Properties of G-martingales with finite variation and the application to G-Sobolev spaces

As is known, if $B={\left(B_t\right)}_{t\in [0,T]}$ is a $G$-Brownian motion, a process of form ${\int }_0^t{\eta }_{s}d{〈B〉}_s?{\int }_0^{t}2G\left({\eta }_s\right)ds$, $\eta \in M_G^1(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale cannot be form of ${\int }_0^t{\eta }_{s}ds$ or ${\int }_0^t{\gamma }_{s}d{〈B〉}_s$, $\eta ,\gamma \in M_G^1(0,T)$, which implies that the decomposition for generalized $G$-Itô processes is unique: For arbitrary $\zeta \in H_G^1(0,T)$, $\eta \in M_G^1(0,T)$ and non-increasing $G$-martingales $K,L$, if ${\int }_0^t{\zeta }_{s}d{B}_s+{\int }_0^t{\eta }_{s}ds+K_t=L_t,t\in [0,T],$then we have $\eta \equiv 0$, $\zeta \equiv 0$ and$K_t=L_t$. As an application, we give a characterization to the $G$-Sobolev spaces introduced in Peng and Song (2015).     

Development and validation of an ultra‐high‐performance liquid chromatography–tandem mass spectrometry method to determine the bioavailability of warfarin and its major metabolite 7‐hydroxy warfarin in rats dosed with oral formulations containing different polymorphic forms

A simple, sensitive and rapid ultra‐high‐performance liquid chromatography–electrospray ionization–tandem mass spectrometry method was developed and validated for the quantification of warfarin and 7‐hydroxy warfarin in Sprague Dawley (SD) rats. Animals were administered a single dose of warfarin sodium formulations (crystalline and amorphous) at 12 mg/kg via oral gavage and blood was drawn over a 96‐h time course. Sample process recoveries, matrix effect and analyte stability were determined. The linearity for warfarin and 7‐hydroxy warfarin was from 5 to 2000 ng/mL in blank SD rat plasma. Correlation coefficients (r²) for standard calibration curves were >.98 and analytes quantified within ±15% of target at all calibrator concentrations. The average percent accuracy and precision for intra‐ and inter‐day were 93.7%–113.8% and ≤12.1%, respectively, for warfarin and 7‐hydroxy warfarin, across the quality control standards (5, 10, 500, 1800 and 2000 ng/mL). Acceptable analytical recovery (>55%) was achieved with process efficiencies >41.5% and matrix effects <139.9% over the analytical range. Both analytes were stable in stock solution, autosampler, benchtop and three cycles of freeze–thaw with percent accuracy ≥90.2% and precision (percent relative standard deviation) ≤14%. The validated method was successfully applied to a pre‐clinical bioavailability study of crystalline and amorphous warfarin sodium formulations in SD rats.     

On the Discrete Criteria and JØ rgensen Inequalities for SL(m,F((t)))

In this paper, the author gives the discrete criteria and J\o rgensen inequalities of subgroups for the special linear group on $\overline{\mathrm{F}}((t))$ in two and higher dimensions.     

Facile Synthesis of Ultra-Small Few-Layer Nanostructured MoSe2 Embedded on N,P Co-Doped Bio-Carbon for High-Performance Half/Full Sodium-Ion and Potassium-Ion Batteries

Sodium/potassium-ion batteries (SIBs/PIBs) arouse intensive interest on account of the natural abundance of sodium/potassium resources, the competitive cost and appropriate redox potential. Nevertheless, the huge challenge for SIBs/PIBs lies in the scarcity of an anode material with high capacity and stable structure, which are capable of accommodating large-size ions during cycling. Furthermore, using sustainable natural biomass to fabricate electrodes for energy storage applications is a hot topic. Herein, an ultra-small few-layer nanostructured MoSe₂ embedded on N, P co-doped bio-carbon is reported, which is synthesized by using chlorella as the adsorbent and precursor. As a consequence, the MoSe₂/NP-C-2 composite represents exceedingly impressive electrochemical performance for both sodium-ion batteries (SIBs) and potassium-ion batteries (PIBs). It displays a promising reversible capacity (523 mAh g⁻¹ at 100 mA g⁻¹ after 100 cycles) and impressive long-term cycling performance (192 mAh g⁻¹ at 5 A g⁻¹ even after 1000 cycles) in SIBs, which are some of the best properties of MoSe₂-based anode materials for SIBs to date. To further probe the great potential applications, full SIBs pairing the MoSe₂/NP-C-2 composite anode with a Na₃V₂(PO₄)₃ cathode also exhibits a satisfactory capacity of 215 mAh g⁻¹ at 500 mA g⁻¹ after 100 cycles. Moreover, it also delivers a decent reversible capacity of 131 mAh g⁻¹ at 1 A g⁻¹ even after 250 cycles for PIBs.     

Functional Organic Semiconductors Based on Bay‐Annulated Indigo (BAI)

The advancement of organic electronics has been continually pushed by the need for stable and high performance acceptor materials. By utilizing inexpensive and stable indigo dye as a starting material, Bay‐Annulated Indigo (BAI) provides a new motif for the development of semiconducting materials. Modular and straightforward synthesis makes BAI an outstanding platform for molecular design, while excellent stability, strong absorption, and high ambipolar mobility render BAI‐based materials excellent candidates for organic electronics. BAI‐based polymers and small molecules have taken advantage of these properties to show promising results in a variety of applications.     

Estimation of viscosities of 1-alkyl-3-methylimidazolium ionic liquids over a range of temperatures using a simple correlation

In this study, a new correlation is proposed for estimating 1-alkyl-3-methylimidazolium ionic liquid (IL) viscosities at different temperatures and atmospheric pressure. Since ILs are rather novel, many of their physical properties are still unavailable. Because of this limitation, the aim of this work was to propose a correlation with a new insight and approach, which requires a minimum number of physical properties as input parameters. In addition to minimal dependency on physical properties, further goals in the development of the model were generality, ease-of-use, simplicity and high accuracy. A total of 2073 literature viscosity datapoints at different temperatures for 38 different ILs were used and a correlation was developed which satisfied the above-mentioned goals. The IL viscosity models of Lazzús and Pulgar-Villarroel, and Gardas and Coutinho were compared to the proposed correlation. More reliable results were obtained by the proposed relation in comparison to literature models.     

Dialkoxymethano[60]fullerenes as electron acceptors in thin-film organic solar cells

This study presents the synthesis, characterization, and electrochemical properties of four new dialkoxymethanofullerenes, as well as their performance in organic solar cells (OSCs) devices. Dialkoxymethanofullerenes were synthesized in 27%–32% yield by thermolysis of dialkoxyoxadiazolines and reaction with C₆₀ under reflux in toluene. The prepared compounds were then characterized and used for the first time as electron-acceptor materials in thin-film bulk heterojunction OSCs with PBTZT-stat-BDTT-8 as the electron donor material. The devices made with ethoxy-hexyloxymethanofullerene and methoxy-hexyloxymethanofullerene exhibited optimal power conversion efficiencies (PCEs) of 3.79% and 4.65%, with open-circuit voltage of 0.832 and 0.831 V, respectively. In contrast, the devices made with ethoxy-ethoxymethanofullerene and methoxy-ethoxymethanofullerene exhibited very low PCEs of <0.01% for both, indicating a large impact of the substituents on device performance.