The concept of the strain energy as a Gibbs function difference Af and exerting a force normal to the shearing face is compatible with the information obtained from optical birefringence studies of fluids undergoing shear.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

Such a function, intuitively, represents a programming language with the property that no valid program can be obtained as a proper extension of another valid program.

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

The practical motivation for partial application is that very often the functions obtained by supplying some but not all of the arguments to a function are useful ; for example, many languages have a function or operator similar to.

coefficients, a transfer function relating the input and output can be obtained by taking their Laplace transform.

It was Euler ( presumably around 1740 ) who turned his attention to the exponential function instead of logarithms, and obtained the correct formula now named after him.

The frequency response or transfer function of a filter can be obtained if the impulse response is known, or directly through analysis using Laplace transforms, or in discrete-time systems the Z-transform.

In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable.

In other words, the probability is obtained by integrating the characteristic function of B against the countably additive measure

This can be thought of as learning with a " teacher ," in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.

The expression patterns obtained under given conditions can provide insight into the function of that gene.

After the measurement is performed, having obtained some result x, the wave function collapses into a position eigenstate centered at x.

The values of the zeta function obtained from integral arguments are called zeta constants.

In other words, is a function representing the measurement at the i-th experiment and is the value actually obtained when making the measurement.

Solving the differential equation above, a solution which is a sinusoidal function is obtained.

In spite of this, a transfer matrix can be always obtained for any linear system, in order to analyze its dynamics and other properties: each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.

The wave equation is obtained by letting in which case takes the form where is continuous function of two variables, takes the form and

In some mathematical contexts, zero-based numbering can be used without confusion, when ordinal forms have well established meaning with an obvious candidate to come before first ; for instance a zeroth derivative of a function is the function itself, obtained by differentiating zero times.

Thus the Green's function describes the influence at of the data f and g. For the case of the interior of a sphere of radius a, the Green's function may be obtained by means of a reflection ( Sommerfeld, 1949 ): the source point P at distance ρ from the center of the sphere is reflected along its radial line to a point P that is at a distance

`` Mr. Gross, your report says that ' our function is investigative and advisory and does not in any way derogate from or prejudice Mr. Bang-Jensen's rights as a staff member.

The relation between osmotic pressure and the Gibbs function may also be developed in an analogous way.

The function f{t} defined in this way is multi-valued.

In a way the rules of evidence can function to give a judge limited inquisitorial powers as the judge may exclude evidence he / she believes is not trustworthy or irrelevant to the legal issue at hand.

Careful study of the different function and processes of the eyes, ears, and other organs paved the way for improved cameras, television, radio transmitters and receivers, and many other useful tools.

His own view is that consciousness has subjective, first-person causal powers by being essentially intentional due simply to the way human brains function biologically ; conscious persons can perform computations, but consciousness is not inherently computational the way computer programs are.

All physical quantities are defined this way at each instant of time, in the current configuration, as a function of the vector position.

Another way of computing this derivative is to view the composite function as the composite of and h. Applying the chain rule to this situation gives:

One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

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 ).

Gurevich adds the pointer machine model of Kolmogorov and Uspensky ( 1953, 1958 ): "... they just wanted to ... convince themselves that there is no way to extend the notion of computable function.

All of these drugs affect cell division or DNA synthesis and function in some way.

The equations are one way of looking at the condition on a function to be differentiable in the sense of complex analysis: in other words they encapsulate the notion of function of a complex variable by means of conventional differential calculus.

The manner in which Xavier's powers function indicates that his telepathy is physical in some way, as it can be enhanced by physical means ( for example, Cerebro ) and can be disrupted by physical means ( for example, Magneto's alteration of the Earth's magnetic field ).

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

Linking a particular generic function to a method in a class is accomplished this way:

An equivalent way to view an extractor is as a bivariate function

A variety of definitions exist: F. Stuart Chapin and coauthors define it as " the application of ecological science to resource management to promote long-term sustainability of ecosystems and the delivery of essential ecosystem goods and services ", while Norman Christensen and coauthors defined it as " management driven by explicit goals, executed by policies, protocols, and practices, and made adaptable by monitoring and research based on our best understanding of the ecological interactions and processes necessary to sustain ecosystem structure and function " and Peter Brussard and colleagues defined it as " managing areas at various scales in such a way that ecosystem services and biological resources are preserved while appropriate human use and options for livelihood are sustained ".

Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed ( i. e., recomposed ) from those parts by function composition.

In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.