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Page "Commutative property" ¶ 63
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If and operation
If any official operation abroad begins to go wrong, we shall look to the ambassador to find out why and to get suggestions for remedial action.
If that's done, the house can be designed and oriented for best operation, and this can mean savings both in the size of equipment and in the cost of the house itself.
If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.
* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:
If f is not a function, but is instead a partial function, it is called a partial operation.
* If the operation is associative, ( ab ) c = a ( bc ), then the value depends only on the tuple ( a, b, c ).
* If the operation is commutative, ab = ba, then the value depends only on
If, for instance, an addition operation was requested, the arithmetic logic unit ( ALU ) will be connected to a set of inputs and a set of outputs.
If the addition operation produces a result too large for the CPU to handle, an arithmetic overflow flag in a flags register may also be set.
If n ≥ 1 and is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation ; it is written as ( Z / nZ )< sup >×</ sup > or Z < sub > n </ sub >< sup >*</ sup >.
" If you look at it as a whole ," a senior S / LPD official said, " the Office of Public Diplomacy was carrying out a huge psychological operation of the kind the military conducts to influence a population in denied or enemy territory.
If these relations are stored physically as separate disk files, completing a database query that draws information from several relations ( a join operation ) can be slow.
If this operation has to be done in real time video games there is an easy trick to boost performance.
# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.
If the reader evaluates an expression but does not follow the correct order of operation, the reader will come forth with a different value.
If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input.
If one could achieve reliable operation of VLB at 50mhz it was extremely fast-but again this was notoriously difficult to achieve, and often it was discovered not to be possible with a given hardware configuration.
If the weather is below VMC, pilots are required to use instrument flight rules, and operation of the aircraft will primarily be through referencing the instruments rather than visual reference.
If the check in operation succeeds, then the version numbers of all files involved automatically increment, and the CVS-server writes a user-supplied description line, the date and the author's name to its log files.
If an operation is to be performed on the whole structure, each node calls the operation on its children ( recursively ).
If the annular muscles are contracted, the body cross-section is reduced, and the corresponding segment stretches, since its volume must remain constant due to the incompressible behaviour of the coelom's liquid contents ; this is the usual mode of operation of the hydrostatic skeleton as also employed by other worms.
If ( G ,*) is a group, we define its opposite group ( G < sup > op </ sup >,*< sup > op </ sup >) as follows: G < sup > op </ sup > is the same set as G, and the operation *< sup > op </ sup > is defined by.
If the operation is associative then if an element has both a left inverse and a right inverse, they are equal.
If ~ is a unary operation, then h (~ x ) = ~ h ( x ).

If and additionally
If each node additionally records the size of its subtree ( including itself and its descendants ), then the nodes can be retrieved by index in O ( log n ) time as well.
If both are accepted, one has to additionally signal a preference.
If the aging for one of these types of whiskey reaches two years or beyond, the whiskey is then additionally designated as " straight " e. g., " straight rye whiskey ".
If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.
If UV / Vis spectrophotometry is used in quantitative chemical analysis then the results are additionally affected by uncertainty sources arising from the nature of the compounds and / or solutions that are measured.
If, additionally, the recipient of the criticism is not the intended target, that is also a factor to consider.
If we additionally assume that the image plane is perpendicular to the ground plane ( an imaginary plane Tangential to the surface of the Earth ), and that the waterfall flows on a plane that is parallel to the image plane, we can estimate the height by measuring the vertical separation of waterfall head and base in
If additionally is injective we say is 1-reducible to and write
If additionally
If, additionally, the real part of s is positive, then the limit γ ( s, u ) → 0 for u → 0 applies, finally arriving at the complex integral definition of γ
If not, then the judge must additionally assess the application under the " centralized mode of existence " approach, guided by the non-exhaustive factors set out in Koo ( Re ).
If the poset P additionally is a join-semilattice ( i. e., if it has binary suprema ) then these conditions are equivalent to the following statement:
If the surface is additionally known to be axisymmetric with,
If a player cannot follow suit, he must play a trump card if able, and additionally, the player is compelled to play a higher trump than any existing trump in the trick if he is able ( The " Petit " or 1 is valued lowest, and the " Monde " or 21 is valued highest ).
If it were a warship, and repairable, usually the Crown bought it at a fair price ; additionally, the Crown added " head money " of 5 pounds per enemy sailor aboard the captured warship.
Their sets included songs spanning Strummer's career to that point, including works from The 101ers and The Clash, additionally material co written with Mick Jones for Big Audio Dynamite's No. 10, Upping St. album as well as a cover of The Pogues ' famous " If I Should Fall From Grace With God.
If the sample is depolarizing the Mueller matrix formalism should be used, because it gives additionally access to the amount of depolarization.
If additionally then is called Turing complete for.
If X was in good faith, and additionally was in legal possession of the house, then any vindicatio brought by Y could be defeated by X using the defence of fraud ( exceptio dolus malus ) until Y paid X for the materials.
If the two vertices are additionally connected by a path of length 1, i. e. by a single edge, the vertices are called adjacent.
If police additionally have reasonable suspicion that a person so detained may be armed, they may " frisk " the person for weapons, but not for contraband like drugs.
If the officer additionally has reasonable suspicion that the person is armed, the officer may perform a search of the person's outer garments for weapons.
If abstract index notation is used also for spinors then these will carry a spinorial index and the Dirac gamma will carry one Lorentzian and two spinorian indices, but it is more common to regard spinors as column matrices and the Dirac gamma as a matrix which additionally carries a Lorentzian index.

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