Cellular pH homeostasis is essential for many physiological and pathological processes. pH monitoring is helpful for the diagnosis, treatment and prevention of disorders and diseases. Herein, we developed a ratiometric fluorescent pH probe (TCC) based on a coumarin derivative containing a highly active lactone ring. TCC exhibited a typical AIE effect and emitted blue fluorescence under weak acidic condition. When under weak basic condition, the active lactone moiety underwent a hydrolysis reaction to afford a water-soluble product, which gave red-shifted emission. The emission color change from blue through cyan and then to yellow within pH 6.5–9.0 which is approximate to the biological pH range. And the fluorescence color change along with pH value is reversible. Furthermore, TCC was successfully utilized in the detection of the intracellular pH change of live HeLa cells, which indicated that TCC had practical potential in biomedical research.
In this paper we study the convergence of adaptive finite element methods for the gen- eral non-attine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and D6fler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic partial equations is proved. Our analysis is effective for all conforming Qm elements which covers both the two- and three-dimensional cases in a unified fashion. 相似文献
In this paper, we analyze the convergence of the adaptive conforming and nonconforming $P_1$ finite element methods with red–green refinement based on standard Dörfler marking strategy. Since the mesh after refining is not nested into the one before, the usual Galerkin-orthogonality or quasi-orthogonality for newest vertex bisection does not hold for this case. To overcome such a difficulty, we develop some new quasi-orthogonality instead under certain condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive methods by establishing the reduction of some total errors. To weaken the condition on the initial mesh, we propose a modified red–green refinement and prove the convergence of the associated adaptive methods under a much weaker condition on the initial mesh (Condition B). Furthermore, we also develop an initial mesh generator which guarantee that all the interior triangles are equilateral triangles (satisfy Condition A) and the other triangles containing at least one vertex on the boundary satisfy Condition B. 相似文献