This is the primary function of the imagination operating in the absence of the original experiential stimulus by which the images were first appropriated.

But because it is the function of the mind to turn the one into the other by means of the capacities with which words endow it, we do not unwisely examine the type of distinction, in the sphere of politics, on which decisions hang.

It was this fear which explained the development of a priestly caste whose function in society was to mollify and appease the angry deities.

A primary function is the operation of a Government Bid Center, which receives bids daily from the Federal Government's principal purchasing agencies.

Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

The values Af are the ordinary values at Af of a multi-valued function g{t} which has components corresponding to those of f{t}.

Closely related to this function is the fact that the religious system provides a body of ultimate ends for the society, which are compatible with the supreme eternal ends.

Tone languages use for linguistic contrasts speech parameters which also function heavily in nonlinguistic use.

The form of the industry demand function is one which makes quantity demanded vary inversely with the product price, and vary directly with the level of Aj.

The extent to which the public-limit price is raised by a given increase in the basic wage rate is itself a function of three things: the passage of time, the level of GNP, and the size of the wage increase.

We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.

Moreover, whereas in Interstate Commerce Commission parlance `` variable cost '' means a cost deemed to vary in direct proportion to changes in rate of output, in the type of analysis now under review `` variable cost '' has been used more broadly, so as to cover costs which, while a function of some one variable ( such as output of energy, or number of customers ), are not necessarily a linear function.

271 - 307 ) indicate, that the concept of function in sociology has been built up from physiological and biological models, in which the notions of teleology, i.e., metaphysical purpose, are central.

In a properly ordered society the massive force of public law performs the function which in natural law theory ineptly is left altogether to a small voice so often still.

Extreme caution should be used, however, to avoid the conflicting usage of an index word or electronic switch which may result from the assignment of more than one name or function to the same address.

The specification of the objective function of which the optimization is desired.

The objective function, which is to be maximized, is some function, usually piecewise continuous, of the product state.

An optimal policy is an admissible policy Af which maximizes the objective function P.

We thus have an optimal policy which maximizes the expected value of the objective function for a given Af.

As retinal images are conceded to be an integral function of the brain it seems logical to suppose that the nerves, between the inner brain and the eyes, carry the direct drive for cooperation from the various brain centers -- rather than to theorize on the transmission of an image which is already in required location.

A local church which conceives its function to be entirely that of ministering to the conscious desires and concerns of its members tends to look on everything ecumenical as an extra, not as a normal aspect of its own life as a church.

Exceptions are Lambertian surfaces, which scatter radiation in all directions according to a cosine function, so their albedo does not depend on the incident distribution.

Area can be defined as a function from a collection M of special kind of plane figures ( termed measurable sets ) to the set of real numbers which satisfies the following properties:

For example the arctangent function satisfies

Nevertheless, if a function satisfies the Cauchy – Riemann equations in an open set in a weak sense, then the function is analytic.

* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.

This length function satisfies the required properties of a norm and is called the Euclidean norm on R < sup > n </ sup >.

This is true since the von Mangoldt function satisfies the identity

For example, the function for x ∈ Q satisfies f ( 0 )

Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies

A function from to the extended real number line is called a measure if it satisfies the following properties:

In a more general sense, a vector norm can be taken to be any real-valued function that satisfies these three properties.

The work function satisfies

For bipartite pure states, the von Neumann entropy of reduced states is the unique measure of entanglement in the sense that it is the only function on the family of states that satisfies certain axioms required of an entanglement measure.

The Riemann zeta function satisfies the functional equation ( also called the Riemann (' s ) functional equation )

A Green's function is a fundamental solution that also satisfies a suitable condition on the boundary S of a volume V. For instance, may satisfy

Thus we cannot get a simple generalization of the Schrödinger equation under the naive assumption that the wave function is a relativistic scalar, and the equation it satisfies, second order in time.

In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.

Over the right half plane, the minimum value of the real part of a PR function occurs on the imaginary axis ( because the real part of an analytic function constitutes a harmonic function over the plane, and therefore satisfies the maximum principle ).

Hence, an antitone function f satisfies the property

If a function is harmonic ( that is, it satisfies Laplace's equation ) over a particular space, and is transformed via a conformal map to another space, the transformation is also harmonic.