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Binomial Heap Merge1
Binomial may refer to: In mathematics *Binomial (polynomial), a polynomial with two terms *Binomial coefficient, numbers appearing in the expansions of powers of binomials * Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition * Binomial theorem, a theorem about powers of binomials * Binomial type, a property of sequences of polynomials * Binomial series, a mathematical series In probability and statistics *Binomial distribution, a type of probability distribution * Binomial process * Binomial test, a test of significance In computing science *Binomial heap, a data structure In linguistics * Binomial pair, a sequence of two or more words or phrases in the same grammatical category, having some semantic relationship and joined by some syntactic device In biology * Binomial nomenclature In taxonomy, binomial nomenclature ("two-term naming system"), also called binary nomenclature, is a formal system of naming species of living things by giving each a name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binomial (polynomial)
In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of a sparse polynomial after the monomials. Definition A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can be written in the form :a x^m - bx^n , where and are numbers, and and are distinct non-negative integers and is a symbol which is called an indeterminate or, for historical reasons, a variable. In the context of Laurent polynomials, a ''Laurent binomial'', often simply called a ''binomial'', is similarly defined, but the exponents and may be negative. More generally, a binomial may be written as: :a\, x_1^\dotsb x_i^ - b\, x_1^\dotsb x_i^ Examples :3x - 2x^2 :xy + yx^2 :0.9 x^3 + \pi y^2 :2 x^3 + 7 Operations on simple binomials *The binomial , the difference of two squares, can be factored as the product of two other binomials: :: x^2 - y^2 = (x - y) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binomial Coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the term in the polynomial expansion of the binomial power ; this coefficient can be computed by the multiplicative formula : \binom nk = \frac, which using factorial notation can be compactly expressed as : \binom = \frac. For example, the fourth power of is : \begin (1 + x)^4 &= \tbinom x^0 + \tbinom x^1 + \tbinom x^2 + \tbinom x^3 + \tbinom x^4 \\ &= 1 + 4x + 6 x^2 + 4x^3 + x^4, \end and the binomial coefficient \tbinom =\tfrac = \tfrac = 6 is the coefficient of the term. Arranging the numbers \tbinom, \tbinom, \ldots, \tbinom in successive rows for gives a triangular array called Pascal's triangle, satisfying the recurrence relation : \binom = \binom + \binom . The binomial coefficients occur in many areas of mathematics, and espe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binomial QMF
A binomial QMF – properly an orthonormal binomial quadrature mirror filter – is an orthogonal wavelet developed in 1990. The binomial QMF bank with perfect reconstruction (PR) was designed by Ali Akansu, and published in 1990, using the family of binomial polynomials for subband decomposition of discrete-time signals. Akansu and his fellow authors also showed that these binomial-QMF filters are identical to the wavelet filters designed independently by Ingrid Daubechies from compactly supported orthonormal wavelet transform perspective in 1988 ( Daubechies wavelet). It was an extension of Akansu's prior work on Binomial coefficient and Hermite polynomials In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: * signal processing as Hermitian wavelets for wavelet transform analysis * probability, such as the Edgeworth series, as well a ... wherein he developed the Modified Hermite Transformation (MHT) in 1987. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binomial Theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying and the coefficient of each term is a specific positive integer depending on and . For example, for , (x+y)^4 = x^4 + 4 x^3y + 6 x^2 y^2 + 4 x y^3 + y^4. The coefficient in each term is known as the binomial coefficient or (the two have the same value). These coefficients for varying and can be arranged to form Pascal's triangle. These numbers also occur in combinatorics, where gives the number of different combinations (i.e. subsets) of elements that can be chosen from an -element set. Therefore is usually pronounced as " choose ". Statement According to the theorem, the expansion of any nonnegative integer power of the binomial is a sum of the form (x+y)^n = x^n y^0 + x^ y^1 + x^ y^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |