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.     

CoFe2O4@SiO2‐CPTES‐Guanidine‐Cu(II): A novel and reusable nanocatalyst for the synthesis of 2,3‐dihydroquinazolin‐4(1H)‐ones and polyhydroquinolines and oxidation of sulfides

CoFe₂O₄@SiO₂‐CPTES‐Guanidine‐Cu(II) magnetic nanoparticles were synthesized and used as a new, inexpensive and efficient heterogeneous catalyst for the synthesis of polyhydroquinolines and 2,3‐dihydroquinazoline‐4(1H)‐ones and for the oxidation of sulfides. The structure of this nanocatalyst was characterized using Fourier transform infrared spectroscopy, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, vibrating sample magnetometry, thermogravimetric analysis, X‐ray diffraction and inductively coupled plasma optical emission spectrometry. Simple preparation, high catalytic activity, simple operation, high yields, use of green solvents, easy magnetic separation and reusability of the catalyst are some of the advantages of this protocol.     

Rhodium(III)-Catalyzed C−H/N−H Functionalization with Hydrogen Evolution

A rhodium(III)-catalyzed C−H/N−H bond functionalization of benzimidates with α-chloroaldehydes to afford isoquinolin-3-ol derivatives is reported. No external oxidants are needed in this process, and interestingly, evolution of hydrogen gas is observed.     

通过宽线固体核磁共振氢谱研究半晶高分子的相结构

宽线固体核磁共振氢谱（¹H NMR）是一种研究半晶高分子相结构的经典方法.本文以半晶聚乙烯的宽线固体¹H NMR谱为例，探讨了通过Gaussian/Sinc、Gaussian和Lorentzian函数组合对宽线固体¹H NMR谱图进行拟合的方案，并根据半晶聚乙烯的相结构成分对拟合得到的各信号成分进行归属.并在此基础上探讨了各个相结构中分子链运动与信号线型的相关性，以及利用宽线固体¹H NMR谱测量半晶高分子结晶度存在的困难.     

Er3+单掺、Er3+/Yb3+共掺杂Ca12Al14O32F2的 制备及上转换发光性质

利用高温固相法成功制备了Er~(3+)单掺、Er~(3+)/Yb~(3+)共掺杂Ca_(12)Al_(14)O_(32)F_2上转换发光样品。在980 nm激光激发下,Er~(3+)单掺和Er~(3+)/Yb~(3+)共掺杂样品均呈现出较强的绿光(528,549 nm)和较弱的红光(655 nm)发射,分别归因于Er~(3+)离子的~2H_(11/2),~4S_(3/2)→~4I_(15/2)和~4F_(9/2)→~4I_(15/2)能级跃迁。随着Er离子浓度的增加,单掺杂样品上转换发光强度先增大后减小,最佳掺杂浓度为0.8%。共掺杂Yb~(3+)后,Er~(3+)的发光强度明显增大。还原气氛下合成的样品上转换发光强度增大约两倍,可能和笼中阴离子基团变化有关。发光强度和激发光功率的关系表明所得上转换发射为双光子吸收过程,借助Er~(3+)-Yb~(3+)体系能级结构详细讨论了上转换发射的跃迁机制。     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Graphene oxide‐catalyzed CSp3–H activation of methylarenes in aqueous medium: A unified metal‐free access to amides and benzimidazoles

Graphene oxide (GO)‐catalyzed selective synthesis of amides via C_Sp3–H activation of methylarenes and consequent C–N bond formation with anilines under aqueous medium has been described. Oxygen functionality allied with GO surface played a dual role both as acid catalyst and oxidizing agent to some extent. However, GO has a copious effect on the reaction, shown by a high TOF value with TBHP as co‐oxidant. The decisive role of carboxylic acid functional groups on GO nanosheets in this metal‐free strategy has been confirmed and was monitored by various analytic techniques viz. Fourier transform‐infrared, UV–Vis, Raman and XPS. A plausible mechanism was proposed by control experiments and by the isolation of the intermediate. Over‐oxidation of methylarenes was not detected, and high recyclability of the carbocatalyst with its heterogeneous behavior facilitated the isolation and purification of the desired products. We have further explored the utility of this process for the chemoselective synthesis of benzimidazoles.     

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.