Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

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.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

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.     

Lysosome‐targeted potent half‐sandwich iridium(III) α‐diimine antitumor complexes

Fifteen organometallic Ir(III) half‐sandwich complexes ( 1A – 5C ) having the general formula [(η⁵‐Cp^x)Ir(N^N)Cl]PF₆ (Cp^x = Cp*, tetramethyl(phenyl)cyclopentadienyl (Cp^xph) or tetramethyl(biphenyl)cyclopentadienyl (Cp^xbiph); N^N = diamine) have been synthesized and characterized. The molecular structure of 1A was determined using single‐crystal X‐ray diffraction analysis. The hydrolysis of 1A – 5C was monitored using UV–visible spectra. Complexes 3A – 3C showed catalytic activity for the oxidation of NADH to NAD⁺, where 3C showed the highest turnover number of 29.9 within 450 min. Cytotoxicity examination by MTT assay was carried out against two human cancer cell lines (HeLa and A549) after 24 or 48 h drug treatment. The complexes showed high potency, where the most potent complex ( 3C ; IC₅₀ = 3.4 μM) was six times more active than cisplatin against A549 cells after 24 h drug exposure. Cytotoxic potency towards A549 cells increased with phenyl substitution on Cp ring: Cp^xbiph > Cp^xph > Cp*. In addition, the biological studies showed that 3C caused cell apoptosis and cell cycle arrest at G₁ phase in A549 cancer cells. Moreover, 3C increased the level of reactive oxygen species markedly after 24 h, which may provide an important basis for killing cancer cells. Confocal laser scanning microscopy was used to track 3C in A549 cells. The cellular localization experiment showed that 3C targeted lysosomes and caused lysosomal damage.     

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.     

Kinetic study of the reaction of nucleophilic cyclopropanation of C60 fullerene with halogenated maleopimarimide

The kinetics of nucleophilic fullerene cyclopropanation by halomethyl ketones with a diterpene fragment has been studied by the Bingel method, and the influence of the biologically active cyclopropanating agent on the process has been estimated. It has been revealed that favorable conditions for carrying out the reaction result in maximum monofunctionalized methanofullerenes formation with the maximum yield.     

Correlations between microstructure of α‐row nuclei and polymorphism of shear‐induced iPP/carbon fiber cylindrite

Herein, we reported the formation mechanism of hybrid crystalline (cylindrite) in isotactic polypropylene (iPP)/carbon fiber (CF) via pulling a CF within the iPP melt. The α‐row nuclei layer closely attached to the surface of CF acts as a self‐nucleation site, rather than a heterogeneous nucleation one, to grow cylindrites. As a result, the polymorphic feature of iPP/CF cylindrite is significantly influenced by the microstructure of α‐row nuclei. With decreasing crystallization temperature (T_c), the polymorphic cylindrite changes from pure α‐form to mixed α‐/β‐form and to β‐rich form. The main characteristics of this change include: (a) the outlines of α‐row nuclei layer correspond to wave‐like, saw‐like, and straight lines; (b) the orientation level of iPP molecules in the α‐row nuclei layer become higher; (c) the α‐lamellae rearrange from loose to compact; and (d) the distance between the growth sites of β‐sectors and the surface of CF is evidently longer than in the case of α‐sectors. Moreover, this study provides a guideline for developing the interfacial enhanced iPP/CF composites through manipulation of polymorphic structure in cylindrites. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 368–377     

Baclofen impurities: Facile synthesis and novel environmentally benign chromatographic method for their simultaneous determination in baclofen

An efficient, economic and high yielding method was described for the synthesis of baclofen (BAC) pharmacopoeial impurities (impurity A and impurity B) which can be used for gram‐scale synthesis. Furthermore, a novel ecofriendly thin‐layer chromatographic TLC–densitometric method was established and validated for the determination of BAC and its synthesized impurities. The developed TLC–densitometric method is based on the chromatographic separation using TLC plates (60 F₂₅₄) using a green mobile phase of ethyl acetate–methanol–ammonia solution, 33% (8:2:0.1, by volume) with UV scanning at 220 nm. The proposed method was validated with respect to International Conference on Harmonization guidelines. The validated method was successfully applied for determination of BAC in pure form and in its commercial dosage form. Additionally, the greenness profile of the developed method was evaluated and compared with those of the reported chromatographic methods. The developed method was found to be superior to the published methods, being environmentally benign.