Binomial sentence example

binomial
  • Converted species names are based on the accepted binomial under the preexisting code.
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  • A converted name is a name established under the PhyloCode and derived from a preexisting Linnaean binomial.
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  • As these indices represent discontinuous data, it would be preferable to use the negative binomial or the Poisson distribution.
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  • Living below the special service delivery a negative binomial.
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  • The second part of the Latin binomial, acris, completes the unique scientific name of this species.
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  • This study focuses negative binomial distribution but business groups.
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  • If we make large enough to expand the numerator using the binomial theorem (so that behaves as ), then as.
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  • Also, you will need to know very basic combinatorial concepts, in particular binomial coefficients.
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  • Example 1.. 15 Use the binomial theorem to expand (x + y) 5.
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  • 1112 which Cayley denotes by (a, b, c, ...)(xi, x2)n (i),(2)��� being a notation for the successive binomial coefficients n, 2n (n-I),....
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  • Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-��� +asas) +(as+1as +1 +o-8+2as+2+��� +ooae), such that Q1 +a2+...
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  • (v.) Permutations and Combinations may be regarded as arithmetical recreations; they become important algebraically in reference to the binomial theroem (�� 41, 44)� (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers.
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  • - The numbers denoted by n (r) in � 41 are the binomial coefficients shown in the table in � 40; n (r) being the (r+ i) th number in the (n+ i) th row.
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  • The use of negative coefficients leads to a difference between arithmetical division and algebraical division (by a multinomial), in that the latter may give rise to a quotient containing subtractive terms. The most important case is division by a binomial, as illustrated by the following examples: - 2.10+1) 6.100+5.10+ 1(3.10+I 2.10+I) 6.100+I.10 - I (3.10 - I 6.100+3.10 6.100+3.10 2.10+ I - 2.10 - I 2.10 +I - 2.10 - I In (1) the division is both arithmetical and algebraical, while in (2) it is algebraical, the quotient for arithmetical division being 2.10+9.
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  • It has been mentioned in � 41 (ix.) that the binomial theorem can be used for obtaining an approximate value for a power of a number; the most important terms only being taken into account.
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  • Comparison with the table of binomial coefficients in � 43 suggests that, if m is any positive integer, (I +x)-m =Sr+Rr (25), where Sr=I -m[1]x+m[2]x2...+(-)rm[r]xr (26), Rr_(_)r+1xr+11m[r] (1Fx) - 1+(m - I[r](I+x) m) (27).
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  • (ix.) The extension of n (r), and therefore of n [r ], to negative and fractional values of n, enables us to extend the applicability of the binomial coefficients to the summation of series (� 46 (ii.)).
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  • Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (� 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.
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  • Continued fractions, one of the earliest examples of which is Lord Brouncker's expression for the ratio of the circumference to the diameter of a circle (see Circle), were elaborately discussed by John Wallis and Leonhard Euler; the convergency of series treated by Newton, Euler and the Bernoullis; the binomial theorem, due originally to Newton and subsequently expanded by Euler and others, was used by Joseph Louis Lagrange as the basis of his Calcul des Fonctions.
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  • Gmelin availed himself of every publication he could, but he perhaps found his richest booty in the labours of Latham, neatly condensing his English descriptions into Latin diagnoses, and bestowing on them binomial names.
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  • (v.) Permutations and Combinations may be regarded as arithmetical recreations; they become important algebraically in reference to the binomial theroem (�� 41, 44)� (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers.
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  • This is the binomial theorem for a positive integral index.
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  • There are extensions of the binomial theorem, by means of which approximate calculations can be made of fractions, surds, and powers of fractions and of surds; the main difference being that the number of terms which can be taken into account is unlimited, so that, although we may approach nearer and nearer to the true value, we never attain it exactly.
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  • More generally, if we have obtained a as an approximate value for the pth root of N, the binomial theorem gives as an approximate formula p,IN =a+6, where N = a P + pap - 19.
