Sentence examples for solution described by from inspiring English sources

end{aligned} (25) Figure 1 shows the single soliton solution for Eq. (1) for some special values of the solution's parameters in Eq. (24). Figure 1 Plots of the solution described by Eq. ( 24 ).

end{aligned} (30) Figure 2 shows the two soliton solutions for Eq. (1) for some special values of the solution's parameters in Eq. (29). Figure 2 Plots of the solution described by Eq. ( 29 ).

end{aligned} (33) Figure 3 shows the three soliton solutions for Eq. (1) for some special values of the solution's parameters in Eq. (32). Figure 3 Plots of the solution described by Eq. ( 32 ).

end{aligned} (48) Figure 5 shows the two singular soliton solutions for Eq. (1) for some special values of the solution's parameters in Eq. (47). Figure 5 Plots of the solution described by Eq. ( 47 ).

end{aligned} (43) Figure 4 shows the single singular soliton solution for Eq. (1) for some special values of the solution's parameters in Eq. (42). Figure 4 Plots of the solution described by Eq. ( 42 ).

Grundmann and Rötter differentiated the extremely homogeneous, fine (1 2 μm in diameter) bright yellow particles when obtained from a thioacetamide solution described by FitzHugh from the even smaller (0.1-0.4 0.1-0.4ticles obtained when prepared from hydrogen sulfide [3].

Attempts to define weak solutions to nonconservative hyperbolic systems have lead to the development of several approaches, most notably the path-based theory of Dal Maso, LeFloch, and Murat (DLM) and the vanishing viscosity solutions described by Bianchini and Bressan.

In case of unsolvable problems, solutions described by undergraduates were inconsistent with problem text that they described.

Instead it is more profitable to look for new eigenmode solutions described by the collective modes delocalized over the entire structure.

For example, in the case of discontinuous solutions described by Heaviside functions H a ( t ), we can use its connection with δ-function: H a ( t ) = ∫ − ∞ t δ a d ξ and to get to a system of integro-differential equations.

The solutions described by Brinkmann et al. [ 24], Spitzer et al. [ 25], and Lablans et al. [ 26] are also based on the German model, and therefore these references contain short descriptions of the model.