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In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force. By spectral analysis and energy methods, we obtain the optimal time decay estimate of the solution. We show that the global classical solution converges to its equilibrium state at the same decay rate as the solution of the linearized equations.

In this paper, we have developed a fluorescent probe based on thiazole derivative-functionalized carbon dots (CDs-AP) for the rapid, simple, and selective testing of commonly used antibiotics tetracyclines (TCs). Using citric acid (CA) and diethylenetriamine (DETA) as precursors, CDs rich in carboxyl groups were first synthesized, and then thiazole derivatives (AP) were covalently attached to the surface of CDs through an amidation coupling reaction. CDs-AP has high quantum yield (QY), excellent stability and good solubility. Response surface methodology (RSM) and the central composite design (CCD) were used to evaluate and optimize the operating parameters, including temperature, reaction time, and pH. Under the best operating conditions, CD-AP shows a good linear relationship for tetracycline (TET, an example for TCs), with a range of 0–18 μM and a detection limit of 0.7 nM. After detailed research, the inner filter effect (IFE) was proposed as the sensing mechanism. In addition, the probe has been successfully used for the determination of TET in milk samples and cell imaging for MDA-MB-231 cells.

We study the Holder continuity of weak solution u to an equation arising in the stationary motion of electrorheological fluids. To this end, we first obtain higher integrability of Du in our case by establishing a reverse Holder inequality. Next, based on the result of locally higher integrability of Du and difference quotient argument, we derive a Nikolskii type inequality; then in view of the fractional Sobolev embedding theorem and a bootstrap argument we obtain the main result. Here, the analysis and the existence theory of a weak solution to our equation are similar to the weak solution which has been established in the literature with $\frac{3d}{d+2}\leq p_{\infty}\leq p(x)\leq p_{0}