Note however that in a three dimensional flow, vorticity ( as measured by the volume integral of its square ) can be intensified when a vortex-line is extended — known as vortex stretching ( see say Batchelor, section 5. 2 ).

Note that though the ideal gas itself contains no additional energy, the compressed gas does exert an increased pressure.

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 " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

* Note: Botswana does not have a westernmost point as the western section is formed by the 22nd meridian of longitude east of Greenwich.

Note that the associative property does not hold for expressions that include non-linear operators, such as the antilinear time reversal operator in physics.

Note that traditional Berkeley DB also supports a Java API, but it does so via JNI and thus requires an installed native library.

* Note: technically Chad does not have an easternmost point, the northern section of the border being formed by the 24 ° of latitude

Note: in Greek, the term for " consul " is " ypatos ", which translates as " supreme one ", and hence does not necessarily imply a joint office.

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 in many cases, digital cable telephone service is separate from cable modem service being offered by many cable companies and does not rely on Internet Protocol ( IP ) traffic or the Internet.

Note that this does not require 100 % awareness from the onset of the data warehousing effort, no master plan is required upfront.

Note that a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.

( Note that anti-trust regulation does take into account cases when only large companies are viable because of the nature of an industry, but favors many participants over few, whenever possible.

Note that materialism does not necessarily imply egoism, as indicated by Karl Marx, and the many other materialists who espoused forms of collectivism.

( Note, chart does not include population statistics.

Note that this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.

Note that Reynolds does not object to the Marxist use of the term feudalism.

* * Note: Guinea does not have a northern-most point, this section of the border being formed by a straight horizontal line

* * Note: Guinea-Bissau does not have a northern-most point, the border here being formed by a straight horizontal line

Note that chair does not change form between " the chair is here " ( subject ) and " I saw the chair " ( direct object ), a distinction made by word order and context.

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 this " high temperature " approximation does not distinguish between fermions and bosons.

* * Note: Morocco does not have a southern-most point, the border being formed by a straight horizontal line

Note: In cases where the optical design of a microscope produces an appreciable lateral separation of the two beams we have the case of classical interference microscopy, which does not result in relief images, but can nevertheless be used for the quantitative determination of mass-thicknesses of microscopic objects.

( Note that while Mercury does allow impure functionality, it is not necessary in most software, and serves primarily as a way of calling foreign language code.

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, 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 2: The term " center " does not imply a physical location.

Note that when considering an antenna's directional pattern, " gain with respect to a dipole " does not imply a comparison of that antenna's gain in each direction to a dipole's gain in that direction.

Note that lack of credit does not imply plagiarism.

Note that cardinality does NOT imply direct measurability, in which Jevons did not believe.

Note: in non-medical contexts, the word " fistula " is often used to imply urogenital fistula

Note that empty cells do not imply that a particular language is lacking a word to describe the concept, but rather that the word for the concept in that language is formed from another stem and is not a cognate with the other words in the row.

Note that the validity of this alternative within this dilemma does not in any way imply that money can both exist and not exist.

Note, that the third axiom is actually redundant, because the second and fourth axioms imply is also an identity, and identities are unique.

Note that " ma " would technically imply a milliannum ( also called a milliyear in English usage ), a period of a thousandth of a year or about 8 hours.

Note also the diction used within the imagery: words like " forked " and " fallen " imply a kind of hell that he is trapped in.

Note that the unpaired electron does not imply charge-free radicals can be positively charged, negatively charged, or neutral.

Note that just because the Soumpasis can be fitted adequately to data does not necessarily imply that the assumptions are true and that diffusion dominates recovery.

Note that resetting test logic doesn't necessarily imply resetting anything else.

Note that these imply that

However, many DNS resolvers process a domain name that contains a dot in any position as being fully qualified < ref group = note > Note: On Unix-like systems, this is controlled by the option in the resolv. conf configuration file, specifying the number of dots ( default 1 ) recognized to imply a FQDN.

Note that this is an astronomical description of the precessional movement and the vernal equinox position in a given constellation may not imply the astrological meaning of an Age carrying the same name, as they ( ages and constellations ) only have an exact alignment in the " first point of Aries ", meaning once in each ca.

Note that the effective computability of these functions does not imply that they can be efficiently computed ( i. e. computed within a reasonable amount of time ).

Note that the above perfect forms refer to possibility, not permission ( although the second sense of might have might sometimes imply permission ).

Note, that as such, this does not imply that an increase in savings must lead directly to an increase in investment.

Note that current population genetic structure does not necessarily imply that the different current clusters / components found correspond to only one ancestral home per group.