Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis...

In the case of functions of several real variables and real vector spaces, a slightly more general form of homogeneity called positive homogeneity is...

positive length. Most real functions that are considered and studied are differentiable in some interval. The most widely considered such functions are...

a positive-definite function is, depending on the context, either of two types of function. Let R {\displaystyle \mathbb {R} } be the set of real numbers...

In mathematics, the set of positive real numbers, R > 0 = { x ∈ R ∣ x > 0 } , {\displaystyle \mathbb {R} _{>0}=\left\{x\in \mathbb {R} \mid x>0\right\}...

and characterization for any holomorphic function on the unit disc with positive real part. Such functions had already been characterized in 1907 by...

requires p {\displaystyle p} to be real-valued. A function p : X → R {\displaystyle p:X\to \mathbb {R} } is called positive or nonnegative if p ( x ) ≥ 0 {\displaystyle...

of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued...

f(x)=\Gamma (x)} is the unique interpolating function for the factorial, defined over the positive reals, which is logarithmically convex, meaning that...

mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on...

In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered...

mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member...

sign of a given real number is positive or negative, or the given number is itself zero. In mathematical notation the sign function is often represented...

{\displaystyle M} with real entries is positive-definite if the real number x T M x {\displaystyle \mathbf {x} ^{\mathsf {T}}M\mathbf {x} } is positive for every nonzero...

mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle...

behavior is similar to the limit of a function lim x → x 0 f ( x ) {\textstyle \lim _{x\to x_{0}}f(x)} in which the real number x {\displaystyle x} approaches...

mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals...

In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential...

applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables...

defined on a sub-domain of the real line with respect to the Lebesgue measure. The integral of a positive real function f between boundaries a and b can...

necessarily positive ( | x | = − x > 0 {\displaystyle |x|=-x>0} ). From an analytic geometry point of view, the absolute value of a real number is that...

In mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle...

In mathematics, the positive part of a real or extended real-valued function is defined by the formula f + ( x ) = max ( f ( x ) , 0 ) = { f ( x )  if ...

pri, a notation for the scalar projection onto the i-th component Positive-real function, in mathematics Proportional representation, a property of some...

reticular formation Positive-real function in mathematics Programmed ribosomal frameshifting during mRNA translation Pseudorandom function family Pulse repetition...

supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex...

the upper incomplete gamma function, as defined above for real positive s and x, can be developed into holomorphic functions, with respect both to x and...

from a given rational function in s. For synthesis to be possible in passive elements, the function must be a positive-real function. To synthesise as an...

setting of order theory. In calculus, a function f {\displaystyle f} defined on a subset of the real numbers with real values is called monotonic if it is...

In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion...