General Mathematics

1409 Submissions

[2] viXra:1409.0120 [pdf] submitted on 2014-09-15 15:02:25

Examples of Solving PDEs by Order Completion

Authors: Elemer E Rosinger
Comments: 15 Pages.

So far, the order completion method for solving PDEs, introduced in 1990, can solve by far the most general linear and nonlinear systems of PDEs, with possible initial and/or boundary data. Examples of solving various PDEs with the order completion method are presented. Some of such PDEs do not have global solutions by any other known methods, or are even proved not to have such global solutions. The presentation next aims to be as summary, and in fact, sketchy as possible, even if by that it may create some difficulty. However, nowadays, being subjected to an ever growing ``information overload", that approach may turn out to be not the worst among two bad alternatives. Details can be found in [1], while on the other hand, alternative longer "short presentations" are in [6-8].
Category: General Mathematics

[1] viXra:1409.0053 [pdf] replaced on 2014-09-12 01:30:00

On a Unit that Has to be an Integral of the Delta-Function: One Cannot Detach Mathematics from Physics Here!

Authors: Emanuel Gluskin
Comments: 4 Pages. A simple, but important observation, relevant both to mathematics and physics

The integral of the delta-function is 1, but when does '1' have to be interpreted as an integral of the delta-function? In order to make an interpretation of the volumes of figures of different dimensions more homogeneous, we follow a line of thought that leads us "back" to the original physical arguments from which the concept of delta-function arose.
Category: General Mathematics