Note however that both in algebra and model theory the binary operations considered are defined on all of S × S.

Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.

* Note: Contains both the original version ( Japanese audio with English subtitles only ) and the edited G version ( English audio only ).

* Note: Contains both the Japanese version and uncut English dub and audio commentary with Steve Ryfle and Stuart Galbraith IV.

Note: The above definition of group velocity is only useful for wavepackets, which is a pulse that is localized in both real space and frequency space.

) Note that not all airports are assigned codes in both systems — for example, airports that do not have airline service may not need an IATA code.

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

Note that there is no contradiction among these two results ; both computations are correct.

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: the president is both the chief of state and head of government

On April 23, 1998, the Ministry of Foreign Affairs of the Republic of the Marshall Islands issued an official Circular Note, denouncing representatives of both " EnenKio " and " Melchizedek " for making fraudulent representations.

Note the coats of arms both bear on their clothing — Malcolm wears the Lion of Scotland, which historically was not used until the time of his great-grandson William I of Scotland | William the Lion ; Margaret wears the supposed arms of Edward the Confessor, her grand-uncle, although the arms were in fact concocted in the later Middle Ages.

( Note that in both of those examples those quantities would be maximized rather than minimized ).

( Note: Lava flows refer to both actively flowing lava and the solidified landforms they produce.

Note the intersection of the two circles — the distinction between short a, i and u is made by both speakers, but Arabic lacks the mid articulation of short vowels, while Hebrew lacks the distinction of vowel length.

Note that both " persons and estates " are to be protected from the arbitrary power of any magistrate, inclusive of the " power and will of a legislator.

Note that in both three-and four-level lasers, the energy of the pumping transition is greater than that of the laser transition.

Note that an enzyme that displays both PLA1 and PLA2 activities is called a Phospholipase B.

Note that both arrows point in the same direction.

Note that the letter ' h ' in both the transcription and transliteration forms should logically be omitted.

Note that only two sequences of moves by O ( both starting with center, top-right, left-mid ) lead to a draw, with the remaining sequences leading to wins from X.

Note that in this equation, both force and displacement are vector quantities.

Note that both the limit and the colimit functors are covariant functors.

Note that the weighted ski is on-edge and forming an arc ; if both legs were parallel the skis would begin to smoothly carve.

Note 2: A data transmission circuit may transfer information in ( a ) one direction only, ( b ) either direction but one way at a time, or ( c ) both directions simultaneously.

Note another piece of wood six inches wide is fastened to the transom between these pieces.

Note extent of these interests and how available they will be for the public to enjoy.

Note however, that the allemandes, that occur in these suites do not correspond to a French dance from the same period.

( Note that prior to the 1995 renovations, some of these houses, particularly North and Caven, ' traditionally ' sat elsewhere )

: Note: Individual casinos may pay some of these bets at different payout ratios than those listed below.

Note that these should not be called concentrations.

Note, not all CUC members like this playful reading and so when these people write the abbreviation they leave out the star (*), just writing UU instead.

Note that any valid SGML or XML document that references an external subset in its DTD, or whose body contains references to parsed external entities declared in its DTD ( including those declared within its internal subset ), may only be partially parsed but cannot be fully validated by validating SGML or XML parsers in their standalone mode ( this means that these validating parsers will not attempt to retrieve these external entities, and their replacement text will not be accessible ).

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 that these categories reflect levels of enhancement not clarity.

Note: Many of the essays found in these works have been individually translated and can be found in the English collections.

Note that these drugs do not treat hyperthyroidism or any of its long-term effects if left untreated, but, rather, they treat or reduce only symptoms of the condition.

Note that these concerns have nothing to do with the importance of messages.

Note that these arguments may indeed have validity, but they require some independent justification of the connection between their terms: otherwise the argument ( as a logical tool ) remains fallacious.

Note that these efficiencies are for the LED chip only, held at low temperature in a lab.

( Note that these relations are true for theoretical and experimental values, but not between experimental and theoretical values.

Note that not all of these countries maintain embassies in the country

Note that these treatments need to be prescribed and monitored carefully to avoid harmful side-effects such as neuroleptic malignant syndrome with the antipsychotic medications.

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 these equations are for fissions caused by slow-moving ( thermal ) neutrons.

Note this does not restrict dormant forms of life to these environments, so this argument only contradicts the widest interpretation of panspermia — that life is ongoing and is spread across many different environments throughout the Universe — and presupposes that any life needs those elements, which the proponents of alternative biochemistries do not consider certain.

Note that most of these verses do not distinguish between the conditional election ( Arminian ) and unconditional election ( Calvinist ), but are simply evidence of some type of election.

Note that few database servers implement the entire SQL standard and in particular do not allow some of these deviations.