coefficient

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Related to Leading coefficient: polynomial, degree of a polynomial

coefficient

 [ko″ĕ-fish´ent]
1. an expression of the change or effect produced by the variation in certain variables, or of the ratio between two different quantities.
2. in chemistry, a number or figure put before a chemical formula to indicate how many times the formula is to be multiplied.
Bunsen coefficient the number of milliliters of gas dissolved in a milliliter of liquid at atmospheric pressure (760 mm Hg) and a specified temperature. Symbol, α.
confidence coefficient the probability that a confidence interval will contain the true value of the population parameter. For example, if the confidence coefficient is 0.95, 95 per cent of the confidence intervals so calculated for a large number of random samples would contain the parameter.
correlation coefficient a numerical value that indicates the degree and direction of relationship between two variables; the coefficients range in value from +1.00 (perfect positive relationship) to 0.00 (no relationship) to −1.00 (perfect negative or inverse relationship).
diffusion coefficient see diffusion coefficient.
coefficient of digestibility the proportion of a food that is digested compared to what is absorbed, expressed as a percentage.
dilution coefficient a number that expresses the effectiveness of a disinfectant for a given organism. It is calculated by the equation tcn = k, where t is the time required for killing all organisms, c is the concentration of disinfectant, n is the dilution coefficient, and k is a constant. A low coefficient indicates the disinfectant is effective at a low concentration.
linear absorption coefficient the fraction of a beam of radiation absorbed per unit thickness of absorber.
mass absorption coefficient the linear absorption coefficient divided by the density of the absorber.
phenol coefficient see phenol coefficient.
sedimentation coefficient the velocity at which a particle sediments in a centrifuge divided by the applied centrifugal field, the result having units of time (velocity divided by acceleration), usually expressed in Svedberg units (S), which equal 10−13 second. Sedimentation coefficients are used to characterize the size of macromolecules; they increase with increasing mass and density and are higher for globular than for fibrous particles.

co·ef·fi·cient

(kō'ĕ-fish'ĕnt),
1. The expression of the amount or degree of any quality possessed by a substance, or of the degree of physical or chemical change normally occurring in that substance under stated conditions.
2. The ratio or factor that relates a quantity observed under one set of conditions to that observed under standard conditions, usually when all variables are either 1 or a simple power of 10.
[L. co- + efficio (exfacio), to accomplish]

coefficient

Vox populi A variable or factor which allows the calculation of a property or quantity of a substance under various conditions. See Absorption coefficient, Activity coefficient, Adsorption coefficient, Attenuation coefficient, Dice coefficient of similarity, Inbreeding coefficient, Intraclass correlation coefficient, Mass attentuation coefficient, Mass energy absorption coefficient, Octanol-water partition coefficient, Spearman's rank (order) correlation.

co·ef·fi·cient

(kō'ĕ-fish'ĕnt)
1. The expression of the amount or degree of any quality possessed by a substance, or of the degree of physical or chemical change normally occurring in that substance under stated conditions.
2. The ratio or factor that relates a quantity observed under one set of conditions to that observed under standard conditions, usually when all variables are either 1 or a simple power of 10.
[L. co- + efficio (exfacio), to accomplish]
References in periodicals archive ?
By Definition 4 from [5] the leading coefficient matrix is
One may also observe that the leading coefficient matrix of P(z) has the full rank, i.e.,
Later on we will require also the leading coefficient [[k.sup.2m]][S.sub.m](k) of [S.sub.m](k), i.e., the function [f.sub.0](m).
1 Compute n zeros, [mathematical expression not reproducible] of [mathematical expression not reproducible], and leading coefficient [[gamma].sub.n] ofpn.
Formulas for Leading Coefficients of [p.sub.[alpha]](k)
Incidentally, one ingredient in the proof of Theorem 5.1 is an auxiliary theorem which shows that for each t [greater than or equal to] 0, the quantity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a polynomial in b of degree k + t with leading coefficient t!/(k+t)!.
Homogenizing the leading coefficient. We first construct a canonical transformation [PHI] that, while defined on the region of phase space [0, 2[pi]] x R, arises from a simple change of variable in physical space, y = [PHI](x), where [PHI](x) is a differentiable function and
Finally, recall that the leading coefficient [k.sub.n], of the orthonormal polynomial [[phi].sub.n] is expressed in terms of Y by [Y.sub.21](0) = -2[pi][k.sup.2.sub.n-1].
By evaluating both sides of this formula at the point z = 0, we obtain the following simple expression for the leading coefficients of p(z),
where z = [e.sup.i[theta]] and [C.sub.l] = 1/2[pi] [[integral].sup.2.sub.0] [e.sup.il[theta]] dW([theta]), then taking into account that the leading coefficients of the polynomials [[PSI].sub.n] and [[PHI].sub.n] are nonsingular matrices, as well as the orthonormality conditions, we get
This text is a research monograph that explores second-order (degenerate) elliptic differential operators whose leading coefficients are generated by a positive operator, by means of which it is possible to construct suitable approximation processes which approximate the relevant semigroups.
monic if the sum of absolute values of its leading coefficients is 1, i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]