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 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: Step ( in the description below ) is defined as: a transfer / change of weight to the opposite foot while hopping ( this is usually minimal ; almost more of a scoot than a literal hop ).

Note that this brain-in-a-vat argument conflates cyberspace with reality, while the more common descriptions of cyberspace contrast it with the " real world ".

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

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 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 19-year cycle is also close ( to somewhat more than half a day ) to 255 draconic months, so it is also an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses.

Note that some of these tasks have direct real-world applications, while others more commonly serve as subtasks that are used to aid in solving larger tasks.

Note that some languages have more such ambiguity than others.

Note that the following is a classical ( Newtonian ) analysis of orbital mechanics, which assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible.

Note: while the 741 was historically used in audio and other sensitive equipment, such use is now rare because of the improved noise performance of more modern op-amps.

Note that pot odds do not matter in this situation, because the factor here is whether it is more profitable to raise or call, rather than to call or fold.

Note that with this construction multiple preorders "" can give the same relation "<", so without more information, such as the equivalence relation, "" cannot be reconstructed from "<".

" ( Note: The original study showed that " error-free " code went from 70 % to 85 %; it may be more intuitive to call this a 50 % ( rather than 15 %) decrease of errors, from 30 % to 15 %.

Note that the set-theoretic union, in some contexts closely related to logical disjunction ( or ), is used here for sets of statements in such a way that it is more related to logical conjunction ( and ).

( Note that in SQL the heading is not always a set of column definitions as described above, because it is possible for a column to have no name and also for two or more columns to have the same name.

Note, however, that this type of signature is not related to electronic signatures or digital signatures, which are more technical in nature and not directly readable by human eyes.

( Note that when DAW published his first book he was able to obtain the " Superstar " imprint for it, resulting in other authors-many who had more than one Hugo-requesting the same and a great deal of discontent ).

Note that personal ( per capita ) income distribution, given in this table, is not exactly comparable with household income distribution, given in the previous table, because poor households tend to have more members.

Note that these numbers are one more than the formal ordinal numbers according to the isomorphic order, because these are equal to the number of earlier objects ( which corresponds to counting from zero ).

Note that the Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers ; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.

Note, however, that they pre-date the appearance of the Minaeans themselves, and, hence, are called now more appropriately as " Madhabic " rather than " Minaic ".

Note that the excreted droplet patently is not whole blood, being far more dilute ).

Note that in a few cases the accidental might change the note by more than a semitone: for example, if a G sharp is followed in the same measure by a G flat, the flat sign on the latter note means it will be two semitones lower than if no accidental were present.

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 )

The subgroup of generated by all commutators is called the derived group or the commutator subgroup of G. Note that one must consider the subgroup generated by the set of commutators because in general the set of commutators is not closed under the group operation.

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: this book contains very useful, information dense chapters on primate evolution in general, and human evolution in particular, including fossil history ).

To this plan both Britain and France gave a general assent, and the Andrássy Note was adopted as the basis of negotiations.

Note that, in general, the corresponding graphs may be cyclic graphs: preorders may have cycles in them.

( Note: Astronomy should not be confused with astrology, which assumes that people's destiny and human affairs in general are correlated to the apparent positions of astronomical objects in the sky -- although the two fields share a common origin, they are quite different ; astronomers embrace the scientific method, while astrologers do not.

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 much of history from 1800-1950 is often not reflected well in general parlance as they are overshadowed by the ' big three ', games on other subjects in this era are often referred to by the actual war they deal with.

Note, however, that unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time.

Note that the requirement d ( T ( x ), T ( y )) < d ( x, y ) for all unequal x and y is in general not enough to ensure the existence of a fixed point, as is shown by the map T: < nowiki >

Note that in common use the term convection may refer loosely to heat transfer by convection, as opposed to mass transfer by convection, or the convection process in general.

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 that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying " elements " of group – categories in general do not have elements to their objects.

Note, this general expression for total radiated power simplifies to the above expression for the specific case of acceleration parallel to velocity (), by noting that and.

( Note: " plebeian secession " was a tactic used by the Roman plebs of vacating a city entirely and leaving its ruling elite to fend for itself, thus an even more radical action than a " general strike ", yet unlike the latter term, it does not pertain to withholding labor within a wage-system.

Note that the fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that it is impossible to trisect all angles: for example, it is relatively straightforward to trisect a right angle ( that is, to construct an angle of measure 30 degrees ).

Note that this usage of the term linear is not the same as the above, because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity.

( 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 General Aviation Building ( GAB Terminal ) is used for general / non-commercial aviation or private jets.

( Note that some other algorithms may also output confidence values, but in general, only for probabilistic algorithms is this value mathematically grounded in probability theory.

Note however, that it is not uncommon to express aqueous concentrations — particularly in drinking-water reports intended for the general public — using parts-per notation ( 2. 1 ppm, 0. 8 ppb, etc.

Note that the above construction of the Galois group for a fifth degree polynomial only applies to the general polynomial, specific polynomials of the fifth degree may have different Galois groups with quite different properties, e. g. has a splitting field generated by a primitive 5th root of unity, and hence its Galois group is abelian and the equation itself solvable by radicals.