Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming

Science China Mathematics - In this paper, we accomplish the unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the...     

Photoelectrochemical Cytosensors

Photoelectrochemical (PEC) cytosensors, a combination of the PEC process and the living-cell assay, have emerged as a powerful tool in the analytical and biological science. This mini review provides a brief introduction of this arena and summaries the key steps about the development of PEC cytosensors with representative examples, followed by future prospects based on our own opinions.     

Facile preparation of Ag/Ag2WO4/g‐C3N4 ternary plasmonic photocatalyst and its visible‐light photocatalytic activity

Introducing plasmonic metals into semiconductor materials has been proven to be an attractive strategy for enhancing photocatalytic activity in the visible region. In this work, a novel and efficient Ag/Ag₂WO₄/g‐C₃N₄ (AACN) ternary plasmonic photocatalyst was successfully synthesized using a facile one‐step in situ hydrothermal method. The composition, structure, morphology and optical absorption properties of AACN were investigated using X‐ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy, and UV–visible diffuse reflectance spectroscopy, respectively. Photocatalytic performance of AACN was evaluated via rhodamine B and tetracycline degradation. The results indicated that AACN had excellent photocatalytic performance for rhodamine B degradation with a rate constant of 0.0125 min^?1, which was higher than those of Ag₂WO₄ and Ag/Ag₂WO₄. Characterization and photocatalytic tests showed that the strong coupling effect between the Ag/Ag₂WO₄ nanoparticles and the exfoliated ultrathin g‐C₃N₄ nanosheets was superior for visible‐light responsivity and reduced the recombination rate of photogenerated electrons and holes. A proposed mechanism is also discussed according to the band energy structure and the experimental results.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Global Regularity of 3D Nonhomogeneous Incompressible Micropolar Fluids

This paper is concerned with the global well-posedness of strong and classical solutions for the 3D nonhomogeneous incompressible micropolar equations with vacuum. We prove that the problem (1.1)–(1.5) has a unique global strong/classical solution \((\rho,u,w)\), provided \(\mu_{1}\) is sufficiently large, or \(\|\rho_{0}\|_{L^{\infty}}\) or \(\|\rho_{0}^{1/2}u_{0}\| ^{2}_{L^{2}}+\|\rho_{0}^{1/2}w_{0}\|^{2}_{L^{2}}\) is small enough.

     

An efficient approach to isoquinoline via AgNO3-promoted 6-endo-dig cyclization followed by oxidative elimination of o-alkynylarylaldimines and its application in fluoride recognition

A novel 6-endo-dig cyclization followed by oxidation/elimination of o-alkynylarylaldimines with 4-hydroxybenzylamine was developed for preparation of isoquinolines. The intermediates of this tandem reaction were monitored by mass spectroscopy (MS) to confirm the reaction pathway. This methodology was further applied to the design and synthesis of a novel ratiometric chemosensor for determination of fluoride.     

New lower bounds on 2-spontaneous emission error designs

The combinatorial object named $t$-spontaneous emission error design ($t$-SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of $t$-SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2-$(q^2,k;m)$ SEEDs, some of which outperform the known ones.     

Graphs are (1,Δ+1)-choosable

A graph $G$ is $(k,k^{\prime })$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L\left(v\right)$ of $k$ real numbers, and assigns to each edge $e$ a set $L\left(e\right)$ of $k^{\prime }$ real numbers, there is a total weighting $?:V\left(G\right)\cup E\left(G\right)\to R$ such that $?\left(z\right)\in L\left(z\right)$ for $z\in V\cup E$, and ${\sum }_{e\in E\left(u\right)}?\left(e\right)+?\left(u\right)\ne {\sum }_{e\in E\left(v\right)}?\left(e\right)+?\left(v\right)$ for every edge $uv$. This paper proves that if $G$ is a connected graph of maximum degree $\Delta \ge 2$, then $G$ is $(1,\Delta +1)$-choosable.