# Functions and Analysis

## 1301 Submissions

[2] **viXra:1301.0036 [pdf]**
*submitted on 2013-01-07 01:37:06*

### Exact Solutions of Space Dependent Korteweg-de Vries Equation by the Extended Unified Method

**Authors:** Hamdy I. Abdel-Gawad, Nasser S. Elazab, Mohamed Osman

**Comments:** 6 Pages. IOSR Journals

Abstract: Recently the unified method for finding traveling wave solutions of non-linear evolution equations
was proposed by one of the authors a. It was shown that, this method unifies all the methods being used to find
these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de
Vries (KdV) equation with space dependent coefficients. A new class of multiple-soliton or wave trains is
obtained.
Keywords: Exact solution, Extended unified method, Korteweg-deVries equation, variable coefficients

**Category:** Functions and Analysis

[1] **viXra:1301.0010 [pdf]**
*submitted on 2013-01-02 18:58:54*

### P vs NP Graphed

**Authors:** Andrew Nassif

**Comments:** 2 Pages.

For many years lied a problem called the P vs NP. The question is to find the number of factorial possibilities to its orders. An example of this is finding the possibilities and comparison of improbabilities of picking 100 students out of 400 students. According to Lardner's theorem the number of known atoms in the universe is less then the number of combinations of possible orders and combinations of the answer to the P vs. NP problems. Finding the equation for the number of different orders a group of 400 people can be put into and subtracting 300 different people that couldn't get picked is equal to ((400!)-(100!*3)). My project is to represent this data through algorithms and different diagrams. When looking at my project you will know how I found a solution and the importance of it. My project will include all the required schematics, and graphs that coordinates with this answer. It will also acquire data showing different possibilities between P vs NP. As well as the combination where P can equal NP and N equals 1, or the possibilities where P doesn't equal NP and N isn't 1. P and NP is believed to stand for the number of possibilities and impossibilities.

**Category:** Functions and Analysis