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Page "Vertex operator algebra" ¶ 17
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Note and translation
Note that the line-coded signal and a signal produced at a terminal may differ, thus requiring translation.
Note: The English is not necessarily a direct translation of the Japanese.
Skene ( 1858 ) ( Note: Skene's text and translation are not reliable by the standards of modern scholarship )
The American term half note is a 19th-century loan translation of German halbe Note.
The American name is a loan translation of the German ganze Note.
( Note: The German version ( s ) of the Lord's Prayer most likely to have been used by Pennsylvania Germans would have been derived in most cases from Martin Luther's translation of the New Testament.
Note that many tools make a distinction between Business Rules Engines and Business Rules Management, and require a translation between the two.
Note: rhymes are not rendered in English in the translation below, and several short Italian words ( bella, ciao ) translate into long English words ( beautiful, goodbye ), without keeping meter.
" ( Note: free translation )
Note: Most of the fiction, poetry, and several of the essay books were published in translation in Romanian, French, German, Spanish, Japanese, Greek, Czech, Slovak, and Russian.
( Note this line follows the German original in Das Akkumulations-und Zusammenbruchsgesetz des kapitalistischen Systems ( zugleich eine Krisentheorie ), because it is misspecified in the condensed English translation.
Note these scholars translation refers to washing the feet.
Note this scholars translation refers to wiping the feet.
While the story can stand on its own, independent of Matsumoto's other works, it mostly assumes that the viewer has seen the other Harlock titles, especially Galaxy Express 999 ( the TV series and the movies ), which featured Maetel, Emeraldas ' sister, but had the occasional appearance of Emeraldas ( Note: Maetel, for some reason in the English dub is referred to as Mataire, possibly as a translation error ).
: Note: The main author of this section is French and has therefore never read the English version of the game ; there may thus be discrepancies with the terms used in the official translation
Note that the last section of the story, " Trurl and the construction of happy worlds ," does not appear in Michael Kandel's English translation of The Cyberiad.
* Note on the text and translation – Cambridge Books Online
Note that ROUGE is similar to the BLEU measure for machine translation, but BLEU is precision-based, because translation systems favor accuracy.
Note: The second rank of Lance Corporal, formerly " Private ", was changed in January 2010, due to the French translation " Soldat " being the word " soldier ".
Note that a Lexicon, like any other translation aid, is entirely dependent on the interpretation of the authors.
Note on translation: although the terms " Special City ", " Metropolitan City ", " Province ", and " City " are commonly used on English-language government websites, the other translations — " county ", " town ", " district ", etc.
Note that occasionally in English, writers will use the term translatology to refer to translation studies.
Note that the German version is Kaisertum Österreich, i. e. the English translation empire refers to a territory ruled by an emperor, not just to a " widespreading domain ", more accurately the " Emperordom of Austria ".
Note that this rotation is kinematic, rather than physical, because usually when a rigid object moves freely in space its rotation is independent of its translation.

Note and axiom
**** Note that this axiom precludes the possibility that the consumer cannot decide, and that a consumer is able to make this comparison with respect to every conceivable bundle of goods.
Note that there is one axiom for every such predicate φ ; thus, this is an axiom schema.
Note that the existence of the Cartesian product can be proved without using the power set axiom, as in the case of the Kripke – Platek set theory.
Note that there is no corresponding axiom of intersection.
Note, that the third axiom is actually redundant, because the second and fourth axioms imply is also an identity, and identities are unique.
Note that modern set-theoretic definitions usually define operations as maps between sets, so adding closure to a structure as an axiom is superfluous, though it still makes sense to ask whether subsets are closed.
It is then a theorem that there are in fact infinitely many such lines through P. Note that this axiom still does not uniquely characterize the hyperbolic plane uniquely up to isometry ; there is an extra constant, the curvature K < 0, which must be specified.
Note how, applying the reduction substitution axiom, occurrences of are now labeled as.
) Note that even without such an axiom we could form the first n terms of such a sequence, for any natural number n ; the axiom of dependent choices merely says that we can form a whole sequence this way.
Note that in this case, the axiom of extensionality must be formulated to apply only to objects that are not urelements.
Note also that there exists a number of alternative axiomatizations of S5 which do not employ the axiom 5 ( of course, 5 remains a theorem of S5 independently of a given axiomatization ).
Note that an everywhere defined extension exists for every operator, which is a purely algebraic fact explained at Discontinuous linear map # General existence theorem and based on the axiom of choice.

Note and implies
Note that this case in this example implies that the user was next to the solid object, and not inside it.
Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).
Note that the bilinearity and alternating properties imply anticommutativity, i. e., for all elements x, y in, while anticommutativity only implies the alternating property if the field's characteristic is not 2.
( Note that " altruism " refers only to the reproductive cost of the trait, and implies no sentience or foresight.
Note: Bandwidth compression implies a reduction in normal bandwidth of an information-carrying signal without reducing the information content of the signal.
Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).
Note that the figure to the right implies that the MAC occurs at a point where leading or trailing edge sweep changes.
) Note that Pearson's original paper was entitled " On Lines and Planes of Closest Fit to Systems of Points in Space " – " in space " implies physical Euclidean space where such concerns do not arise.
Note in the above example that shoigeg does not have the same meaning in Yeshivish as it does in its original context, wherein it implies negligence.
Note that implies.
Note: symmetry is not the exact opposite of antisymmetry ( aRb and bRa implies b = a ).
Note that this implies that the glass transition is dependent on strain rate in addition to temperature.
( Note that this implies a 20 ° " proportional band " ( PB ) from full to no power input, evenly spread around the setpoint value ).
( Note that this implies a 20 ° " proportional band " ( PB ) from full to no power input, evenly spread around the setpoint value ).
Note that this implies that M and N must have the same dimension at p.
Note that such a method implies that the synthesizer is monophonic.
Note the date of expiration ; this implies that the holder is neither a permanent resident, nor a Canadian citizen.
Note that this construction implies a desire to remain calm and defuse tension:
: Note again that a negative magnification implies an inverted image.
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 also that this definition is slightly more general than the one given by since it requires only to consider finite partitions of the space ': this implies that it can be used also to define the total variation on finite-additive measures.
Note that this conversely implies the negativity of the derivative of duration by differentiating.
Note that the above relationship implies that one can study the equation for only two of the three variables.
Note that in the presence of spinor fields, the Palatini action implies that d < sub > A </ sub > e is nonzero, that is, have torsion.

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