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.

In 1822, Charles Babbage proposed the use of such a machine in a paper to the Royal Astronomical Society on 14 June entitled " Note on the application of machinery to the computation of astronomical and mathematical tables ".

* 1822 – Charles Babbage proposes a difference engine in a paper to the Royal Astronomical Society entitled " Note on the application of machinery to the computation of astronomical and mathematical tables ".

( 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 that in the case of an astronomical crescent, such as the moon observed in the sky, the outer arc will be 180 ° ( a half-circle as previously mentioned ), while the Islamic crescent symbol ( Arabic هلال hilāl ) is often shown with an outer arc significantly greater than 180 ° ( as seen in the illustrations below ).

Note of Guillaume Postel on the Arabic astronomical manuscript of al-Kharaqī, Muntahā al-idrāk fī taqāsīm al-aflāk (" The Ultimate Grasp of the Divisions of Spheres "), 1536, Constantinople

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 in the case of an astronomical crescent, such as the moon observed in the sky, the outer arc will be 180 ° ( a half-circle as previously mentioned ), while the Islamic crescent symbol ( Arabic هلال hilāl ) is generally shown with an outer arc significantly greater than 180 ° ( as seen in the illustrations here ).

* < cite id =" fn_c "> Note c :</ cite > That Europa and to a lesser extent Titan ( respectively, 3. 5 and 8 astronomical units outside the Sun ’ s putative habitable zone ) are considered prime extraterrestrial possibilities underscores the problematic nature of the HZ criterion.

Note that, because a name translated to an address, which included a socket number as well as a node number, a name in AppleTalk mapped directly to a service being provided by a machine, which was entirely separate from the name of the machine itself.

Note that the number of points used in braille computing is not 6, but 8, as this allows the user, among other things, to distinguish between small and capital letters, as well as identify the position of the cursor.

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 reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides.

Note also that until well into the 20th Century, rather than an official readying the ball for scrimmage, the side entitled to the snap had complete custody of the ball and could snap it from the required spot at any time ; for instance, a tackled ball carrier might feign injury, then suddenly snap the ball while recumbent, there being no stance requirement yet.

( Note, however, that the term " powder magazine ", a store for gunpowder, as e. g. in the town of Williamsburg, Virginia, restored to its colonial form, would be well understood by current English speakers, though recognized as an archaicism.

Note that with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

Note that many of the basic chemical compounds used as detergents ( example: calcium sulfonate ) serve the purpose of the first seven items in the list as well.

Note the yellow main charge wrapped around a red explosive booster | booster charge, and the secondary fuze well on the side of the mine designed for an anti-handling device

Note that the Kuchurhan crossing as well as the Tighina – Tiraspol – Kuchurhan segment are under the control of the Transnistrian separatist authorities, the circulation of trains on the route depending on the level of political tensions between the separatists and the Government of Moldova.

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 as well that points A and B on the rotor and e-shaft turn at different speed, point B moves 3 times faster than point A, so that one full orbit of the rotor equates to 3 turns of the e-shaft.

( Note: the population figures are estimates by historians ; they do not include the native tribes outside the jurisdiction of the colonies ; they do include Natives living under colonial control, as well as slaves and indentured servants.

Note that the definition is somewhat ambiguous because the user of a program can be another program and, if the latter is a portion of the set of program that is required to be interoperable, it might well be that it does need to have knowledge of the characteristics of other units.

Note, if the west hand happens to hold a small spade instead of the jack, both the LTC as well as the NLTC count would remain unchanged, whilst the chance of making 13 tricks falls to 67 %.

Note that molten salts can be electrolytes as well.

Note that the Apple ISO 9660 Extensions do not technically follow the SUSP standard ; however the basic structure of the AA and AB fields defined by Apple are forward compatible with SUSP ; so that, with care, a volume can use both Apple extensions as well as RRIP extensions.

Note that there is ongoing controversy in Canada, as in other countries, about inclusion of expensive drugs and discrepancies in their availability, as well as in what if any provisions are made for allowing medications not yet approved to be administered under " exceptional drug " provisions.

Note that standalone ICDs do not have any pacemaker functions, but they can be combined with a pacemaker, and modern versions also have advanced features such as anti-tachycardic pacing as well as synchronized cardioversion.

12 to General Sir H. Rawlinson, 16 June 1916 Stating the Objectives ') and that preparations should be made for an advance of to Bapaume should German resistance crumble, " If the first attack goes well every effort must be made to develop the success to the utmost by firstly opening a way for our cavalry and then as quickly as possible pushing the cavalry through to seize Bapaume ...." ( Note O. A. D.

* 1938: Spawn of the North-Gordon Jennings, assisted by Jan Domela, Dev Jennings, Irmin Roberts and Art Smith ; transparencies by Farciot Edouart, assisted by Loyal Griggs ( Note: Award also given to sound effects artists as well )

Note that the MPI libraries and the HPF runtimes are optimized to perform as well as possible both in the hybrid and flat parallelization.

Note well that if a culture did include one's clan name in one's name and routinely handed it down to all children in the descent group then it would automatically be the family name or surname for one's descent group ( as well as for all other descent groups in one's clan ).

Monk's recordings for Blue Note between 1947 and 1952 did not sell well, but have since come to be regarded as amongst the most important of the bebop era.