The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity field. At first, we rewrite the relativistic Newton’s second law as a field equation in terms of the velocity field, which directly reveals a new relationship...

The Blasius problem f ′′′ + ff ′′ = 0, f(0) = −a, f ′(0) = b, f ′(+∞) = λ is investigated, in particular in the difficult and scarcely studied case b < 0 λ. The shape and the number of solutions are determined. The method is first to reduce to the Crocco equation uu′′ + s = 0 and then to use an associated autonomous planar vector field. The most useful properties of Crocco solutions appear to b...

in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...

We show in detail the general relationship between the Schrödinger equation approach to calculating the MSW effect and the quantum field-theoretical S-matrix approach. We show the precise form a generic neutrino propagator must have to allow a physically meaningful ‘‘oscillation probability’’ to be decoupled from neutrino production fluxes and detection cross sections, and explicitly list the c...

Both single emitters and large area field (LAFEs) are generally characterized using the slope intercept of a Murphy–Good (or Fowler–Nordheim) plot, which used to extract enhancement factor emission area. Using shielding model that has been developed recently for LAFE, validity underlying assumption is investigated. It found in case contributions from as well rate at effective number superemitte...