Before we can treat this relationship as a single-valued function, the range of the resulting value must be restricted somehow.

The structure constants are required to be single-valued functions, rather than sections of some vector bundle.

A single-valued function is an emphatic term for a mathematical function in the usual sense.

The corresponding result for single-valued functions is the Tychonoff fixed-point theorem.

In this case, the height, Z, is a single-valued function, defined over a geometrically rectangular grid.

Using the branch points, these functions may be redefined to be single-valued functions, by restricting the range.

The additional constraint W 1 defines a single-valued function W(x).

Branch cuts allow one to work with a collection of single-valued functions, "glued" together along the branch cut instead of a multivalued function.

Normally, the interface dynamics is described by a single order parameter, the profile, which is assumed to be a single-valued function of the position along the interface.

Since virtual displacements are automatically compatible when they are expressed in terms of continuous, single-valued functions, we often mention only the need for consistency between strains and displacements.

If a univariate single-valued function is multiply periodic, then such a function cannot have more than two periods, and the ratio of the periods cannot be a real number.

In other parts of mathematics, non-single-valued relations are similarly conflated with functions: these are called multivalued functions, with the corresponding term single-valued function for ordinary functions.

Some identities for powers and logarithms for positive real numbers will fail for complex numbers, no matter how complex powers and complex logarithms are defined "as single-valued functions".

Complex numbers, unlike real numbers, do not in general satisfy the unmodified power and logarithm identities, particularly when naïvely treated as single-valued functions; see failure of power and logarithm identities.

An equivalent local (differential) definition of a conservative field is that it can be written in terms of the gradient of the potential energy as (provided the potential energy is a single-valued function of position).

In ferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis: B is not a single-valued function of H, but depends also on the history of the material.

A solution for this is to introduce a parameter so that the input data would be represented as single-valued functions depending on that parameter; after this the smoothing will be performed for each function.

It is concluded that the independence of K0 from OCR may be quite widespread, a finding that contradicts the widely held tenet regarding the existence of a single-valued function relating K0, , and OCR.

However, there are other cases where this kind of loop is useful, such as when binding a variable to the result of applying a single-valued function, or when the semantics of the current domain require that a set evaluates to a singleton set.

Noting that the search for a minimum or maximum of a single-valued function is nothing else than the search for the zeroes of the gradient of that function, quasi-Newton methods can be readily applied to find extrema of a function.

In other words, if is the gradient of then searching for the zeroes of the multi-valued function corresponds to the search for the extrema of the single-valued function ; the Jacobian of now becomes the Hessian of .

One of these is a LC oscilloscope developed by Scopex Instruments in conjunction with the Royal Signals and Radar Establishment (RSRE), An oscilloscope needs only display waves - single-valued functions - so drastic simplifications can be made to the addressing.