This invariant conserved quantity
Q[[xi]] was given before in [102-106].
Corresponding to each Noether symmetry, one can find a conserved quantity
Conversely, each conserved quantity
has a corresponding symmetry.
As an example, the conservation law (30) is applied to derive conserved quantity
of the BVP
Finally, the conserved quantity
may involve contributions from the interactions between nearby cells, in which case the corresponding probability distribution becomes a Markov measure.
Since, [i.sub.v][gamma] = 0 by duality relations, this function is a conserved quantity
of the Darboux-Halphen system and, as we pointed out earlier, the Halphen symmetries, when acted upon [H.sub.1] produces new conserved quantities two of which will be sufficient to establish the bi-Hamiltonian structure.
Problems for the Conserved Quantity
Theory: Counterexamples, Circularity, and Redundancy, CHRISTOPHER HITCHCOCK
(If the space-time metric is not stationary, then one must also include gravitational energy to get a conserved quantity
, and further complications arise.
Thus, the check to which extent a conserved quantity
of the respective equation is also numerically conserved could provide some control of the quality of the numerical scheme in a specific case.
Since the Born-Oppenheimer curves do not depend on f it is a conserved quantity
. There is also a restriction on the permissible quantum numbers due to the homonuclear nature of the dimer since the basis states must be antisymmetric with respect to exchange of the two nuclei.
Dowe, Phil, 2000, "The Conserved Quantity
Theory Defended", Theoria, 15, pp.
These theories permit, and some even require, that the number of baryons, elementary particles that include protons and neutrons, is not a strictly conserved quantity
. Baryon nonconservation "leads to a whole host of decay channels for the proton," Adams says.