Note that when N = R, the map dφ < sub > x </ sub >: T < sub > x </ sub > M → R coincides with the usual notion of the differential of the function φ.

Note that this more general concept of boundedness does not correspond to a notion of " size ".

Note When applied to normed spaces, the definitions in this section coincide with the notion of reflexivity for normed spaces.

Note that x does not have to be an element of S. This concept profitably generalizes the notion of a limit and is the underpinning of concepts such as closed set and topological closure.

Note Hume's use of the word number in the ancient sense, to mean a set or collection of things rather than the common modern notion of " positive integer ".

Note: In SGA4, tome I, section 1, the notion of left ( right ) exact functors have been defined for general categories, and not just abelian ones.

Note that all 4 of these hypothetical Fredkin measuring devices assume some sort of weird notion of absolute space, time, and information that would depend upon the ' alternate-universe engine ' for any empirical validity.

Note that there are other notions of compactness in mathematics ; also, the term " finite " in its normal set theoretic meaning does not coincide with the order-theoretic notion of a " finite element ".

Note that this notion of ontology is different from ( and weaker than ) ontology as is sometimes understood in philosophy ; in our sense there is no claim that the expressions actually denote anything which exists physically or spatio-temporally ( to use W. Quine's formulation ).

Note that there is no notion of a group action in this sense.

Note from the earlier discussion of representation that both the Churchlands ' connectionist systems and Fodor's symbolic systems use this notion of computation.

Note, however, that while the notion of an association scheme generalizes the notion of a group, the notion of a commutative association scheme only generalizes the notion of a commutative group.

Note that the polarization direction is perpendicular to the wires ; the notion that waves " slip through " the gaps between the wires is incorrect.

Note that this expression indicates compositing C with all of the layers below it in one step and then blending all of the layers on top of it with the previous result to produce the final image in the second step.

Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.

Note the image of the Mozilla mascot, and the Mosaic logo in the top-right corner.

Note that E ( at 2f ) has an equal-size, real and inverted image ; I ( at f ) has its image at infinity ; and K ( at f / 2 ) has a double-size, virtual and upright image.

Note that the actual image ( be it 4: 3 or 16: 9 ) is always contained in the center 704 horizontal pixels of the digital frame, regardless of how many horizontal pixels ( 704 or 720 ) are used.

Note the correct layout of this type, in the image to the right.

( Note that the color differences in the image are introduced by limitations of the camera system.

( Note, however, that in multiprocessing systems, many processes may run off of, or share, the same reentrant program at the same location in memory — but each process is said to own its own image of the program.

Note the people in the lower-right corner of the image.

* Note that oncotic pressure is not illustrated in the image.

Note that E ( at 2f ) has an equal-size, real and inverted image ; I ( at f ) has its image at infinity ; and K ( at f / 2 ) has a double-size, virtual and upright image.

Note: Because the refresh rate has been slowed down by a factor of three, and the resolution is less than half that of typical interlaced video, the flicker in the simulated interlaced portions and also the visibility of the black lines in this image are exaggerated.

Note that with the cube ( see image ) the perimeter of the 2D drawing is a perfect regular hexagon: all the black lines are of equal length and all the cube's faces are the same area.

Comparison of a $ 5 Demand Note ( upper image ) and an 1862 issue $ 5 United States Note ( lower image ).

Note that strengthened negations may be compatible with weakened forms of AC.

Note that the RGB color may be premultiplied, hence saving the additional multiplication before RGB in the equation above.

Note that this expression is not well-defined for all time series or processes, because the variance may be zero ( for a constant process ) or infinite.

Note: Some web browsers may display the Hebrew text in this article in the opposite direction.

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

Note that orthography is not a good guide for identifying clitics: clitics may be written as independent words, bound affixes, or separated by special characters ( e. g., apostrophe ).

Note that such engines may not produce their full rated power using 87 octane gasoline under all circumstances due to the delayed ignition timing.

Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").

Note: This study only involved male subjects which may be significant as sex steroids may have different effects in the responses to cortisol administration.

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

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 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 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 front panel sizes are slightly less than the subrack sizes: for example a 3U front panel may only be high whereas the 3U subrack itself is high.

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

Note also that ' br ' is an empty element in that, while it may have attributes, it can take no content and it may not have an end tag.

Methods PUT and DELETE are defined to be idempotent, meaning that multiple identical requests should have the same effect as a single request ( Note that idempotence refers to the state of the system after the request has completed, so while the action the server takes ( e. g. deleting a record ) or the response code it returns may be different on subsequent requests, the system state will be the same every time ).

Note: The head of state in a " presidential " system may not actually hold the title of " president "-the name of the system refers to any head of state who actually governs and is independent of the legislature.

) 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.

( Note: Some older operating systems may handle such values incorrectly ( i. e., signed instead of unsigned ), which would make it impossible to access files larger than 2 GB in size.

Note that the longitude is singular at the Poles and calculations that are sufficiently accurate for other positions, may be inaccurate at or near the Poles.

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 a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (" saturated ") states.