AND molecular logic gates based on host-guest complexation operational in live cells

We report supramolecular AND logic gates based on host-guest complexation between acid-labile acyclic cucurbit[n]uril(CB[n]) molecular container and Na Cl O-responsive dye. Supramolecular AND logic gate is turned on due to acid-triggered degradation of molecular container and the release of the dye, followed by Na Cl O-induced fluorescence “switch on” effect of the dye. The reason for AND molecular logic gate is discovered to be the combination of oxidation inhibition and fluorescence “switch of...     

Space-Time Regularity for the Three Dimensional Navier–Stokes and MHD Equations

In this paper, we investigate the space-time regularity of solutions to (1) the three dimensional incompressible Navier–Stokes equations for initial data \(u_{0}=(u_{0}^{h},u_{0}^{3}) \in \dot{B}_{p,r}^{ \frac{3}{p}-1} (\mathbb{R}^{3})\) with large initial vertical velocity component; and (2) the three dimensional incompressible magneto-hydrodynamic equations for initial datum \(u_{0}=(u_{0}^{h},u _{0}^{3})\in \dot{B}_{p,r}^{\frac{3}{p}-1} (\mathbb{R}^{3})\) with large initial vertical velocity component and \(b_{0}=(b_{0}^{h},b_{0}^{3}) \in \dot{B}_{p,r}^{\frac{3}{p}-1} (\mathbb{R}^{3})\) with large initial vertical magnetic field component.

     

Bifurcation analysis of an SIRS epidemic model with standard incidence rate and saturated treatment function

An epidemic model with standard incidence rate and saturated treatment function of infectious individuals is proposed to understand the effect of the capacity for treatment of infective individuals on the disease spread. The treatment function in this paper is a continuous and differential function which exhibits the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. It is proved that the existence and stability of the disease-free and endemic equilibria for the model are not only related to the basic reproduction number but also to the capacity for treatment of infective individuals. And a backward bifurcation is found when the capacity is not enough. By computing the first Lyapunov coefficient, we can determine the type of Hopf bifurcation, i.e., subcritical Hopf bifurcation or supercritical Hopf bifurcation. We also show that under some conditions the model undergoes Bogdanov-Takens bifurcation. Finally, numerical simulations are given to support some of the theoretical results.     

Generation of Hermite-Gaussian modes and vortex arrays based on two-dimensional gain distribution controlled microchip laser

We have demonstrated high-order Hermite-Gaussian (HG) mode generation based on 2D gain distribution control edge-pumped, composite all-ceramic Yb:YAG/YAG microchip lasers using a V-type cavity. Several hundred milliwatts to several watts HG(mn) modes are achieved. We also generated different kinds of vortex arrays directly from the oscillator with the same power level. In addition, a more than 7 W doughnut-shape mode can be generated in the same cavity.     

Highly efficient and chemoselective direct aldol reaction of acyldiazomethane with aldehydes promoted by MgI2 etherate

College of Pharmaceutical Sciences, Zhejiang University of Technology, Hangzhou 310032, China MgI₂(Et₂O)_n promoted aldol condensation of various aldehydes with acyldiazomethane was described in the presence of DIPEA in good to excellent yields under mild conditions with high chemoselectivity.     

Codimension 2 bifurcations of double homoclinic loops

In this work, the double-homoclinic-loop bifurcations in four dimensional vector fields are investigated by setting up local coordinates near the double homoclinic loops. We get the existence, uniqueness and incoexistence of the large 1-hom and large 1-per orbit, and their corresponding existence regions are located. Furthermore, the inexistence of the large 2-hom and large 2-per orbit are also demonstrated.