Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, the Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state.

Matthew Kapell, a historian and anthropologist, examined this re-writing in his essay, " Mack Reynolds ' Avoidance of his own Eighteenth Brumaire: A Note of Caution for Would-Be Utopians ".

Note: except where noted the following are based on Quarterly Report of November 4, 1868 from Brevet Major General J. J. Reynolds to Secretary of War

Note the freely moving airborne water droplets, a phenomenon typical of high Reynolds number flows ; the intricate non-spherical shapes of the droplets show that the Weber number is high.

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: 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 this case in this example implies that the user was next to the solid object, and not inside it.

Note that the color red is an objective property of an object.

Note that the concept of an indirect object may be rendered by a prepositional phrase.

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.

The following example of an ASP page with VBScript displays the current time in 24-hour format ( Note that an '=' sign occurring after a context switch (<%) is short-hand for a call to Write () method of the Response object ), but it is also used as the default script for error messages with the windows operating systems.

Note: A managed object may represent a physical entity, a network service, or an abstraction of a resource that exists independently of its use in management.

Note that, for conciseness, this class diagram only shows the class relations for creating one type of object.

Note: this article concerns the discipline of intellectual history, and not its object, the whole span of human thought since the invention of writing.

Note that because a nullary biproduct will be both terminal ( a nullary product ) and coterminal ( a nullary coproduct ), it will in fact be a zero object.

Note that the zero object is the trivial group.

Note also that this category does not have a zero object.

Note that this does not depend on how large the orbiting object is, but only on the ratio of densities.

Note that the zero morphism in item 3 can be identified as the identity element of the hom-set Hom ( A, B ), which is an abelian group by item 1 ; or as the unique morphism A → O → B, where O is a zero object, guaranteed to exist by item 2.

Note that the verb " see " can often be used instead of " call ": " Bob saw Carol's bet ", although the latter can also be used with the bettor as the object: " I'll see you " means ' I will call your bet '.

Note that in turbulent motion, where is the velocity of turbulent cells relative to the mean gas motion, and is the size of the largest turbulent cells, which is estimated as and, where is the Keplerian orbital angular velocity, is the radial distance from the central object of mass.

Note that in many concrete contexts, one would refer to the object K as the " kernel ", rather than the morphism k.

Note that using a separate object for each invocation of a command is also an example of the chain of responsibility pattern.

Note that the meaning of the verb can be affected by the presence or absence of an object.

Note that the reference is to the shared Point and not to the SurveyMonument, since any feature object can have more than one geometry object property.

Note that when using the Point Profile, the only geometry object is the '< gml: Point >' object.

* A cogenerator is an object C such that for every nonzero object H there exists a nonzero morphism f: H → C. ( Note the reversed order ).