Abstract:
We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created fluctuationally from a background Zero Point Field. We conclude that these conservation laws are to be taken in the spirit of thermodynamic laws.

Abstract:
There are six standard conservation laws of
physics: energy, momentum, angular momentum, charge, baryon number and lepton
number. It is not generally recognized that there are also a vast number of
other conservation laws in physics which are rigorously conserved and quite
inde-pendent of these six. A simple proof of these other conservation laws is
given as well as examples. The implication of these additional conservation
laws is discussed for elementary particles.

Abstract:
By means of a direct approach, a complete set of conservation laws for incompressible fluids is determined. The problem is solved in the material (Lagrangian) description and the results are eventually rewritten in the spatial (Eulerian) formulation. A new infinite family of conservation laws is determined, besides those for linear momentum, angular momentum, energy and helicity.

Abstract:
The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved space presents many challenges. The implementation of conservation laws in the General Relativity theory is revised, and the possibility of the generalization of the usual expression is discussed. The Rastall's theory of gravity, which considers a modification of the usual conservation of the energy-momentum tensor, is discussed in more detail. Some applications of the Rastall's theory to cosmology are presented, showing that it can lead to competetive results with respect to the Standard Cosmological Model.

Abstract:
For some ideal quantum measurements, conservation laws would seem to be violated systematically. It is argued that the intrinsically non-"ideal" nature of quantum measurements rescues the conservation laws.

Abstract:
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law and its associated conserved quantity are invariant (and, more generally, homogeneous) under the action of a symmetry. These results are used to show that a recent conservation law formula (due to Ibragimov) is equivalent to a standard formula for the action of an infinitesimal symmetry on a conservation law multiplier.

Abstract:
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.

Abstract:
We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws.

Abstract:
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under the constraint of the flat universe. Conservation laws for fundamental forces are related to gauge theories for fundamental forces, their resulting fundamental constants are quantitatively analyzed, and their possible violations at different energy scales are proposed based on experimental evidences.

Abstract:
There has been certain criticism raised by A. Rescigno [2,8,9,12-15] against the standard formulation of pharmacokinetics. In 2011 it has been suggested that inconsistencies in pharmacokinetics should be eliminated after deriving "pharmacokinetic parameters" from conservation laws [3]. In the following text a simple system of conservation laws for extra - vascular administration of a drug is explicitly given and preliminary discussion concerning this issue is included.