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In practice, this means that alpha particles from all alpha-emitting isotopes across many orders of magnitude of difference in half-life, all nevertheless have about the same decay energy. Formulated in 1911 by Hans Geiger and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air, [ 1 ] in its ...
Oresme's geometric verification of the Oxford Calculators' Merton Rule of uniform acceleration, or mean speed theorem. Galileo's demonstration of the law of the space traversed in case of uniformly varied motion. It is the same demonstration that Oresme had made centuries earlier.
For example, although general relativity includes equations that do not have exact solutions, it is widely accepted as a valid theory because all of its equations with exact solutions have been experimentally verified. Likewise, a theory of everything must work for a wide range of simple examples in such a way that we can be reasonably ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
and are the half-lives (inverses of reaction rates in the above equation modulo ln(2)) of the parent and daughter, respectively, and BR is the branching ratio. In transient equilibrium, the Bateman equation cannot be simplified by assuming the daughter's half-life is negligible compared to the parent's half-life.
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In the general case a conservation equation can be also a system of this kind of equations (a vector equation) in the form: [10]: 43 + = where y is called the conserved (vector) quantity, ∇y is its gradient, 0 is the zero vector, and A(y) is called the Jacobian of the current density.