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However and some
However, an initial perusal and comparison of some of the famous passages with the same parts of other versions seems to speak well of the efforts of the British Biblical scholars.
However, some formulas are used more than others.
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, among the girls, there are some morale-enhancing compensations for not going to college.
However, some productions have recorded success: Carnival fi Dachra produced by Mohamed Oukassi and Athmane Aliouet in 1994, or as " Salut Cousin!
However, wall depictions of this instrument have not been discovered, casting some doubt over the extent to which this instrument was used.
However this ideal is not normally achieved in practice ; some languages ( such as Spanish and Finnish ) come close to it, while others ( such as English ) deviate from it to a much larger degree.
However, some linguistic contexts do not provide sufficient information to disambiguate a used word.
However, in some areas the aardwolf is hunted for its fur.
However, recent work suggests that some agnostids were benthic predators, engaging in cannibalism and possibly manifesting pack-hunting behavior.
However, some species with hairy seeds ( e. g. Eriospermum, family Asparagaceae s. l.
However, most modern abjads, such as Arabic, Hebrew, Aramaic and Avestan, are " impure " abjads, that is, they also contain symbols for some of the vowel phonemes.
However, some experimental evidence suggests astatine may have lower melting and boiling points than those implied by the halogen trend.
However, this has now been replaced by a more professional exhibition space incorporating laser, video, slide shows, audio commentaries, and some interactive elements.
However, since some feel that being the children of the main characters is too limiting, it is fairly common to either start with King Oberon's death before the book begins and roleplay the Elder Amberites as they vie for the throne ; or to populate Amber from scratch with a different set of Elder Amberites.
However, in general, the books only feature mental battles when there is some reason for mind-to-mind contact ( for example, Trump contact ) and magic or Trump is involved in all three of the above conflicts, so it is not clear whether Zelazny intended his characters to have such a power ; the combination of Brand's " living trump " powers and his high Psyche ( as presented in the roleplaying game ) would have guaranteed him victory over Corwin.
However, some alloys can also have their properties altered by heat treatment.
However, on some columns their hands remain.
However, there are certain limitations: they may not administer the sacraments and related functions whose celebration is reserved to bishops, priests, deacons, or seminarians ( the male clergy ), namely, Holy Orders ( they may make provision for an ordained cleric to help train and to admit some of their members, if needed, as altar servers, Eucharistic ministers, or lectors-the minor ministries which are now open to the non-ordained ).
However, other neutral particles are their own antiparticles, such as photons, the hypothetical gravitons, and some WIMPs.
However, the goal of serious or skilled anagrammatists is to produce anagrams that in some way reflect or comment on the subject.
However, since it is capable of being greatly altered and even discharged by heat, the color was believed by some authorities to be from an organic source.
However, the connection that has derived ambrosia from the Greek prefix a-(" not ") and the word brotos (" mortal "), hence the food or drink of the immortals, has been questioned as coincidental by some modern linguists.
However, some systems have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.

However and polynomial
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, this is not a polynomial time algorithm because the number of digits in the solution may be as large as √ n, far larger than a polynomial in the number of digits in the input value n.
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, 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

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