note: A seven-official system was not used until the 1978 season.

Note that a system need not include source code derived in any way from AT & T Unix to meet the specification.

Note this publication predated the modern pinyin transliteration system

Note that, in a linear time-invariant system, the input frequency has not changed, only the amplitude and the phase angle of the sinusoid has been changed by the system.

Note that when a T-carrier system is used as in North America, robbed bit signaling can mean that a DS0 channel carried over that system is not an error-free bit-stream.

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 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 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: 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.