体ｋ上のアフィン代数群とは、ｋ上の可換多元環の圏から群の圏への表現可能な共変関手で、有限生成な多元環によって表現される。の英語

An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.

when the regression line is linear (y = ax + b) the regression coefficient is the constant (a) that represents the rate of change of one variable (y) as a function of changes in the other (x)

the organic phenomenon in which one of a pair of alleles present in a genotype is expressed in the phenotype and the other allele of the pair is not

the part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential

a function that takes the value 1 if a specified function of the arguments exceeds a given threshold and 0 otherwise

the image of f(x) = x^2 is the set of all non-negative real numbers if the domain of the function is the set of all real numbers

an index of the relation between any two sets of scores that can both be represented on ordered binary dimensions (e.g., male-female)

a word or morpheme used in some languages in certain contexts (such as counting) to indicate the semantic class to which the counted item belongs

a wave (as a sound wave in a chamber or an electromagnetic wave in a transmission line) in which the ratio of its instantaneous amplitude at one point to that at any other point does not vary with time

a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other

relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values)

a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)

the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions

a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on

a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1

two laws governing electric networks in which steady currents flow: the sum of all the currents at a point is zero and the sum of the voltage gains and drops around any closed circuit is zero

an instrument that indicates whether two periodic motions are synchronous (especially an instrument that enables a pilot to synchronize the propellers of a plane that has two or more engines)

a gene that by itself has little effect on the phenotype but which can act together with others to produce observable variations

a number puzzle in which the numbers 1 through 9 must be placed into a grid of cells so that each row or column contains only one of each number

the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural)

the conversion from analogue quantity to digital quantity

a relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third

a quantifier that can be used with count nouns and is often preceded by `as' or `too' or `so' or `that'

a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets

a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality

of or relating to or being an integer that cannot be factored into other integers

the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)

a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane

the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant

an English verb followed by one or more particles where the combination behaves as a syntactic and semantic unit