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In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately. We first use the Laplace transform and the modified Fourier transform to study the analytical solution of the Cauchy problem. Then, using the Galerkin finite element method in space, we generate a semi-discrete scheme and study the convergence analysis. Furthermore, using the L1 scheme of the Caputo derivative in time, we construct a fully discrete scheme and then discuss the stability and error estimation in detail. Finally, the numerical experiments are displaced to verify the theoretical results.

In order to promote the catalytic activity of starch-based biomimetic glutathione peroxidase (GPx), the selenized starch (SCS) and cationic starch (CCS) prepared from cassava starch (CS) were mixed, resulting in the targeted starch (SCS/CCS) with both the catalytic center and the recognition site of substrate. First, CS was modified with octenyl succinic anhydride and sodium selenide hydride, respectively, to prepare SCS. The CCS was synthesized by modifying CS with 3-chloro-2-hydroxypropyltrimethylammonium chloride. Some technologies including nuclear magnetic resonance (1H NMR), Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), thermal analysis (TG) and scanning electron microscopy (SEM) were used to characterize the samples. Finally, the effect of the mixture of SCS and CCS on the catalytic activity of GPx was investigated by changing the molar ration of nitrogen and selenium. Results showed that the 1H NMR spectrum of SCS with selenium content of 11.35 μg/g revealed some new peaks (0.6~2.5 ppm) attributed to protons of the octenyl succinate compared with CS. In comparison to the FT-IR spectrum of CS, SCS showed lower intensities in the characteristic peaks of hydroxyl (3300 cm−1) and bound water (1639 cm−1), indicating the consumption of hydroxyl groups of CS in the synthesis of SCS. This would increase the hydrophobicity of the resultant starch. The appearances of the proton signal quaternary ammonium group (3.22 ppm) in the 1H NMR spectrum of CCS and the C−N stretching (1483 cm−1) in the FT-IR spectrum indicated the introduction of the positively charged quaternary ammonium group on the CCS backbone. With a similar particle size to the CS, SCS and CCS revealed a rough surface, indicating that the modification reaction mainly occurred on the surface of starch granules. No significant change was observed in the XRD patterns and TG curves of CS, SCS and CCS, indicating that the modified reaction did not dramatically affect the crystalline structure and thermal stability of starch. When the molar ratio of nitrogen and selenium in SCS/CCS was 1200, the catalytic activities of the biomimetic GPx in the reaction systems of 4-nitrothiophenol+cumene hydroperoxide (NBT+CUOOH), 3-carboxy-4-nitrothiophenol+hydrogen oxide (TNB+H2O2), NBT+CUOOH and NBT+H2O2 were 13.94, 11.25, 12.91 and 10.87 µmol/min, respectively, which were 22.1%, 25.8%, 17.5%, 19.6% higher than that of SCS, respectively. This study provided a simple method for constructing starch-based biomimetic GPx with high catalytic activity.

In this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element method in spatial direction, we apply a second order symmetric difference method in time. Next we discuss the regularity analysis of the weak solution and convergence analysis of the semi-discrete scheme. Then we further study the stability analysis and the error estimation of the fully discrete problems, according to the properties of fractional Ritz-Volterra projection, Ritz projection and so on. Numerical examples with comparisons among the proposed schemes verify our theoretical analyses.

The selenium-rich Moringa oleifera leaves protein was extracted from the selenium-rich Moringa oleifera leaves. The preparation of angiotensin-converting enzyme (ACE) inhibitory peptides from selenium-rich Moringa oleifera leaves was optimized by single factor experiments and response surface method. The ACE inhibitory activity, amino acid composition and selenium content of the optimal enzymatic hydrolysate were analyzed and characterized. The results showed that the optimal hydrolysis conditions of ACE inhibitory peptides were as follows: time 3 h, pH7.5, enzyme to substrate ratio 0.23%, substrate concentration 5.97% and temperature 39.2 ℃. The ACE inhibitory peptides prepared under these conditions showed strong ACE inhibitory activity (IC50=0.522 mg/mL), rich in essential amino acids (24.05%) and hydrophobic amino acids (20.6%), and the selenium content was 1.86 times that of the raw material of Moringa oleifolia leaves. The ACE inhibitory peptides of selenium-rich Moringa oleifolia leaves protein had dual characteristics of functional factor and natural food. This study could provide theoretical basis for the development of antihypertensive drugs and related functional foods.

