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It can be thought of as the rate of change of the function in the -direction.. Sometimes, for = (,, …), the partial derivative of with respect to is denoted as . Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in:
The partial trace operator can be defined invariantly (that is, without reference to a basis) as follows: it is the unique linear map : such that
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
Formally, the partial correlation between X and Y given a set of n controlling variables Z = {Z 1, Z 2, ..., Z n}, written ρ XY·Z, is the correlation between the residuals e X and e Y resulting from the linear regression of X with Z and of Y with Z, respectively.
Intuitively, partial function application says "if you fix the first arguments of the function, you get a function of the remaining arguments". For example, if function div(x,y) = x/y, then div with the parameter x fixed at 1 is another function: div 1 (y) = div(1,y) = 1/y.
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable.It is also called the PPT criterion, for positive partial transpose.
A partial function arises from the consideration of maps between two sets X and Y that may not be defined on the entire set X.A common example is the square root operation on the real numbers : because negative real numbers do not have real square roots, the operation can be viewed as a partial function from to .
Coyote en Ayuno ("Fasting Coyote"), also known as Coyote Hambriento ("Hungry Coyote") and Cabeza de Coyote ("Coyote Head"), is an outdoor steel sculpture by abstract monumental artist Enrique "Sebastián" Carbajal, installed on a roundabout in the intersection of Adolfo López Mateos Avenue and Pantitlán Avenue, in the municipality of Nezahualcóyotl, State of Mexico.