Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Hitherto-Unexplored Photodynamic Therapy of Ag2S and Enhanced Regulation Based on Polydopamine In Vitro and Vivo

Given their superior penetration depths, photosensitizers with longer absorption wavelengths present broader application prospects in photodynamic therapy (PDT). Herein, Ag₂S quantum dots were discovered, for the first time, to be capable of killing tumor cells through the photodynamic route by near-infrared light irradiation, which means relatively less excitation of the probe compared with traditional photosensitizers absorbing short wavelengths. On modification with polydopamine (PDA), PDA-Ag₂S was obtained, which showed outstanding capacity for inducing reactive oxygen species (increased by 1.69 times). With the addition of PDA, Ag₂S had more opportunities to react with surrounding O₂, which was demonstrated by typical triplet electron spin resonance (ESR) analysis. Furthermore, the PDT effects of Ag₂S and PDA-Ag₂S achieved at longer wavelengths were almost identical to the effects produced at 660 nm, which was proved by studies in vitro. PDA-Ag₂S showed distinctly better therapeutic effects than Ag₂S in experiments in vivo, which further validated the enhanced regulatory effect of PDA. Altogether, a new photosensitizer with longer absorption wavelength was developed by using the hitherto-unexplored photodynamic function of Ag₂S quantum dots, which extended and enhanced the regulatory effect originating from PDA.     

Direct visualization of the nanoscopic three‐phase structure and stiffness of NBR/PVC blends by AFM nanomechanical mapping

The PeakForce Quantitative Nanomechanical Mapping based on atomic force microscope (AFM) is employed to first visualize and then quantify the elastic properties of a model nitrile rubber/poly(vinyl chloride) (NBR/PVC) blend at the nanoscale. This method allows us to consistently observe the changes in mechanical properties of each phase in polymer blends. Beyond measuring and discriminating elastic modulus and adhesion forces of each phase, we tune the AFM tips and the peak force parameters in order to reliably image samples. In view of viscoelastic difference in each phase, a three‐phase coexistence of an unmixed NBR phase, the mixed phase, and PVC microcrystallites is directly visualized in NBR/PVC blends. The nanomechanical investigation is also capable of recognizing the crosslinked rubber phase in cured rubber. The contribution of the mixed phase was quantified and it was found that the mechanical properties of blends are mainly determined by the homogeneity and stiffness of the mixed phase. This study furthers our understanding the structure–mechanical property relationship of thermoplastic elastomers, which is important for their potential design and applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 662–669     

Gamma peak search and peak fitting algorithm for a low-resolution detector with applications in gamma spectroscopy

A Savitzky–Golay filtering for smoothing and peak search written in Python is presented in this paper alongside its applications in the list-mode digital data acquisition dual gamma–gamma coincidence bismuth germanate (BGO) detector. The study has demonstrated that the software provides a reliable and effective way to quantify trace amounts of ²²Na and ⁷Be in aerosol samples collected at Resolute Bay, Canada with a critical limit of 3 mBq and 5 Bq respectively for a 20 h counting interval, which are believed to be the inherent limitations of the dual-BGO system.

     

Nanocomposite hydrogel consisting of Na‐montmorillonite with enhanced mechanical properties

A new kind of nanocomposite (NC) hydrogel with Na‐montmorillonite (MMT) is presented in this article. The NC hydrogels were synthesized by free radical copolymerization of acrylamide and (3‐acrylamidopropyl) trimethylammonium chloride (ATC) in the presence of MMT and N,N′‐methylene‐bis‐acrylamide used as chemical cross‐linker. Due to the cation‐exchange reaction between MMT and ATC (cationic monomer) during the synthesis of NC hydrogels, MMT platelets were considered chemical “plane” cross‐linkers, different from “point” cross‐linkers. With increasing amount of MMT, the crosslinking degree enhanced, causing a decrease of the swelling degree at equilibrium. Investigations of mechanical properties indicated that NC hydrogels exhibited enhanced strength and toughness, which resulted from chemical interaction between exfoliated MMT platelets and polymer chains in hydrogels. Dynamic shear measurements showed that both storage modulus and loss modulus increased with increasing MMT content. The idea described here provided a new route to prepare hydrogels with high mechanical properties by using alternative natural Na‐MMT. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1020–1026