How to Distribute Math

Introduction to how to distribute math:
Distribution functions in mathematics are mainly used for generalizing the functions. By distributing the function, the derivatives cannot exists in the classical sense. The formulations of partial differential equations are done by using the distribution function. In the partial differential equation, the classical solutions are very difficult to use. But when we using the distribution function it is very easy.

Various types for how to distribute math


There are many types of functions are used to distribute math. They are given in the following,

Distribute test function
Distribute operations
Distribute the localization functions



Explanation for how to distribute math


Distribute test function:

Distribution functions are defined as one of the types of distribution in the mathematics. For example, the distribution function on U is given by S: (U) `|->` R has the values in the R function. Then it can be given by,

`lim_(n->oo)` S(φn ) = S ( `lim_(n->oo)` φn )

where,

φn = convergent sequence present in D(U).
D' (U) = continuous dual space
Distribute of operations:

Distributions of operations are also one of the types of the distribution function in mathematics. Therefore, most of the operation is mainly defined on the smooth functions. Therefore the formula is given by,

T : D(U) `|->` D(U)

The above function is defined as the linear mapping functions.where, T is used to represent the topology.

By extending the function og T we get,

T  : D' (U) `|->` D' (U)

Distribute of localization functions:

Localization is also one of the distribution functions of mathematics. The value of U present in the distribution function is not given easily in D' (U) . Some restrictions are given to the U value. Therefore the open function of U is given as distribution function. The restrictions formula is given by,