However, the system is designed, ingeniously and hopefully, so that no one man could initiate a thermonuclear war.

However, there is always the possibility that chance will make demands the dancers find impossible to execute.

However, it is important to trace the philosophy of the French Revolution to its sources to understand the common democratic origin of individualism and socialism and the influence of the latter on the former.

However, it was not of innocence in general that I was speaking, but of perhaps the frailest and surely the least important side of it which is innocence in romantic love.

However, neither of these two cities is on the desired July 1 to June 30 fiscal year.

However, there is a more profound consideration to this proposed merger than profit and loss.

However, if their United States income is not subject to the withholding of tax on wages, their returns are due June 15, 1962, if they use a calendar year, or the 15th day of the 6th month after the close of their fiscal year.

However, its modern one-story layout is designed to increase our production capacity, permit more efficient manufacturing, and substantially reduce current repair and maintenance costs.

However, because this vulnerability is mutual, it is to the advantage of neither side to destroy the opponent's cities, at least so long as the opponent has nuclear weapons with which to effect reprisal.

However, there is a minimum of legislative restriction on boating.

However, it is essential that the various mathematical symbols used in the equations be understood so that the mathematical processes can be done properly and in their correct order.

However, the use of tripods is not allowed.

However, there is also much to be gained by making use of the abilities of the local people who are available and interested in recreation.

However, that is not all he has to do.

However one looks at it, therefore, I'd say that your horoscope for this autumn is the reverse of rosy.

However, a major factor in binding dirt is the attraction between surfaces that goes under the name of Van der Waal's forces.

However, the conversion from mass to size is unreliable, since many photographic meteors give evidence of a fluffy, loosely bound meteorite structure with densities as low as Af.

However, as a field measurement, it is open to question.

However, this artery is known to be a nutrient vessel with a distribution primarily to the proximal airways and supportive tissues of the lung.

However, if there is no additional complex of singular lines, the order of the image regulus of a pencil is precisely Af.

However, the factor of physical isolation is not a static situation.

However, any such suggestion accounts for only some of the difficulties in hearing tone, or in developing a realistic attitude about tone, but not for the analytic difficulties that occur even when tone is meticulously recorded.

However, there always is some limit to the numbers who will spend the time and effort to acquire training.

However, this tends to be complicated by the fact that this requires finding the roots of a high degree polynomial, and there can be multiple roots that represent local maxima.

However, one can obtain an explicit formula for majority of polynomial size using a sorting network of Ajtai, Komlós, and Szemerédi.

However for certain sets of such polynomials it may happen that for only finitely many combinations all polynomial functions take the value zero.

However, a quantum computer can compute the answer to some of these problems in polynomial time ; one well-known example of this is Shor's factoring algorithm.

However, probably the most important work on polynomial curves and sculptured surface was done by Pierre Bézier ( Renault ), Paul de Casteljau ( Citroen ), Steven Anson Coons ( MIT, Ford ), James Ferguson ( Boeing ), Carl de Boor ( GM ), Birkhoff ( GM ) and Garibedian ( GM ) in the 1960s and W. Gordon ( GM ) and R. Riesenfeld in the 1970s.

However, choosing a reducible polynomial can result in missed errors, due to the ring's having zero divisors.

However, in 1702 Leibniz said that no polynomial of the type x < sup > 4 </ sup > + a < sup > 4 </ sup > ( with a real and distinct from 0 ) can be written in such a way.

However, if the set of numbers ( called the knapsack ) is superincreasing — that is, each element of the set is greater than the sum of all the numbers before it — the problem is ' easy ' and solvable in polynomial time with a simple greedy algorithm.

However in expressions that involve terms with other types of factors than constants and powers of variables, the notion of constant term cannot be used in this sense, since that would lead to calling " 4 " the constant term of, whereas substituting 0 for x in this polynomial makes it evaluate to 13. so

) However some polynomial equations, of arbitrarily high degree, are solvable with such operations.

However, since the splitting field of a quintic polynomial has at most 5!

However, the quotient group ( isomorphic to itself ) is not an abelian group, and so is not solvable, so it must be that the general polynomial of the fifth degree has no solution in radicals.

However, since the result is on the general polynomial, it does say that a general " quintic formula " for the roots of a quintic using only a finite combination of the arithmetic operations and radicals in terms of the coefficients is impossible.

However, certain classes of puzzles, such as those in which each row or column has only one block of cells and all cells are connected, may be solved in polynomial time by transforming the problem into an instance of 2-satisfiability.

However, one can combine these remainders recursively to reduce the cost, using the following trick: if we want to evaluate modulo two polynomials and, we can first take the remainder modulo their product, which reduces the degree of the polynomial and makes subsequent modulo operations less computationally expensive.

However, this assumption does leave out finite energy states like solitons which can't be generated by a polynomial of fields smeared by test functions because a soliton, at least from a field theoretic perspective, is a global structure involving topological boundary conditions at infinity.

However, Vieta created many innovations: the binomial formula, which would be taken by Pascal and Newton, and the link between the roots and coefficients of a polynomial, called Vieta's formula.

However, a polynomial in several variables may be regarded as a polynomial in only " the last " variable, but with coefficients being polynomials in the others.

However, the directions on links are a vital detail to retain as one recurses through a polynomial calculation.

However, more sophisticated top-down parsers have been created by Frost, Hafiz, and Callaghan which do accommodate ambiguity and left recursion in polynomial time and which generate polynomial-sized representations of the potentially exponential number of parse trees.

However, when G is part of the input but H is fixed, it can be solved in polynomial time.

However the polynomial will satisfy the criterion for p after substitution of for x: this gives