They arise in situations in which one believes that what happens depends not only on the external world, but also on the precise pattern of behavior of the individual or group.

The internal energy of an ideal gas depends on temperature only and is independent of pressure or volume.

It may be that the objective function depends not only on Af but also on Af, as when the cost of the operating policy is considered.

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

" Noting that " It depends on the data we use, but roughly speaking, per capita income in developing countries grew at 3 % per year between 1960 and 1980, but has grown only at about 1. 5 % between 1980 and 2000.

In contrast, stellar aberration is independent of the distance of a celestial object from the observer, and depends only on the observer's instantaneous transverse velocity in certain frame of reference, at the moment of observation.

Light-time correction does not depend on the motion of the Earth – it only depends on Earth's position at the instant when the light is observed.

Wedge-shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness, the precise value of which depends on deposition temperature, background pressure and various other process parameters.

* If the operation is associative, ( ab ) c = a ( bc ), then the value depends only on the tuple ( a, b, c ).

* If the operation is commutative, ab = ba, then the value depends only on

In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed.

It is not a vector field because it depends not only on the position of a particular material point, but also on the local orientation of the surface element as defined by its normal vector.

The utility of Cauchy sequences lies in the fact that in a complete metric space ( one where all such sequences are known to converge to a limit ), the criterion for convergence depends only on the terms of the sequence itself.

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.

The rate of a first-order reaction depends only on the concentration and the properties of the involved substance, and the reaction itself can be described with the characteristic half-life.

Whether or not a certain cycloaddition would proceed depends on the electronic orbitals of the participating species, as only orbitals with the same sign of wave function will overlap and interact constructively to form new bonds.

The entries can be numbers or expressions ( as happens when the determinant is used to define a characteristic polynomial ); the definition of the determinant depends only on the fact that they can be added and multiplied together in a commutative manner.

− 1 / 30, … are the Bernoulli numbers, and R is an error term which is normally small for suitable values of p and depends on n, m, p and f. ( The formula is often written with the subscript taking only even values, since the odd Bernoulli numbers are zero except for B < sub > 1 </ sub >.

The energy of formation of a molecule containing only single bonds then can be approximated from an electronegativity table, and depends on the constituents and sum of squares of differences of electronegativities of all pairs of bonded atoms.

Note that the error, e, depends not only on the estimator ( the estimation formula or procedure ), but on the sample.

Note that the sampling deviation, d, depends not only on the estimator, but on the sample.

Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.

Weather and GW Bridge traffic screen off other influences. Intuitively, this reduction in representation size is achieved simply because each variable depends only on a subset of the other variables.

Thus, variable only depends directly on variable, rather than depending on the entire set of variables.

`` It depends on who does it.

Prieur has gout and depends on Louis' pills and bleedings.

And yet we obviously also believe that the avoidance of the disaster depends in some obscure or at least uncertain way on the details of how we behave.

As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.

The third type, however, wrenches attention from the life of action and interests in the community and focuses it on the ground of being on which the community depends for its existence.

A great deal depends on the crystallization of Mr. Kennedy's views on the world struggle.

The amount which may be borrowed from the SBA depends on how much is required to carry out the intended purpose of the loan.

This includes assistance in -- assembling the basic economic, financial, technological, and educational information on which programing depends ; ;

Since the validity of all subsequent planning depends on the accuracy of the basic inventory information, great care is being taken that the inventory is as complete as possible.

The extent of such interference -- which may be so slight as to be undetectable at any point where either of the stations renders a usable signal, or may be so great as to virtually destroy the service areas of both stations -- depends on many factors, among the principal ones being the distance between the stations, their respective radiated power, and, of particular significance here, the time of day.

The number of locking bars required depends on how many false moves must be prevented.

How large a cooling unit you need, and the method of its installation, depends on a variety of factors.

This, of course, depends on the character of the site itself, the previous experience of the investigator, and the number of factors needed to arrive at a good decision.

The selection of materials depends on skills of available labor for installation, cost of materials available locally, and your own preference.

The number depends on who is talking at the moment.

This energy transfer depends on the current, the temperature in the arc column, the anode material, and the conditions in the anode sheath.

It is on them alone that the future of their race depends, for all their relatives ( mothers, husbands, brothers, and unmated sisters ) have perished with the arrival of the cold weather.

but basically that pace depends on changes in the supply of resources and in the human attitudes, political institutions, and social structure which each society must generate.

In the written language then can be underlined or italicized to guide the reader here, but much of the time the written language simply depends on the reader's alertness, and a careless reader will have to back up and reread.

The U.N.F.P. learned that its urban organization, which depends heavily on U.M.T. support, was most effective.