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To this end, we optimized different combinations of such dynamic parameter subsets with respect to their influence on contraction solutions.
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The absence of shortening was verified by observing myofibrils irrigated with the contraction solution in a Nomarski microscope.
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories.
According to the Banach contraction principle, the solutions Ỹ and Ŷ can be obtained as a limit of the convergent sequences (P^{m}Y_{0}^{ast}) and (Q^{m}Y_{0}^{ast}), respectively.
To assess the effect of L-cis-diltiazem on U-46619-induced contraction, the bathing solution was changed to 60 mM K+ solution to open the voltage-gated Ca2+ channels, followed by an addition of 1 µM nifedipine to block L-type voltage-gated Ca2+ channels.
Afterwards, the dilatometer was put into the water jacket (the temperature of heat carrier was maintained at 80.0 °C) and the contraction of the solution was monitored with cathetometer.
In the case where (a_{1}) and (a_{2}) satisfy the Lipschitz condition with respect to the second variable, the result for (f(theta) equivtheta) was established by Gikhman and Skorohod [6] showing that the associated mapping to (1.1) is a contraction and the solution was obtained by means of the successive approximations method.
After contraction with KCl solution and then relaxation with low-dose dopamine, tissue preparations were exposed to either cumulative log concentrations (10-9 10-5 M) of propofol (n = 8) or midazolam (n = 10).
Let us go now to the contraction property and take solutions m 1, m 2 ∈ X two solutions to (35).
In order to get reasonable selection pressure and maintain the diversity of solutions, the contraction degree for different solutions is different, i.e., for solutions close to Pareto optimal solutions the degree of contraction is bigger.
But, according to Lemma 2.2, (x t)<0) for t which are close to 0. This contraction demonstrates that the solution (x t)) cannot change its sign for nonnegative (f(t)).
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