Equations
- Type I : equations derived by simple operations on the basic equation itself
- Type II : equations derived by multiplying the basic equation or other Type I equations with a scalar
- Type III : equations derived by multiplying the basic equation or other Type I equations with a pseudoscalar
- Type IV : equations derived by multiplying the basic equation or other Type I equations with a vector
- Type V : equations derived by multiplying the basic equation or other Type I equations with a pseudovector
- Type VI
: equations derived by exploiting the cardinality of the basic equation
Equations (Type I)
Top Axiom
\[\sum_{i=0}^{N_\Phi}\Phi_i=1\]
Basic Equation (power n)
\[\left(\sum_{i=0}^{N_\Phi}\Phi_i\right)^n=1\]
\[\sum_{i=-\infty}^{-1}\Phi_i +\sum_{i=0}^{N_\Phi}\Phi_i +\sum_{N_\Phi+1}^{\infty}\Phi_i=1\]
\[S= - \sum_{i=0}^{N_\Phi}\Phi_i ln \Phi_i\]
\[-\sum_{i,j=0,i\neq j}^{N_\Phi}\Phi_i\Phi_j=\sum_{i=0}^{N_\Phi}(\Phi_i^2-\Phi_i)\]
(approximation)
\[\sum_{i,j=0,i\neq j}^{N_\Phi}\Phi_i\Phi_j \cong S\]
\[\sum_{i=0}^{N_\Phi-1} \frac {\Delta\Phi_i} {\Phi_{max}-\Phi_{min}}\ = 1\]
Transient Equation
\[\sum_{i=0}^{N_\Phi-1}\dot{\Phi_i}{\tau} = 1\]
Gradient Equation
\[\sum_{i=0}^{N_\Phi-1}\vec{l}\vec{\nabla}\Phi_i = 1\]
Gradient Entropy
\[S=-\sum_{i=0}^{N_\Phi-1}\vec{l}\vec{\nabla}\Phi_i ln\left ( \vec{l}\vec{\nabla}\Phi_i \right )\]
Basic Lagrangian
\[\left (\sum_{i=0}^{N_\Phi-1}\vec{l}\vec{\nabla}\Phi_i \right )^m - \left (\sum_{i=0}^{N_\Phi}\Phi_i\right )^n= T-V= 0\]
Equations (Type II)
Ideal Gas Equation
\[pV=(N+1)kT\]
Equations (Type III)
Scalar Field Equation
Equations (Type IV)
Conservation of momentum
\[\sum_{i=0}^{N_\Phi}\dot{\vec{p_i}}=\vec{0}\]
Equations (Type V)
Conservation of angular momentum
\[\sum_{i=0}^{N_\Phi}\dot{\vec{L_i}}=\vec{0}\]
Equations (Type VI)
Energy levels in Hydrogen
\[\ <E_m> - <E_n> = Ry(\frac{1}{n^2}-\frac{1}{m^2})\]
