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.

( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.

Note that the chaotic behavior of complex systems is not the issue.

Note that ƒ cannot be extended to a homomorphism of rings ( from the complex numbers to the real numbers ), since it does not preserve addition:

Note that only the step of substrate unfolding requires energy from ATP hydrolysis, while ATP-binding alone can support all the other steps required for protein degradation ( e. g., complex assembly, gate opening, translocation, and proteolysis ).

Note that the waves shown here are real for illustrative purposes only whereas, in quantum mechanics the wave function is generally complex.

:: Note: The physical fully connected mesh topology is generally too costly and complex for practical networks, although the topology is used when there are only a small number of nodes to be interconnected ( see Combinatorial explosion ).

Note that when they are considered within the complex plane the Gaussian integers may be seen to constitute the 2-dimensional integer lattice.

The Julia set of a function ƒ is commonly denoted J ( ƒ ), and the Fatou set is denoted F ( ƒ ).< ref > Note that for other areas of mathematics the notation can also represent the Jacobian matrix of a real valued mapping between smooth manifolds .</ ref > These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.

( Note that this differentiability is in the sense of real variables ; compare complex derivatives below.

Note the fact that the set of points mapped into any hyperplane can be quite convoluted as a result, allowing much more complex discrimination between sets which are not convex at all in the original space.

Note that this correction method does not incorporate how to handle complex values of or.

Note that the real part and imaginary part are both real numbers, but complex numbers are buried in the expressions.

Note the bulk of the complex is in fact ncRNA.

The star of S ( denoted St S ) is the set of all simplices in K that have any faces in S. ( Note that the star is generally not a simplicial complex itself ).

Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no effect at all.

Note that any matrix obtained by multiplying by a complex scalar λ determines the same transformation, so a Möbius transformation determines its matrix only up to scalar multiples.

Note however that it is very hard to decide whether a complex manifold is kähler or not.

Let k be a field and L and K be two extensions of k. The compositum, denoted KL is defined to be where the right-hand side denotes the extension generated by K and L. Note that this assumes some field containing both K and L. Either one starts in a situation where such a common over-field is easy to identify ( for example if K and L are both subfields of the complex numbers ); or one proves a result that allows one to place both K and L ( as isomorphic copies ) in some large enough field.

Note the characteristic delta wave ( above the blue bar ), the short PR interval ( red bar ) of 0. 08 seconds, and the long QRS complex ( green ) at 0. 12 seconds.

Note that over the complex numbers factors as and is degenerate because reducible, while defines a non-degenerate curve, an ellipse / hyperbola ( these are not distinct over the complex numbers, because there is no sense of positive or negative ).

Note that if R is a finite-dimensional simple algebra over a division ring E, D need not be contained in E. For example, matrix rings over the complex numbers are finite-dimensional simple algebras over the real numbers.

Note that although the function f has derivatives of all orders over the real line, the analytic continuation of f from the positive half-line x > 0 to the complex plane, that is, the function

Weierstrass P function defined over a subset of the complex plane using a standard visualization technique in which white corresponds to a pole, black to a zero, and maximal saturation to Note the regular lattice of poles, and two interleaving lattices of zeros.