* Injective function

* Injective function

# redirect Injective function

# redirect Injective function

* Injective function

# REDIRECT Injective function

* Injective function –

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

* Ai ( x ), the Airy function, a special function in mathematics

* Binary function, a function in mathematics that takes two arguments

In mathematics, a binary function, or function of two variables, is a function which takes two inputs.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

* Partition function ( mathematics )

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

In mathematics, a continuous function is a function for which, intuitively, " small " changes in the input result in " small " changes in the output.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

A convex function | function is convex if and only if its Epigraph ( mathematics ) | epigraph, the region ( in green ) above its graph of a function | graph ( in blue ), is a convex set.

In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments ( or an n-tuple of arguments ) in such a way that it can be called as a chain of functions each with a single argument ( partial application ).

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes.

* The Dirac delta function in mathematics

A drawing for a booster engine for steam locomotive s. Engineering is applied to design, with emphasis on function and the utilization of mathematics and science.

" However, as Stocking notes, Tylor mainly concerned himself with describing and mapping the distribution of particular elements of culture, rather than with the larger function, and he generally seemed to assume a Victorian idea of progress rather than the idea of non-directional, multilineal cultural development proposed by later anthropologists.

important to distinguish between the notion of algorithm, i. e. procedure and the notion of function computable by algorithm, i. e. mapping yielded by procedure.

On the left side, is a function mapping any point in space to a complex number ; on the right side, is a ket.

For each K, the function E < sub > K </ sub >( P ) is required to be an invertible mapping on

The bilinear transform is a special case of a conformal mapping ( namely, the Möbius transformation ), often used to convert a transfer function of a linear, time-invariant ( LTI ) filter in the continuous-time domain ( often called an analog filter ) to a transfer function of a linear, shift-invariant filter in the discrete-time domain ( often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters ).

The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.

Given x ∈ A, the holomorphic functional calculus allows to define ƒ ( x ) ∈ A for any function ƒ holomorphic in a neighborhood of Furthermore, the spectral mapping theorem holds:

A code is a total function mapping each symbol from S to a sequence of symbols over T, and the extension of M to a homomorphism of into, which naturally maps each sequence of source symbols to a sequence of target symbols, is referred to as its extension.

In the Lagrangian description, the motion of a continuum body is expressed by the mapping function ( Figure 2 ),

Mathematically, the motion of a continuum using the Eulerian description is expressed by the mapping function

Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).

Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

Condition numbers can be defined for any function ƒ mapping its data from some domain ( e. g. an m-tuple of real numbers x ) into some codomain an n-tuple of real numbers ƒ ( x ), where both the domain and codomain are Banach spaces.

* the inverse function f < sup > − 1 </ sup > is continuous ( f is an open mapping ).

* The open interval ( a, b ) is homeomorphic to the real numbers R for any a < b. ( In this case, the bicontinuous forward mapping is given by and the inverse mapping is given by a scaled version of the function ).

This mapping is one-to-one and onto, that is, it is a bijection from the domain to the codomain of the logarithm function.

means " ƒ is a function mapping elements of a set X to elements of a set Y ".

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.

In other words, we wish to infer the mapping implied by the data ; the cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain.

* is the < em > transition function </ em >, mapping into finite subsets of.