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.

     

Selective Decrosslinking in Liquid Crystal Polymer Actuators for Optical Reconfiguration of Origami and Light‐Fueled Locomotion

The ability to optically reconfigure an existing actuator of a liquid crystal polymer network (LCN) so that it can display a new actuation behavior or function is highly desired in developing materials for soft robotics applications. Demonstrated here is a powerful approach relying on selective polymer chain decrosslinking in a LCN actuator with uniaxial LC alignment. Using an anthracene‐containing LCN, spatially controlled optical decrosslinking can be realized through photocleavage of anthracene dimers under 254 nm UV light, which alters the distribution of actuation (crosslinked) and non‐actuation (decrosslinked) domains and thus determines the actuation behavior upon order‐disorder phase transitions. Based on this mechanism, a single actuator having a flat shape can be reconfigured in an on‐demand manner to exhibit reversible shape transformation such as self‐folding into origami three‐dimensional structures. Moreover, using a dye‐doped LCN actuator, a light‐fueled microwalker can be optically reconfigured to adopt different locomotion behaviors, changing from moving in the laser scanning direction to moving in the opposite direction.     

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.     

Large‐Area Aminated‐Graphdiyne Thin Films for Direct Methanol Fuel Cells

A two‐dimensional (2D) carbon nanofilm with uniform artificial nanopores is an ideal material to ultimately suppress the fuel permeation in the proton exchange membrane fuel cells. Graphdiyne has great mechanical strength, high dimensional stability, and controllable nanopores, and has good prospects to play this crucial role. It is found that graphdiyne nanofilm with amino groups and natural nanopores can be easily prepared with high integrity. The aminated graphdiyne has good compatibility with the Nafion matrix owing to the acid–base interaction between them. The excellent comprehensive properties of graphdiyne in selectivity, dimensional stability, and integrity effectively improve the power performance and stability of fuel cells at wide temperature. Our results can be developed into a universal method that can easily realize the selective separation of ions and small molecules, and open a new way for the emerging applications in green energy.     

A Renal‐Clearable Duplex Optical Reporter for Real‐Time Imaging of Contrast‐Induced Acute Kidney Injury

Despite its high morbidity and mortality, contrast‐induced acute kidney injury (CIAKI) remains a diagnostic dilemma because it relies on in vitro detection of insensitive late‐stage blood and urinary biomarkers. We report the synthesis of an activatable duplex reporter (ADR) for real‐time in vivo imaging of CIAKI. ADR is equipped with chemiluminescence and near‐infrared fluorescence (NIRF) signaling channels that can be activated by oxidative stress (superoxide anion, O₂^.?) and lysosomal damage (N‐acetyl‐β‐d ‐glucosaminidase, NAG), respectively. By virtue of its high renal clearance efficiency (80 % injected doses after 24 h injection), ADR detects sequential upregulation of O₂^.? and NAG in the kidneys of living mice prior to a significant decrease in glomerular filtration rate (GFR) and tissue damage in the course of CIAKI. ADR outperforms the typical clinical assays and detects CIAKI at least 8 h (NIRF) and up to 16 h (chemiluminescence) earlier.     

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.     

Synthesis and antifungal activity of carvacrol and thymol esters with heteroaromatic carboxylic acids

Aiming to obtain the more effective pathogen inhibitive ingredients and explore the influence of introducing different heterocyclic units to carvacrol and thymol esters, twenty ester derivatives with different heterocyclic units were synthesized. And the in vitro antifungal activity of title compounds against five plant pathogenic fungi was evaluated by mycelium growth rate method. The results showed that some carvacrol and thymol esters showed good to excellent antifungal activity, and compound 9d (4-bromo-5-isopropyl-2-methylphenyl picolinate) exhibited a broad antifungal spectrum. Preliminary study indicated that the introduction of furan, thiophene and pyridine unit could enhance the antifungal activity of carvacrol and thymol esters against Botrytis cinerea and a bromine atom on the para position of benzene moiety could enhance their antifungal activity.     

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.