# Functions and Analysis

## 1305 Submissions

 viXra:1305.0174 [pdf] submitted on 2013-05-28 22:01:07

### Rational Structure, General Solution and Naked Barred Galaxies

Authors: Jin He, Xiaoli Yang
Comments: 17 Pages. 2 Figures. Two theorems of rational structure are proved,

Rational structure in two dimension means that not only there exists an orthogonal net of curves in the plane but also, for each curve, the stellar density on one side of the curve is in constant ratio to the density on the other side of the curve. Such a curve is called a proportion curve or a Darwin curve. Such a distribution of matter is called a rational structure. Spiral galaxies are blended with dust and gas. Their longer wavelength (e.g. infrared) images present mainly the stellar distribution, which is called the naked galaxies. Jin He found many evidences that galaxies are rational stellar distribution. We list a few examples. Firstly, galaxy components (disks and bars) can be fitted with rational structure. Secondly, spiral arms can be fitted with Darwin curves. Thirdly, rational structure dictates New Universal Gravity which explains constant rotation curves simply and elegantly. This article presents the systematic theory of rational structure, its general solution and geometric meaning. A preliminary application to spiral galaxies is also discussed.
Category: Functions and Analysis

 viXra:1305.0156 [pdf] submitted on 2013-05-27 04:09:38

### A Particular Solution Formula For Inhomogeneous Second Order Linear Ordinary Differential Equations

Authors: Claude Michael Cassano

A formula for Particular solutions to any Linear Second Order Inhomogeneous Ordinary Diffrential equations is presented. For second order ODEs these make the methods of undetermined coefficients and variation of parameters obsolete.
Category: Functions and Analysis

 viXra:1305.0147 [pdf] submitted on 2013-05-23 19:33:33

### Creator's Standard Equation, General Solution and Naked Barred Galaxies

Authors: Jin He, Xiaoli Yang
Comments: 14 Pages. 1 figure. Solve the beautiful equation and reveal the secret of galaxies

We have not found the general solution to the Creator's equation system. However, we have outlined the strategy for determining the solution. Firstly, we should study the stretch equation which is the first order linear and homogeneous partial differential equation, and find its all stretches which correspond to the given vector field (i.e., the gradient of the logarithmic stellar density). Our solution G(x,y), however, must be simultaneously the modulus of some analytic complex function. It is called the modulus stretch. Secondly, among all possible modulus stretches, we find the right solution (i.e., the orthogonal net of curves) which satisfies the Creator's standard equation.
Category: Functions and Analysis

 viXra:1305.0094 [pdf] submitted on 2013-05-15 22:17:49

### The Creator's Equation System Without Composite Functions

Authors: Jin He, Xiaoli Yang
Comments: 11 Pages. 1 Figure. Nobel prizes come from the solutions of the Creator's equation.

Is the sum of rational structures also a rational structure? It is called the Creator's big question for humans. Numerical calculation suggests that it is approximately rational for the fitted parameter values of barred spiral galaxies. However, we need mathematical justification. The authors present the Creator's equation system without composite functions, the equation system being the necessary and sufficient condition for rational structure. However, we have not found its general solution. Please help us find the general solution.
Category: Functions and Analysis

 viXra:1305.0082 [pdf] submitted on 2013-05-14 00:58:36

### Numerical Solution of Nonlinear Sine-Gordon Equation with Local RBF-Based Finite Difference Collocation Method

Authors: Yaqub Azari

This paper presents the local radial basis function based on finite difference (LRBF-FD) for the sine-Gordon equation. Advantages of the proposed method are that this method is mesh free unlike finite difference (FD) and finite element (FE) methods, and its coefficient matrix is sparse and well-conditioned as compared with the global RBF collocation method (GRBF). Numerical results show that the LRBF-FD method has good accuracy as compared with GRBF.
Category: Functions and Analysis

 viXra:1305.0052 [pdf] replaced on 2013-05-15 22:21:50

### The Creator's Equation

Authors: Jin He, Xiaoli Yang
Comments: 8 Pages. 1 Figure. The authors are very old and are not experts in mathematics. Please help us humans to resolve the question.

Is the sum of rational structures also a rational structure? It is called the Creator's big question for humans. Numerical calculation suggests that it is approximately rational for the fitted parameter values of barred spiral galaxies. However, we need mathematical justification. The authors are very old and are not experts in mathematics. Please help us humans to resolve the question.
Category: Functions and Analysis

 viXra:1305.0040 [pdf] submitted on 2013-05-07 04:43:29

### The First Derivative Proof of B^^x , X^^x and X^^f(x) by Differentiation Fundamental Limits Method.

Authors: Nasser Almismari