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Constant term. In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial, The number 3 is a constant term. [1]
The usual order relation on the real numbers is antisymmetric: if for two real numbers and both inequalities and hold, then and must be equal. Similarly, the subset order on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements ...
Martin Huxley. Martin Neil Huxley FLSW (born in 1944) is a British mathematician, working in the field of analytic number theory. He was awarded a PhD from the University of Cambridge in 1970, the year after his supervisor Harold Davenport had died. He is a professor at Cardiff University. Huxley proved a result on gaps between prime numbers ...
Cartan subgroup. In the theory of algebraic groups, a Cartan subgroup of a connected linear algebraic group over a (not necessarily algebraically closed) field is the centralizer of a maximal torus. Cartan subgroups are smooth (equivalently reduced), connected and nilpotent. If is algebraically closed, they are all conjugate to each other.
where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the ...
Counting measure. In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity if the subset is infinite. [1]
Since the difference between two natural logarithms is a dimensionless ratio, the trait may be measured in any unit. Inexplicably, Haldane defined the millidarwin as 10 −9 darwins, despite the fact that the prefix milli-usually denotes a factor of one thousandth (10 −3). [2]
A period-one point is called a fixed point. The logistic map. exhibits periodicity for various values of the parameter r. For r between 0 and 1, 0 is the sole periodic point, with period 1 (giving the sequence 0, 0, 0, …, which attracts all orbits). For r between 1 and 3, the value 0 is still periodic but is not attracting, while the value is ...