The
conserved quantity of the gravitational field has the form [100]
Among different spacetime symmetries isometries or the Killing vectors (KVs) have the importance that they help in understanding the geometric properties of spaces also corresponding to each isometries there is some
conserved quantity. They are also subset of the Noether symmetry (NS) [1-3] i.e.
In other words, each symmetry determines a
conserved quantity. Conservation laws help us to understand and describe a dynamical system.
If every
conserved quantity can be associated this way, we have a well-defined mapping between the fields and conserved quantities.
In order to connect the exclusion principle with a
conserved quantity, supposing "1" (or any other constant) denote "valid", and "does not equal 1" denote "invalid", in this way the exclusion principle (denoted as P) can be written as the following form of
conserved quantity P=1
of (28), if the spatial flux [T.sup.2] vanishes on the boundary x = 0 and x = [infinity] of the semi-infinite medium, then integration from x = 0 to x = [infinity] provides
conserved quantity of the boundary value problem.
A
conserved quantity was utilized to find the unknown exponent in the similarity solution which could not have been obtained from the homogeneous boundary conditions [16].
The above observation states that for any (interaction-free) additive
conserved quantity in a reversible cellular automaton, there corresponds a Bernoulli distribution that is stationary.
(6.6) guarantee that if a function H is a time-dependent
conserved quantity for v, then X (H) with X being any of the vectors in Eq.
From a mathematical point of view it is understood as a consequence of Noether's theorem, if the theory's symmetry is time invariance then the
conserved quantity is called energy.