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Page "Differential operator" ¶ 36
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If and one
If you take the one, you'd better take both ''.
`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.
If one dancer slaps another, the victim may do a pirouette, sit down, or offer his assailant a fork and spoon.
If a child had a single drop of Negro blood, he would revert to the ancestral line which, except as slaves under a superior race, had not made one step of progress in 3,000 years.
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If within one year you can make a success out of the American, you can practically name your own salary thereafter.
If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.
If one finger is raised against the authorities, all our moral power will vanish.
If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.
If he can bounce back with one of those 25 home runs years, the club will have to be better off offensively.
If they do meet and recognize one another, slap backs and embrace, the moment soon is done.
If either one ever started making promises, there is no telling where the promises would end.
If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.
Somebody, got to be somebody If I don't put my two cents in soon, somebody else will I know they're waitin only for one thing: for the bastards what done it to be nailed.
If we had, then one of us would have had to go instead.
`` If I catch you one more time down here without stockings '' --
If, for some reason such as economy, we are not going to develop aircraft nuclear propulsion with a sense of national urgency, then we should turn our effort to developing jet engines with a thrust-to-weight ratio of 12 or 15 to one.
If you don't own a planer and don't want to buy one, it's well worth renting.
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
If you have a full-time doctor now, can he be replaced with a part-time doctor or one who serves on a fee-per-case basis only??
If you use one of the new year-round cooling system fluids such as `` Dowguard '' be sure to check it.
If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.

If and moreover
If they be led by virtue, and uniformity sought to be given them by the rules of propriety, they will have the sense of the shame, and moreover will become good.
If any one of the sides makes the bung reach that end of the churchyard it is victorious .” The actual word hockey was mentioned centuries before, in 1363, when King Edward III of England issued a declaration banning a list of games: " moreover we ordain that you prohibit under penalty of imprisonment all and sundry from such stone, wood and iron throwing ; handball, football, or hockey ; coursing and cock-fighting, or other such idle games.
If a model for a language moreover satisfies a particular sentence or theory ( set of sentences satisfying special conditions ), it is called a model of the sentence or theory.
If P is a common point of two plane algebraic curves X and Y that is a non-singular point of both of them and, moreover, the tangent lines to X and Y at P are distinct then the intersection multiplicity is one.
If these groups have N < sub > p </ sub > and N < sub > q </ sub > elements, respectively, then for any point P on the original curve, by Lagrange's theorem, k > 0 is minimal such that on the curve modulo p implies that k divides N < sub > p </ sub >; moreover,.
If, moreover, as appears quite likely, his Two Bookes of Ayres ( both words and music written by himself ) belongs also to this year, it was indeed his annus mirabilis.
If X is connected, there is a discrete space F such that for every x in X the fiber over x is homeomorphic to F and, moreover, for every x in X there is a neighborhood U of x such that its full pre-image p < sup >− 1 </ sup >( U ) is homeomorphic to U x F. In particular, the cardinality of the fiber over x is equal to the cardinality of F and it is called the degree of the cover p: C → X.
As before, suppose that E is a fibre bundle with structure group G. In the special case when G has a free and transitive left action on F ′, so that F ′ is a principal homogeneous space for the left action of G on itself, then the associated bundle E ′ is called the principal G-bundle associated to the fibre bundle E. If, moreover, the new fibre F ′ is identified with G ( so that F ′ inherits a right action of G as well as a left action ), then the right action of G on F ′ induces a right action of G on E ′.
If, moreover, the doshes are galloons, we know that some galloons are distimmed by the gostak.
If M admits local holomorphic coordinates for J around every point then these patch together to form a holomorphic atlas for M giving it a complex structure, which moreover induces J. J is then said to be ' integrable '.
If the group G is finite and one considers only stem extensions, then there is a largest size for such a group C, and for every C of that size the subgroup K is isomorphic to the Schur multiplier of G. If the finite group G is moreover perfect, then C is unique up to isomorphism and is itself perfect.
If moreover I satisfies the cancellation property so that it can be embedded into a commutative group A which it generates ( for instance the integers if I is the natural numbers ), then one may also define linear maps that are homogeneous of degree i in A by the same property ( but now "+" denotes the group operation in A ).
* If 0 ≤ A < B, the r < sub > A </ sub > ≤ r < sub > B </ sub >, moreover, if A is irreducible, then the inequality is strict: r < sub > A </ sub > < r < sub > B </ sub >.
If the word " prefer " is interpreted in a relative sense, as rating the preferred candidate above any other candidate, the method does not pass, even with only two candidates ; If the word " prefer " is interpreted in an absolute sense, as rating the preferred candidate with the highest available rating then it does if there are moreover no ties.
If, moreover, the curvature has a non-zero local maximum or minimum at P then the osculating circle touches the curve C at P but does not cross it.
If p is a prime number, the quotient is an integer by Wilson's theorem ; moreover, if p is composite, the quotient is not an integer.
If E has a terminal object e and if F is fibred over E, then the functor ε from cartesian sections to F < sub > e </ sub > defined at the end of the previous section is an equivalence of categories and moreover surjective on objects.
If a model for a language moreover satisfies a particular sentence or theory ( set of sentences ), it is called a model of the sentence or theory.
If, moreover, for any ε > 0 the homeomorphism h may be chosen to be C < sup > 0 </ sup > ε-close to the identity map when F < sub > 1 </ sub > belongs to a suitable neighborhood of F depending on ε, then F is called ( strongly ) structurally stable.

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