Page "Lie algebra" ¶ 12
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## Some Related Sentences

Note and alternating
Note for completeness that condition ( 1 ) fails: any map t: B → A must map every two-cycle to the identity because the map has to be a group homomorphism, while the order of a two-cycle is 2 which can not be divided by the order of the elements in A other than the identity element, which is 3 as A is the alternating subgroup of, or namely the cyclic group of order 3.
Note Terry's boyish appearance in this early strip and backgrounds alternating from dark and detailed to blank.
( Note that this hypothesis does not necessarily contradict the scavenging hypothesis: both subsistence strategies could have been in use – sequentially, alternating or even simultaneously.
Note the X ↔ Y ( anti -)/ symmetry in alternating orders of the expansion, since Z ( Y, X ) = − Z (− X ,− Y ).
Note the alternating double and single bonds in the center.
In 2009 he recorded an album ( again for Groove Note ) of trio music with Larry Goldings on Hammond organ, and alternating drummers Jim Keltner and Jeff Hamilton.
Note that different copolymer sequencing is sufficient to define a structural difference, thus an A-B diblock copolymer with A-B alternating copolymer side chains is properly called a graft copolymer.
Note the alternating double and single bonds in the center and the mycosamine group in the bottom right corner.

Note and properties
Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.
Note that this property is itself positive, since it is the conjunction of the ( infinitely many ) positive properties.
Note: A number of other plants have been suggested by biblical scholars, e. g., Most notably Ginseng which looks similar to the mandrake root and has fertility enhancing properties, for which it was picked by Reuben in the Bible.
Note that we require the domains of G < sub > 2 </ sub >, G < sub > 3 </ sub > to be broad enough to make the above properties meaningful.
Note that a compressed gas also exhibits " elastic " properties, for instance inside an inflated car tire.
Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The unchanged properties are called invariant ( mathematics ) | invariant s.
Note that these properties are also satisfied if " interior ", " subset ", " union ", " contained in ", " largest " and " open " are replaced by " closure ", " superset ", " intersection ", " which contains ", " smallest ", and " closed ", respectively.
Note that two natural products were already known with this imidazole riboside structure: substitution at the 5 ' carbon with OH results in pyrazomycin / pyrazofurin, an antibiotic with antiviral properties but unacceptable toxicity, and replacement with an amino group results in the natural purine synthetic precursor 5-aminoimidazole-4-carboxamide-1-β-D-ribofuranoside ( AICAR ), which has only modest antiviral properties.
Note that the matrix defined as above has the following properties:
Note that the above construction of the Galois group for a fifth degree polynomial only applies to the general polynomial, specific polynomials of the fifth degree may have different Galois groups with quite different properties, e. g. has a splitting field generated by a primitive 5th root of unity, and hence its Galois group is abelian and the equation itself solvable by radicals.
Note, any type of board ( such as shortboard or mini-longboard ) can have a fish tail, and these are commonly referred to as a " fish ", but they lack the other properties of a traditional, or " retro ", fish as listed here.
Note that the main symbols of these extensive thermodynamic properties shown here are capital letters.
Note that enhanced antibacterial properties of nanoparticles compared to bulk material is not limited to silver, but has also been demonstrated on other materials such as ZnO
Note that some languages have what are described as " relative pronouns " ( in that they agree with some properties of the head noun, such as number and gender ) but which don't actually indicate the case role of the shared noun in the embedded clause.
Note that there are important physiological differences between nodal cells and ventricular cells ; the specific differences in ion channels and mechanisms of polarization give rise to unique properties of SA node cells, most importantly the spontaneous depolarizations necessary for the SA node pacemaker activity.
( Note that some of the properties of the Lebesgue integral fail here, since our measure is only finitely additive.
Note that this category is for geometrical entities or properties.
Note that the properties calculated by data-flow analysis are typically only approximations of the real
Note: All properties refer to the nephroid as parameterized by the first pair of equations above.
Note that the matrix defined as above has the following properties:
Note that the inequality is not really applicable either to electrons or photons, since it builds in no probabilistic properties in the measurement process.

Note and imply
Note: in Greek, the term for " consul " is " ypatos ", which translates as " supreme one ", and hence does not necessarily imply a joint office.
Note that materialism does not necessarily imply egoism, as indicated by Karl Marx, and the many other materialists who espoused forms of collectivism.
Note, however, that the converse is not true in general, i. e. zero skewness does not imply that the mean is equal to the median.
Note 2: The term " center " does not imply a physical location.
Note that when considering an antenna's directional pattern, " gain with respect to a dipole " does not imply a comparison of that antenna's gain in each direction to a dipole's gain in that direction.
Note that lack of credit does not imply plagiarism.
Note that cardinality does NOT imply direct measurability, in which Jevons did not believe.
Note: in non-medical contexts, the word " fistula " is often used to imply urogenital fistula
Note that empty cells do not imply that a particular language is lacking a word to describe the concept, but rather that the word for the concept in that language is formed from another stem and is not a cognate with the other words in the row.
Note that the validity of this alternative within this dilemma does not in any way imply that money can both exist and not exist.
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 " ma " would technically imply a milliannum ( also called a milliyear in English usage ), a period of a thousandth of a year or about 8 hours.
Note that the vorticity does not imply anything about the global behaviour of a fluid.
Note also the diction used within the imagery: words like " forked " and " fallen " imply a kind of hell that he is trapped in.
Note that the unpaired electron does not imply charge-free radicals can be positively charged, negatively charged, or neutral.
Note that just because the Soumpasis can be fitted adequately to data does not necessarily imply that the assumptions are true and that diffusion dominates recovery.
Note that resetting test logic doesn't necessarily imply resetting anything else.
Note that these imply that
However, many DNS resolvers process a domain name that contains a dot in any position as being fully qualified < ref group = note > Note: On Unix-like systems, this is controlled by the option in the resolv. conf configuration file, specifying the number of dots ( default 1 ) recognized to imply a FQDN.
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 the effective computability of these functions does not imply that they can be efficiently computed ( i. e. computed within a reasonable amount of time ).
Note that the above perfect forms refer to possibility, not permission ( although the second sense of might have might sometimes imply permission ).
Note, that as such, this does not imply that an increase in savings must lead directly to an increase in investment.
Note that current population genetic structure does not necessarily imply that the different current clusters / components found correspond to only one ancestral home per group.

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