If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.

If this is the case, one would expect that not only the various procedures just mentioned which alter the hypothalamic balance would influence emotional state and behavior but that emotion itself would act likewise.

If the moral code were flouted, the proper balance of the universe would be upset, and the disastrous result could be floods, plague, or famine.

If we neglect higher than first order terms in the fluctuations, the mass balance equation becomes

* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.

* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).

* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.

* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).

* If the balance factor of L is-1, two different rotations are needed.

If the balance factor becomes 0 then the height of the subtree has decreased by one and the retracing needs to continue.

If the balance factor becomes − 2 or + 2 then the subtree is unbalanced and needs to be rotated to fix it.

If the rotation leaves the subtree's balance factor at 0 then the retracing towards the root must continue since the height of this subtree has decreased by one.

If weight is added to the boat, the volume below the waterline will increase to keep the weight balance equal, and so the boat sinks a little to compensate.

If an account has a debit balance, the balance amount is copied into column two ( the debit column ).

If an account has a credit balance, the amount is copied into column three ( the credit column ).

In the words of Geoffrey Crowther, then editor of The Economist, " If the economic relationships between nations are not, by one means or another, brought fairly close to balance, then there is no set of financial arrangements that can rescue the world from the impoverishing results of chaos.

If a rotating frame is chosen so that just the angular position of an object is held fixed, more complicated motion, such as elliptical and open orbits, appears because the centripetal and centrifugal forces will not balance.

If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.

If friction cannot do this ( that is, the coefficient of friction is exceeded ), the ball slides to a different radius where the balance can be realized.

If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess, the molecule is said to have a zero oxygen balance.

: e ) If requested by the franchisee, copies of franchisor's balance sheets for the previous three years, or since start-up if that period is shorter.

If we could use all the small airfields we have in this country, we could disperse our strategic aircraft by a factor of 10 or more.

If time is the responsible factor, it may be possible to delay cell division in clones, giving time for proper reprogramming to occur.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

If any of them divides evenly, write 2 at the top of the table and the result of division by 2 of each factor in the space to the right of each factor and below the 2.

If they differ by two orders of magnitude, they differ by a factor of about 100.

If they both used the Attic stadion of about 185 meters, then the older estimate is 1 / 6 too large, and Ptolemy's value is 1 / 6 too small, a difference explained as due to ancient scientists ' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5 / 6, due to air's bending of horizontal light rays by 1 / 6 of the Earth's curvature.

If N is a closed normal subgroup of a profinite group G, then the factor group G / N is profinite ; the topology arising from the profiniteness agrees with the quotient topology.

If other patches are in the way, the view factor will be reduced or zero, depending

If we shift the constant term to the right hand side, factor a p and multiply by q < sup > n </ sup >, we get

If this increased rate of injection ... should raise the present background opacity by a factor of 4, our calculations suggest a decrease in global temperature by as much as 3. 5 ° C.

If the voltage is increased, then the current is decreased by the same factor.

If they factor out of the calculation the fact that the light-time delay of the transmission is increasing at a rate of 0. 8 seconds per second, both can work out that the other twin is aging slower, at 60 % rate.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.

If Af denotes the net profit from stage R and Af, then the principle of optimality gives Af.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

If the thumb points in the direction of the 4th substitutent, the enantiomer is R. Otherwise, it's S.

If the relative priorities of these substituents need to be established, R takes priority over S. When this happens, the descriptor of the stereocenter is a lowercase letter ( r or s ) instead of the uppercase letter normally used.

If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:

If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.

If a vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).

* If x < sub > 0 </ sub > is a real number, we can turn the set R −

( If X is also empty then R is reflexive.

*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.