Then, substituting the labor market equilibrium equation in period 0 into the labor market equilibrium equation in period 1 and rearranging the terms yields the following relationship between wages of natives and the proportion of immigrant workers: mathrm{L}mathrm{n} left({W}_{ki1}right) approx mathrm{constant} + left 1kern0.1em / eta right) {r}_{ki1} (1).
Boutat et al. [8] studied a generalized thin-film equation with period boundary in multidimensional space.
The study of systems governed by ordinary differential equation with period coefficients is of basic importance in many branches such as mathematics, physics, chemistry, biology, mechanics and finance, such systems are known as Floquet systems [1, 2].
Here it is shown (Sleeman, op. cit)., that when the dissipation term in continuous form is added to May's difference equation, solutions period 2 in time for each value of x satisfy a Hamiltonian system in space.
The percentage of change in skin wrinkle parameters and percent body fat were calculated using the following equation: ([treatment period − baseline value]/baseline values) ×100.
Following Bolotin's method, the instability regions are determined from the boundaries of instability, which represents the periodic solution of the differential equations with period T and 2T to the Mathieu equations.
We illustrate our results by finding periodic solutions of the dynamical system of ordinary differential equations with period 2π.
A system of second-order differential equations with period coefficients of the Mathieu type describes the dynamic stability of thin-walled members without damping.
Then each fixed point of T corresponds to a periodic solution of equation (5.8) with period ξ.
Integrating this equation over one period and making use of the T-periodicity of (tilde{x}(t)), we get - int^{T}_{0}tilde{x}(t tilde{x}"(t),dt+lambda int^{T}_{0}a(t) bigl(bar{x}^{2}- tilde{x}^{2}(t bigr),dt=lambda int^{T}_{0}frac{bar{x}-tilde{x}(t)}{x t)},dt.
