On the lifetime of evaporating sessile droplets

The evaporation of sessile droplets with a constant base radius (pinning mode) and a constant contact angle (depinning mode) has been experimentally observed. Here we analyzed the effect of substrate hydrophobicity on the lifetimes of evaporating droplets for the two modes. Theoretical predictions were obtained and compared with available experimental results. The theoretical analysis and experimental results show that linear methods of extrapolating limited experimental data for a transient droplet contact angle and base radius overpredict the droplet lifetime. Likewise, the linear extrapolation of limited experimental data for transient droplet volume underpredicts the droplet lifetime. Correct methods of extrapolating limited experimental data for transient droplet parameters are described, discussed, and validated. The new methods removed inconsistencies in the previous theory and experimental analysis. Master equations and master curves for the droplet lifetime for the two evaporation modes are obtained and experimentally confirmed.     

On Hölder continuity of approximate solutions to parametric equilibrium problems

We establish verifiable sufficient conditions for Hölder continuity of approximate solutions to parametric equilibrium problems, when solutions may be not unique. Many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions. As applications, we derive this Hölder continuity for constrained minimization, variational inequalities and fixed point problems.     

On positivity and stability of linear time-varying Volterra equations

Linear time-varying Volterra integro-differential equations of non-convolution type are considered. Positivity is characterized and a sufficient condition for exponential asymptotic stability is presented.

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The second author thanks the Alexander von Humboldt Foundation for their support.     

A Fourier method and an extrapolation technique for Stokes’ first problem for a heated generalized second grade fluid with fractional derivative

In this article, we consider Stokes’ first problem for a heated generalized second grade fluid with fractional derivative (SFP-HGSGF). Implicit and explicit numerical approximation schemes for the SFP-HGSGF are presented. The stability and convergence of the numerical schemes are discussed using a Fourier method. In addition, the solvability of the implicit numerical approximation scheme is also analyzed. A Richardson extrapolation technique for improving the order of convergence of the implicit scheme is proposed. Finally, a numerical test is given. The numerical results demonstrate the good performance of our theoretical analysis.     

Predicting the subcellular location of apoptosis proteins based on recurrence quantification analysis and the Hilbertben Huang transform

Apoptosis proteins play an important role in the development and homeostasis of an organism. The elucidation of the subcellular locations and functions of these proteins is helpful for understanding the mechanism of programmed cell death. In this paper, the recurrent quantification analysis, Hilbert-Huang transform methods, the maximum relevance and minimum redundancy method and support vector machine are used to predict the subcellular location of apoptosis proteins. The validation of the jackknife test suggests that the proposed method can improve the prediction accuracy of the subcellular location of apoptosis proteins and its application may be promising in other fields.     

Liouville-type theorems for a nonlinear fractional Choquard equation

In this paper, we are concerned with the fractional Choquard equation on the whole space ${\mathbb{R}}^N$ $${(-\mathrm{\Delta })}^{s}u=\left(\frac{1}{{|x|}^{N-2s}}\ast u^p\right)u^{p-1}$$ with , $N>2s$ and $p\in \mathbb{R}$. We first prove that the equation does not possess any positive solution for $p\le 1$. When $p>1$, we establish a Liouville type theorem saying that if then the equation has no positive stable solution. This extends, in particular, a result in [27] to the fractional Choquard equation.