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Additional resources for Shockwave Propagation Through Complex Geometry 2-Phase Media [thesis]
This time like vector can be attached to a fixed frame of reference like aether in older time. In that case, the scattering matrix or S- matrix operator would depend on the parameters of one fixed frame and would immediately violate the equivalence of all Lorentz frames. Therefore, the time-like vectors n must be allowed to vary over the whole set of Lorentz frames. It immediately raises the question regarding the physical meaning of frame dependence. Ingraham put forward a hypothesis regarding this frame dependence.
The increasing degree of fuzziness of the topology so that in the limit W2 can be written globally and we have the corresponding HamiltonJacobi equation for where p = exp[2R]. 28) It should be mentioned that Kramosil and Michalek [Kramosil 1975] have already established that the concepts of statistical metric and fuzzy metric are equivalent in certain sense. So the above procedure can be thoroughly considered in fuzzy metric spaces which might have greater impact in other branches of physical science.
6) I, I, and 9ij52 being the metric tensors when the slit one is open only and slit two open only respectively. It is also assumed that the screen in the experiment is placed far from the slits so that the individual probabilities ( _g51) 1/2 and (_g52) 1/2 can be considered as constants over the screen. ". ". " - 1 0 0 0 1 0 0 0 s 0 0 0 0 0 0 -t Irl ",,1 = -st sand t are yet unspecified function of position. 8) = exp(ia), where a g81 ~v = 1 0 0 0 is some unspecified function, we get 0 1 0 0 0 0 eia 0 0 0 0 _e- ia and, -82 9 where, ~v = 1 0 0 0 0100 0 0 eiß o 0 0 _e-iß ß is another unspecified function.