If this were the restriction, planar graphs would require arbitrarily large numbers of colors.

If we only wanted the tuples for a specific customer, we would specify this using a restriction condition.

If we let be the inclusion functor from CHaus into Top, maps from to ( for in CHaus ) correspond bijectively to maps from to ( by considering their restriction to and using the universal property of ).

If passed by the parliament of South Africa, the Intellectual Property Laws Amendment Bill of 2008 will provide for the protection and restriction on commercial use of the name Rooibos in that country.

If F ( U ) is a module over the ring O < sub > X </ sub >( U ) for every open set U in X, and the restriction maps are compatible with the module structure, then we call F an O < sub > X </ sub >- module.

If f: X → Y is a local homeomorphism and U is an open subset of X, then the restriction f |< sub > U </ sub > is also a local homeomorphism.

If the restriction of Q to a subspace U of V is identically zero, U is totally singular.

If polymerase chain reaction ( PCR ) tests on infected material are positive, subsequent restriction endonuclease pattern analysis of the amplified outer membrane protein A gene can be done to determine the genotype.

If two clones overlap, they will likely have restriction sites in common, and will thus share several fragments.

If gaps between contigs remain after STS landmark mapping and restriction fingerprinting have been performed, the sequencing of contig ends can be used to close these gaps.

If the restriction had not been revoked, the brewery would have been forced either to move back to Newcastle, or stop calling its beer " Newcastle " brown ale.

If then there is a restriction map, satisfying certain compatibility conditions.

If we had missed this restriction, we might have picked θ to go from π to 5π / 6, which would result in the negative of the result.

If T is the multiplicative group, then this gives the restriction of scalars a permutation module structure.

If the leading coefficients were negative, we could expect negative prime values ; this is a harmless restriction, really.

* If the restriction that α and β be algebraic is removed, the statement does not remain true in general.

If the object being bounded is known to be convex, this is not a restriction.

If gravity is included in the theory, so that there is local supersymmetry, then the resulting theory is called a supergravity theory and the restriction on the geometry of the moduli space becomes stronger.

If the name matches, or is similar to a name on the No Fly List, a restriction is placed in their reservation that prevents them from being issued a boarding pass until the airline has determined whether or not they are the actual person whose name is on the No Fly List.

If one does not practice restriction, his existence becomes the automatic outcome of our circumstances, rather than a proactive experience of his creation.

If rain intervenes so that all the allocated overs cannot be bowled in the time available for the game, the overs restriction may be modified so that the game may be completed in the time that remains.

If N is not compact, one needs to consider the restriction of the to any of their sublevel sets.

If the recognition site is outside the region of the cleavage pattern, then the restriction endonuclease is referred to as Type I.

If the recognition sequence overlaps with the cleavage sequence, then the restriction endonuclease restriction enzyme is Type II.

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 action is indicated, what kind of action is relevant to the problem??

If a litigant chooses to enforce a Federal right in a State court, he cannot be heard to object if he is treated exactly as are plaintiffs who press like claims arising under State law with regard to the form in which the claim must be stated -- the particularity, for instance, with which a cause of action must be described.

But this destruction, coupled with a protracted siege of Rain ( 9 – 16 July ), caused Prince Eugene to lament "... since the Donauwörth action I cannot admire their performances ", and later to conclude " If he has to go home without having achieved his objective, he will certainly be ruined.

If the axial load on the column is not concentric, that is, its line of action is not precisely coincident with the centroidal axis of the column, the column is characterized as eccentrically loaded.

If 5 % of Town voters petition the Board of Selectmen within 14 days of Town Meeting any action taken may be submitted to voters.

Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

If such an action had preconditions, such as the door must not be locked, it would have been represented by.

If he has presumed to do this in the past or shall presume to do so in the future, his action shall be null and he shall be subject to the canonical penalties.

If the group G acts on the set X, then we can form the action groupoid representing this group action as follows:

If police action is not sufficient to stop the guerrilla fighters, military sweeps may be necessary.

If G is a group and X is a set then a group action may be defined as a group homomorphism h from G to the symmetric group of X.

If G is a group and X is a set, then a ( left ) group action of G on X is a binary operator:

If is a right action, then the following is a left action:

If the reloaded cartridges are going to be used in the same firearm in which they were previously fired, though, and if that firearm has a bolt action or other action with a strong camming action on closing, then full length resizing may not be needed.

" If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself ; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it.

If g is the metric on this manifold, one defines the action S ( g ) as

If the interrogation was conducted by a person known by the suspect to be a law enforcement officer the state action requirement is unquestionably met.

If not, actors frequently train in preparation for their roles, or the action director may rely more on stylized action or filmmaking tricks like camera angles, editing, doubles, undercranking, wire work, and computer-generated imagery.