Sentence examples for behavior of these solutions from inspiring English sources
We also study the long-time behavior of these solutions and prove a convergence to equilibrium with an exponential rate.
For computation purposes, however, the behavior of these solutions is quite different, and their strengths and weaknesses are discussed.
Nanoparticle concentrations up to 10 mg Fe/ml are shown to have negligible impact on the freezing behavior of these solutions, including the glass transition, critical cooling/warming rates, and specific heat, as measured by differential scanning calorimetry.
This paper revisits the short-term behavior of these solutions and we arrive at different conclusions than those usually accepted in the literature if the Fourier number is based on the borehole radius, which is normally the case.
Particularly, in [8], under some structure conditions, the authors obtained the existence of infinitely many positive symmetric radial entire solutions and investigated the asymptotic behavior of these solutions.
D Bifurcation values (g^{ast}), (g^{H}), and Hopf frequency (omega(g^{H})) as functions of N. The (sqrt{N}) scaling of (g^{ast}), (g^{H}), and (omega(g^{H})) yields insight into the expected behavior of these solutions.
We are interested in the behavior of the solutions of these equations as the number of neurons tends to infinity.
In the study of equations of mathematical physics, the attractor is a proper mathematical concept as regards the depiction of the behavior of the solutions of these equations when time is large or tends to infinity, which describes all the possible limits of solutions.
Until now, we find that no one else has studied the long-time behavior of the solutions about these problems, it is just our interest in this paper.
We have investigated the scaling relationship between rheological behavior and concentration for both salt-free and saline solutions of hyaluronan (HA), and adopted three viscoelastic constitutive models to predict the linear/non-linear viscoelastic behavior of these aqueous solutions of HA with different molecular weights at different concentrations up to 20 mg/ml.
