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.     

The concept of dual roles design in clean organic preparation

Herein we summarized some clean preparation examples to emphasize the concept of dual roles design (or named as “two birds one stone strategy”) in green and sustainable chemistry. In those examples, the reactants and/or solvent play dual roles rendering a cleaner organic preparation process. Consequently, both the chemical waste and manufacturing cost could be reduced.     

A nickel oxide nanoflakes/reduced graphene oxide composite and its high-performance lithium-storage properties

Journal of Solid State Electrochemistry - Since conventional graphite-based anode possesses a low capacity, seeking for high-capacity anode candidates becomes significant for constructing emerging...     

Iteratively weighted thresholding homotopy method for the sparse solution of underdetermined linear equations

Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper,we present a novel weighted l1-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods.     

Quantifying the quantumness of ensembles via generalized α-z-relative rényi entropy

International Journal of Theoretical Physics - Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of...