What is a Functional

First the question is What is a functional One may think of a functional as a function of a function. Thus, one writes F(y(r)) where y is a 

The subscripts n are more than just numbers they change the function and not simply its argument x. For another example, examine the functional 

Clearly, F has a definite value and can be determined provided y is known. One would not, however, expect to get the same value for F for different functions of y. Consider the series y = x as an example. The values obtained for F for some of the functions y are given in Table 37. 

The function inside the functional need not be an analytic function. For example, what approximately is the average age for all lowans given the 

The challenge in modeling adsorption is to first construct a functional of number density of the adsorbed molecule that is capable of calculating the free energy of the system. The density, which is a function of position, is then adjusted to minimize this free energy. 

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As mentioned earlier, density functional theory (DFT) does not yield the wave-function directly. Instead it first determines the probability density p and calculates the energy of the system in terms of p. Why is it called density functional theory and what is a functional anyway We can define functional by means of an example. The variational integral E(trial wavefunction ip and it yields a number (with energy unit) for a given electron density p, which itself is a function of electronic coordinates. 

What is a function For our purposes, a function is defined as an activity, action, process, or condition that operates between two variables, one the input (independent) variable and the other the output (dependent) variable. In between the input and output is a value transformation, because the function creates a more valuable output using a less valuable input. By virtue of the function, value is added. 

What is A function that 1. takes three arguments, and 2. corwes the second argument onto the result of consing the first argument onto... 

What is a functional Recall that a function f x) is a rule that associates a number with each value of the variable x for which the function / is defined. For example, the function f(x) = jc + 1 associates the number 10 with the value 3 of x and associates a number with each other value of x. A functional F[f] is a rule that associates a number with each function /. For example, the functional F[f] = / / (x)/(x) dx associates a number, found by integration of /p over all space, with each quadratically... 

What is a functional A function of another function. In mathematics, a functional is traditionally a map from a vector space to the field underlying the vector space, which is usually the real numbers. In other words, it is a function that takes a vector as its argument or input and returns a scalar. For example, Thomas and Fermi have shown in 1929 that the kinetic energy for an electron gas may be represented as a functional of the density. The first H-K theorem demonstrates that the electronic energy of a system is functional of a single electronic density only. 

What is a functional group Give an example and explain how it fits this definition. 

What is a functional group List some examples. 

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