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  • (0B) = (e), &c. The binomial coefficients appear, in fact, as symmetric functions, and this is frequently of importance.
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  • It has been mentioned in � 41 (ix.) that the binomial theorem can be used for obtaining an approximate value for a power of a number; the most important terms only being taken into account.
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  • Comparison with the table of binomial coefficients in � 43 suggests that, if m is any positive integer, (I +x)-m =Sr+Rr (25), where Sr=I -m[1]x+m[2]x2...+(-)rm[r]xr (26), Rr_(_)r+1xr+11m[r] (1Fx) - 1+(m - I[r](I+x) m) (27).
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  • 2 3 4 The binomial theorem was thus discovered as a development of John Wallis's investigations in the method of interpolation.
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  • These ideas are further developed in various papers in the Bulletin and in his L'Anthropometrie, ou mesure des differentes facultes de l'homme (18'ji), in which he lays great stress on the universal applicability of the binomial law, - according to which the number of cases in which, for instance, a certain height occurs among a large number of individuals is represented by an ordinate of a curve (the binomial) symmetrically situated with regard to the ordinate representing the mean result (average height).
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  • Binomial name Equus caballus Linnaeus, 1758 The horse (Equus caballus, sometimes seen as a subspecies of the Wild Horse, Equus ferus caballus) is a large odd-toed ungulate mammal, one of ten modern species of the genus Equus.
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  • This accounts for the fact that the same table of binomial coefficients serves for the expansions of positive powers of i+x and of negative powers of i - x.
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  • Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (� 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.
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  • The binomial theorem is a celebrated theorem, originally due to Sir Isaac Newton, by which any power of a binomial can be expressed as a series.
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  • It is to be noticed that each number is the sum of the numbers immediately 35 above and to the left of it; and 35 that the numbers along a line, termed a base, which cuts off an equal number of units along the top row and column are the co efficients in the binomial expansion of (I+x) r - 1, where r represents the number of units cut off.
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  • Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-��� +asas) +(as+1as +1 +o-8+2as+2+��� +ooae), such that Q1 +a2+...
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  • A multinomial consisting of two or of three terms is a binomial or a trinomial.
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  • The binomial theorem gives a formula for writing down the coefficient of any stated term in the expansion of any stated power of a given binomial.
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  • - The numbers denoted by n (r) in � 41 are the binomial coefficients shown in the table in � 40; n (r) being the (r+ i) th number in the (n+ i) th row.
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  • The binomial theorem for positive integral index may then be written (x + y) n = -iyi +.
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  • This property enables us to establish, by simple reasoning, certain relations between binomial coefficients.
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  • If we represent this expression by f (x), the expression obtained by changing x into x-+-h is f(x+h); and each term of this may be expanded by the binomial theorem.
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  • (ix.) The extension of n (r), and therefore of n [r ], to negative and fractional values of n, enables us to extend the applicability of the binomial coefficients to the summation of series (� 46 (ii.)).
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  • Linnaeus by his binomial system made it possible to write and speak with accuracy of any given species of plant or animal.
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  • - It is obvious that the Linnaean binomial terminology and its subsequent trinomial refinement for species, sub-species, and varieties was adapted to express the differences between animals as they exist to-day, distributed contemporaneously over the surface of the earth, and that it is wholly inadapted to express either the minute gradations of successive generic series or the branchings of a genetically connected chain of life.
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  • Linnaeus' invention of binomial nomenclature for designating species served systematic biology admirably, but at the same time, by attaching preponderating importance to a particular grade in classification, crystallized the doctrine of fixity.
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  • With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.
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  • Immediately on the completion of his Regne Animale in 1756, Brisson set about his Ornithologie, and it is only in the last two volumes of the latter that any reference is made to the tenth edition of the Systema Naturae, in which the binomial method was introduced.
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  • (v.) It should be mentioned that the notation of the binomial 'coefficients, and of the continued products such as n(n -1).
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  • He introduced the sign (=) for equality, and the terms binomial and residual.
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