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.     

Two-step Estimation for Longitudinal Data When the Working Correlation Matrix is a Linear Combination of Some Known Matrices

Acta Mathematicae Applicatae Sinica, English Series - The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE...     

Precise Synthesis of Poly(thioester)s with Diverse Structures by Copolymerization of Cyclic Thioanhydrides and Episulfides Mediated by Organic Ammonium Salts

The precise synthesis of poly(thioester)s with diverse structures is still a significant challenge in the polymeric materials field. Herein, we report a novel approach to the synthesis of well‐defined poly(thioester)s by the controlled alternating copolymerization of cyclic thioanhydrides and episulfides induced by simple organic ammonium salts. Both the cation and anion have strong effects on the copolymerization. [PPN]OAc ([PPN]=bis(triphenylphosphine)iminium) with a bulky cation was proven to be efficient in initiating this polymerization, yielding poly(thioester)s with a completely alternating structure, controlled molecular weight, and narrow polydispersity. The poly(thioester) obtained from succinic thioanhydride and propylene sulfide is a typical semicrystalline material, possessing a high refractive index of up to 1.78. Because it uses readily available monomers, this method is expected to open up a new route to poly(thioester)s with diverse structures and properties.     

Insight into shear‐induced modification for improving processability of polymers: Effect of shear rate on the evolution of entanglement state

Many experimental results have revealed that the re‐entanglement kinetics of disentangled polymers is much slower than that predicted by tube theory. This retarded recovery of fully entangled state is of practical significance that shear‐induced modification may offer a way to improve processability for a polymer by reducing viscosity. This work tried to figure out the shear‐rate dependence variation of viscosity in the view of evolution of entanglement state through disentanglement and re‐entanglement, aiming to provide fundamental insights into application prospect of shear‐induced modification in preparing “in‐pellet” disentangled polymers prior to final processing. High‐density polyethylene was sheared on a parallel‐plate rotational rheometer with a linearly increased shear rate. Results showed that higher shear rate could induce further disentanglement, resulting in a lower viscosity with a reduction rate up to 93.7%, larger molecular weight between entanglements M_e , and longer re‐entanglement time. Additionally, less entanglement would give a larger lamellar thickness of sheared samples after nonisothermal crystallization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 598–606     

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.     

Nukiangendines A and B,two novel 13,14-seco-abietanes from Abies nukiangensis

From Abies nukiangensis, two novel 13,14-seco-abietane diterpenes, nukiangendines A (1) and B (2) were isolated. Their relative structures were determined by extensive NMR and HRMS spectroscopic analysis. The absolute configuration of 1 was established by ECD calculations. Compound 1 showed significant anti-hepatitis C virus (HCV) effects.     

Elucidating Molecule–Plasmon Interactions in Nanocavities with 2 nm Spatial Resolution and at the Single‐Molecule Level

The fundamental understanding of the subtle interactions between molecules and plasmons is of great significance for the development of plasmon‐enhanced spectroscopy (PES) techniques with ultrahigh sensitivity. However, this information has been elusive due to the complex mechanisms and difficulty in reliably constructing and precisely controlling interactions in well‐defined plasmonic systems. Herein, the interactions in plasmonic nanocavities of film‐coupled metallic nanocubes (NCs) are investigated. Through engineering the spacer layer, molecule–plasmon interactions were precisely controlled and resolved within 2 nm. Efficient energy exchange interactions between the NCs and the surface within the 1–2 nm range are demonstrated. Additionally, optical dressed molecular excited states with a huge Lamb shift of ≈7 meV at the single‐molecule (SM) level were observed. This work provides a basis for understanding the underlying molecule–plasmon interaction, paving the way for fully manipulating light–matter interactions at the nanoscale.     

Miktoarm star‐shaped poly(lactic acid) copolymer: Synthesis and stereocomplex crystallization behavior

The miktoarm star‐shaped poly(lactic acid) (PLA) copolymer, (PLLA)₂‐core‐(PDLA)₂, was synthesized via stepwise ring‐opening polymerization of lactide with dibromoneopentyl glycol as the starting material. ¹H NMR and FTIR spectroscopy proved the feasibility of synthetic route and the successful preparation of star‐shaped PLA copolymers. The results of FTIR spectroscopy and XRD showed that the stereocomplex structure of the copolymer could be more perfect after solvent dissolution treatment. Effect of chain architectures on crystallization was investigated by studying the nonisothermal and isothermal crystallization of the miktoarm star‐shaped PLA copolymer and other stereocomplexes. Nonisothermal differential scanning calorimetry and polarizing optical microscopy tests indicated that (PLLA)₂‐core‐(PDLA)₂ exhibited the fastest formation of a stereocomplex in a dynamic test due to its special structure. In isothermal crystallization tests, the copolymer exhibited the fast crystal growth rate and the most perfect crystal morphology. The results reveal that the unique molecular structure has an important influence on the crystallization of the miktoarm star‐shaped PLA copolymer. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 814–826     

Ground states of two-component attractive Bose–Einstein condensates I: Existence and uniqueness

We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in ${\mathbb{R}}^2$, where the intraspecies interaction $(?a_1,?a_2)$ and the interspecies interaction ?β are both attractive, $i.e$, $a_1$, $a_2$ and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\beta \nearrow {\beta }^{?}=a^{?}+\sqrt{(a^{?}?a_1)(a^{?}?a_2)}$, where $0<a_i<a^{?}:={6w6}_2^2$ ($i=1,2$) is fixed and w is the unique positive solution of $\mathrm{\Delta }w?w+w^3=0$ in ${\mathbb{R}}^2$. The semi-trivial limit behavior of ground states is tackled in the companion paper [12].     

Non-isothermal thermogravimetric analysis of pyrolysis kinetics of four oil shales using Sestak–Berggren method

Journal of Thermal Analysis and Calorimetry - In this study, the non-isothermal pyrolysis method was used to investigate the pyrolysis characteristics of oil shale from four areas: namely Nongan,...