By using a semi-analytical method and an eigenfunction expansion method, we obtain part of expressions about capacitances.
By this method we obtain the almost-sure version of several useful identities that are usually stated under expectations.
By using a Fourier Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations.
Using the bootstrap argument and the difference quotient method, we obtain that if aij∈C0,1loc, then u∈W2,ploc for any p<∞.
It should be noted that by means of this direct method we obtain a maximized reversible entropy change where the hysteresis losses seem to be minimized, probably due to kinetic factors related to the rate of pressure application/removal. Figure 5: Direct isothermal entropy change.
By putting forward a new updating mechanism of the histogram function in energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method.
Therefore, by the same method, we obtain the following theorem.
By a similar method, we obtain the following.
Next, by this method we obtain the regularity in time of the solution.
Following a final convergence of the amplitude using Newton's method, we obtain the fully converged spectrum.
In this paper, through the NSFD-θ method, we obtain general results.
