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Sometimes it is convenient to extend the definition of D to arbitrary E-valued forms, thus regarding it as a differential operator on the tensor product of E with the full exterior algebra of differential forms.
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Sometimes and is
Sometimes it is necessary to roughly calculate the square inch area of the opening but the calculation can usually be made with sufficient accuracy that it won't affect the final computation.
Sometimes it is not a verbal stereotype -- a `` How are you now ''??
Sometimes even the number of syllables is not clear.
Sometimes sprouted wheat is added to bread and causes the children to remark, `` Lillian, did you put nuts in the bread today ''??
Sometimes a desired acreage is offered only as part of a larger tract.
Sometimes this is accompanied by visible shifts of the ground surface ; ;
Sometimes, however, the decision of the lower proceeding is itself admissible as evidence, thus helping to curb frivolous appeals.
Sometimes a significant amount of alcohol ( up to 27 % vol ) is added, as a carrier for the flavor, to provide " bite ".
Sometimes he is sociable, but at other times he shuts himself up in his room.
Sometimes it is possible to " see " anagrams in words, unaided by tools, though the more letters involved the more difficult this becomes.
Sometimes the whole space is taken up with the inscription.
Sometimes this dish is referred to as " chow mein " ( which literally means " fried noodles " in Cantonese ).
Sometimes it is instead only required that the faces that meet at one vertex are related isometrically to the faces that meet at the other.
Sometimes the Kaliningrad Oblast is called the Янтарный край, which means " the amber area ".
Sometimes the name Sporozoa is taken as a synonym for the Apicomplexa, or occasionally as a subset.
Sometimes an internal standard is added at a known concentration directly to an analytical sample to aid in quantitation.
Sometimes medication is combined with psychotherapy but research has found that there is no benefit of combined pharmacotherapy and psychotherapy versus monotherapy.
Sometimes this non linearity is deliberately designed in to reduce the audible unpleasantness of hard clipping under overload.
Sometimes this is referred to as " hornbook law " meaning treatise or textbook, often relied upon as authoritative, competent, and generally accepted in the field of Canadian law.
Sometimes a misdealt card ( such as one of the down cards in poker that has flashed during the deal ) will be used as the burn card — in those cases, the card should be immediately placed face up on the deck after the deal is complete.
Sometimes, especially in computer science, the term is used for any binary function.
Sometimes this carries jurisdiction over metropolitan bishops, but usually it is purely honorific.
Sometimes in desert warfare, there is no nearby town name to use ; map coordinates gave the name to the Battle of 73 Easting in the First Gulf War.
Sometimes a full tree is ambiguously defined as a perfect tree.
Sometimes and convenient
Sometimes the instruments were operated in pairs at each end, making conversation more convenient but also more expensive.
Sometimes it is convenient to restate the definition of connectedness in such fields.
Sometimes these other units are more convenient to use.
Sometimes it is convenient to describe a projective frame by n + 2 representative vectors v < sub > 0 </ sub >, v < sub > 1 </ sub >, ..., v < sub > n + 1 </ sub > in K < sup > n + 1 </ sup >.
Sometimes it is convenient to allow the degenerate hyperplane, which is the whole space S, to belong to an arrangement.
Sometimes and extend
Sometimes the analysis has to extend to jerk for a particular reason.
Sometimes this surgical cut may extend to involve the perineal body and thus reduce anal sphicter function.
Sometimes the favors extend to hundreds of people.
Sometimes and definition
Sometimes the definition of a linear function coincides with that of a linear map, while in analytic geometry it does not.
Sometimes SNR is defined as the square of the alternative definition above.
Sometimes the second or third property above is taken as the definition of the topological interior.
Sometimes, also the definition v = −∇ φ, with a minus sign, is used.
Sometimes it is assumed that mean anomaly is zero at the epoch ( by choosing the appropriate definition of the epoch ), leaving only the five other orbital elements to be specified.
Sometimes these properties are also used for " defining " the dot product, especially in 2 and 3 dimensions ; this definition is equivalent to the above one.
Sometimes the silhouette of the animal was incised in the rock first, and in some caves all or many of the images are only engraved in this fashion, taking them somewhat out of a strict definition of " cave painting ".
Sometimes this condition is included in the definition of a model geometry.
Sometimes the definition of classical economics is expanded to include the earlier 17th century English economist William Petty and the contemporary early 19th century German economist Johann Heinrich von Thünen.
Sometimes, as an alternative to the definition of " home " as a physical locale (" Home is where you hang your hat "), home may be perceived to have no physical location, instead, home may relate instead to a mental or emotional state of refuge or comfort.
Sometimes, however, it is best not to consider the empty function to be constant, and a definition that makes reference to the range is preferable in those situations.
Sometimes, a slightly different definition of subbase is given which requires that the subbase B cover X.
Sometimes the definition is restricted to vocally-produced sounds.
Sometimes, particularly in general or informal discussions ( such as below ), one may drop reference to the basepoint, with the understanding that the definition is good up to conjugation.
Sometimes a different normalization of the invariant is adopted, which is one less than the definition above.
( Sometimes the orientability hypothesis is dropped from this last definition, and one gets a more general kind of handlebody with a non-orientable handle.
Sometimes, the definition of Tsonga is extended to include the closely related Ronga and Tswa peoples of Mozambique.
Sometimes, a more general definition is used, where membership functions take values in an arbitrary fixed algebra or structure ; usually it is required that be at least a poset or lattice.
Sometimes, the definition of a behaviour in an ethogram may have arbitrary components.
Note: Sometimes ( not without controversy ) this definition is extended to include modern day performers of this kind of music, such as Babis Goles and Agathonas Iakovidis.
Sometimes a slightly different definition of propagate is used.
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