Pharmaceutical manufacturing industry is an important industry to ensure human life safety. The innovation efficiency is a significant factor to stimulate the development of pharmaceutical manufacturing industry. At present, there are few studies on the innovation efficiency of pharmaceutical manufacturing industry. To fill this gap, this paper estimates the innovation efficiency of China's pharmaceutical manufacturing industry in 23 provinces of China from 2010 to 2020 based on the super-network SBM model and Global-Malmquist index. The results show that: (1) From the perspective of efficiency of research and development stage (ERDS), the ERDS of China shows an increasing trend, with the most prominent growth in the western region. (2) From the perspective of efficiency of economic transformation stage (EETS), although there are fluctuations in the EETS, the overall development is good. The EETS of the central region and western region is better than that of the eastern region. (3) By comparing the efficiency of the two stages, it is found that the change direction of the efficiency of the two stages is not necessarily the same in some provinces.

Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.

Objectives ‘National Special Stewardship in the Clinical Use of Antibiotics’ was put forward in July 2011 in China. We aimed to retrospectively evaluate the impact of antimicrobial stewardship (AMS) managed by clinical pharmacists on antibiotic utilisation, prophylaxis and antimicrobial resistance (AMR).Design This was a retrospective observational study of trends in antibiotic use and AMR in the context of AMS.Setting Beijing Chaoyang Hospital, a 1400-bed tertiary hospital, in China.Data and participants Antibiotic prescriptions from 820 doctors included all outpatients (n=17 766 637) and inpatients (n=376 627) during 2010–2016. Bacterial resistance data were from all inpatients (n=350 699) during 2011–2016.Interventions Multiaspect intervention measures were implemented by clinical pharmacists (13 persons), for example, formulating the activity programme and performance management, advising on antibacterial prescriptions and training.Outcome measures The proportion of antibiotic prescriptions among outpatients and inpatients, intensity of consumption in defined daily dose (DDD)/100 bed-days, antibiotic prophylaxis in type I incision operations and resistance rates of Escherichia coli, Klebsiella pneumoniae and Pseudomonas aeruginosa were retrospectively analysed.Results The proportion of antibiotic prescriptions decreased in outpatients (from 19.38% to 13.21%) and in inpatients (from 64.34% to 34.65%), the intensity of consumption dropped from 102.46 to 37.38 DDD/100 bed-days. The proportion of antibiotic prophylaxis decreased from 98.94% to 18.93%. The proportion of rational timing of initial dose increased from 71.11% to 96.74%, the proportion of rational duration rose from 2.84% to 42.63%. Time series analysis demonstrated the resistance rates of E. coli and P. aeruginosa to fluoroquinolones decreased, the incidence rate of methicillin-resistant Staphylococcus aureus also decreased, whereas the resistance rates of E. coli and K. pneumoniae to carbapenems increased. The antibiotic use was partly positively correlated with AMR.Conclusions AMS had an important role in reducing antibiotic use and surgical antibiotic prophylaxis. The AMR was positively correlated with antibiotic consumption to some extent.

We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.

[Objectives] To optimize the extraction process of polysaccharides fromleaves of Dendrobiumoffwinale. [Methods] The polysaccharides from D. officinal were extracted by internal boiling method. The extraction rate of polysaccharides from D. officinale was studied. Based on the singe factor experiment' the L9 (3 3) orthogonal experiment was designed to optimize the extraction procees of polysaccharides from D. officinale. [Results] The optimum procees for extracting polysaccharides from D. officinal by internal boiling method was as flows: 1.00 g of D. officinale powder was desorbed with 6.0 mL of 20% ethanol for 20 min' 35.0 mL of 9°C water was rapidly added' and the extraction time was 5 min. [Conclusions] Under this condition' the extraction rate of polysaccharides from D. officinale was 12.31% ' which was 3. 75 percentage points higher than that of traditional reflux extraction. [ABSTRACT FROM AUTHOR]