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 notion of image may not correspond to the usual notion of image, or range, of a function, even assuming that the morphisms in the category are functions.

Note that this is not the usual convention.

Note that the use of natural numbers both in S and the existential quantification merely reflects the usual applications in computability and model theory.

Note that if usual data compression algorithms are used, files that are similar when uncompressed may be very different when compressed, and thus the entire file will need to be transferred – local changes in uncompressed files yield global changes in compressed files.

Note that " d " is made more distinctively different from " b " than is usual in standard typefaces ( which is possible since in the I. T. A.

* Note that the space of rational numbers with the usual topology inherited from the reals is not a Baire space, since it is the union of countably many closed sets without interior, the singletons.

Note that in a twist on the usual way of designating American aircraft, the following were not different models of the X-1, but rather they were the successive ( mostly identical ) units of the X-1 program: the X-1, X-1A, X-1B, X-1C, X-1D, and X-1E.

Note: in those days 2, 400 Baud modems were quite rare ; 1, 200 Baud was the usual speed in the 1980s, although 110 and 300 Baud modems were not uncommon.

Note that the usual Smalltalk class browser does not show metaclasses as separate classes.

Note that in PROIV programs are referred to as " functions ", which can be confusing as it differs from the more usual use of that term in programming languages.

Note that the quantity being traced over is an element of the gauge Lie group and the trace is really the character of this element with respect to one of the infinitely-many irreducible representations, which implies that the operators don't need to be restricted to the " trace class " ( thus with purely discrete spectrum ), but can be generally hermitian ( or mathematically: self-adjoint ) as usual.

Note that the transition between " upper " (" contravariant ") and " lower " (" covariant ") vector or tensor components is trivial for a indices ( e. g. ), whereas for μ and ν it is nontrivial, corresponding e. g. to the usual Lorentz signature,.

Note that the étale site is the name for the usual category of schemes considered together with the étale Grothendieck topology.

Note that the refractive indices of are reversed, when comparing to usual waveguides.

* Note b: " Mormon ," as used in this article, refers to adherents of the Latter Day Saint movement as a whole, and not just to its largest branch, the LDS church ( as is usual among smaller Latter Day Saint sects, many of which dislike this term ).

Note that in common with the nearby Sirhowy River and Rhymney River the correct name for the river is " Ebbw River ", not the more usual " River Ebbw ".

< blockquote style =" font-style: italic ;"> uthors of the materials being commented on Discussion Notes may be given a right of reply ( subject to the usual refereeing ), on the understanding that timely publication of the Note will take priority over the desirability of including both Note and Reply in the same issue of the Journal.

Note being ABC1 broadcasts to 10: 00-12: 00 on school holidays in place of usual educational programming

Note being ABC1 broadcasts to 10: 00-12: 00 on school holidays in place of usual educational programming

Note that when a > b the torus intersects itself, so it does not resemble the usual picture of a torus.

Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.

Note however that working with the current two form itself and the exterior derivative is usually easier than working with the vector field and divergence, because unlike the divergence, the exterior derivative commutes with a change of ( curvilinear ) coordinate system.

( 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 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 establishing this chain of logical implication ( or quantifying the relevant probabilities ) makes this form logically valid.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

Note that the plural suffix "- s " can also influence the form taken by the preceding morpheme, as in the case of the words leaf and knife, which end with in the singular, but have in the plural ( leaves, knives ).

( Historical Note: Prior to the coining of the term " consequentialism " by Anscombe in 1958 and the adoption of that term in the literature that followed, " utilitarianism " was the generic term for consequentialism, referring to all theories that promoted maximizing any form of utility, not just those that promoted maximizing happiness.

( Note that the propagation of the prion depends on the presence of normally folded protein in which the prion can induce misfolding ; animals which do not express the normal form of the prion protein cannot develop nor transmit the disease.

Note: Christian Scientists, Quakers and the Salvation Army cannot be classified as specifically opposing infant baptism, since they generally do not observe baptism in any form.

Note that any element of I must have the form αω, by virtue of our assumption that.

( Note: UTF-16 and UTF-32 without the BOM are formally known under different names, they are different encodings, and thus needs some form of encoding declaration – see UTF-16BE, UTF-16LE, UTF-32LE and UTF-32BE.

Note: this is the first published form of the couplet, quoted from Doreen Valiente in 1964.

Note 1: Burst transmission in isochronous form enables communication between data terminal equipment ( DTE ) and data networks that operate at dissimilar data signaling rates, such as when the information-bearer channel rate is higher than the DTE output data signaling rate.

Note form tractors on each side of the paper and carriage control tape in upper right.

Note that the syllogism above has the abstract form:

Note that both types of predictive distributions have the form of a compound probability distribution ( as does the marginal likelihood ).

Note that the relationships above are only valid for the form of the Fourier transform shown in the Proof section below.

Note also that Peirce held that all deduction can be put into the form of the categorical syllogism Barbara ( AAA ).

Note: the dates of English publications are those of the first publications in a book form.

( Note that Brentano denied the idea that all judgments are of the form: S is P all other kinds of judgment which combine presentations.

Note that the independent columns of the reduced row echelon form are precisely the columns with pivots.

Note the ' grid squares thus formed are far larger than the city blocks described earlier, and the road layouts within the grid squares are generally ' organic ' in form — matching the ' street hierarchy model described above

A principal fractional ideal is one of the form for some nonzero x in K. Note that each principal fractional ideal is invertible, the inverse of being simply.

:: Note: " Just as the coin of Philipp in Hartzheim, historia rei nummariae coloniensis Table 3 No. 14, 16, ( 1754 ), yet without its circumscription ; the other ( coin ) is in square form, showed in the center a cross, accompanied by the sword of jurisdiction, and the crosier ( bishop's crook ) on either side, also without transcription, most certainly it is not younger and can be assumed perhaps to turn out to be a coin by Rainald Dassel.