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).     

具有学习和退化效应的单机干扰管理问题

针对工件同时具有学习和退化效应、机器具有可用性限制这一问题,建立可预见性单机干扰管理模型。在这一模型中,工件的加工时间是既与工件所排的加工位置又与工件开始加工的时间有关的函数。同时,在生产过程中由于机器发生故障或定期维修等扰动事件导致机器在某段时间内不能加工工件。目标是在同时考虑原目标函数和由扰动造成的偏离函数的情况下,构建一个新的最优时间表序列。根据干扰度量函数的不同研究了两个问题,第一个问题的目标函数是极小化总完工时间与总误工时间的加权和;第二个问题的目标函数是极小化总完工时间与总提前时间的加权和。对于所研究的问题,首先证明了最优排序具有的性质,然后建立了相应的拟多项式时间动态规划算法。     

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.     

Investigating undergraduate mathematics learners’ cognitive engagement with recorded lecture videos

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility.

Cognitive engagement was operationalized using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning.

This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.     

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.     

Parallel Translation on K¨ahler Manifolds

In this paper, the author establishs a real-valued function on K¨ahler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K¨ahler manifolds, then they are holomorphically isometric.     

Noise Reduction in Spur Gear Systems

This article lists some tips for reducing gear case noise. With this aim, a static analysis was carried out in order to describe how stresses resulting from meshing gears affect the acoustic emissions. Different parameters were taken into account, such as the friction, material, and lubrication, in order to validate ideas from the literature and to make several comparisons. Furthermore, a coupled Eulerian–Lagrangian (CEL) analysis was performed, which was an innovative way of evaluating the sound pressure level of the aforementioned gears. Different parameters were considered again, such as the friction, lubrication, material, and rotational speed, in order to make different research comparisons. The analytical results agreed with those in the literature, both for the static analysis and CEL analysis—for example, it was shown that changing the material from steel to ductile iron improved the gear noise, while increasing the rotational speed or the friction increased the acoustic emissions. Regarding the CEL analysis, air was considered a perfect gas, but its viscosity or another state equation could have also been taken into account. Therefore, the above allowed us to state that research into these scientific fields will bring about reliable results.