Numerical Methods for Solving Space Fractional Partial Differential Equations Using Hadamard Finite-Part Integral Approach

From Springer Nature via Jisc Publications RouterHistory: received 2018-09-29, rev-recd 2018-11-09, accepted 2018-11-10, registration 2019-06-11, epub 2019-07-26, online 2019-07-26, ppub 2019-12Publication status: PublishedAbstract: We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case. The approximation of the space fractional Riemann–Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h3-α), where h is the space step size and α∈(1, 2) is the order of Riemann–Liouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equations. We obtained the error estimates with the convergence orders O(τ+h3-α+hβ), where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Grünwald–Letnikov formula or higher order Lubich’s methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the first-order convergence, the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Grünwald–Letnikov formula or Lubich’s higher order approximation schemes

Numerical methods for solving space fractional partial differential equations by using Hadamard finite-part integral approach

We introduce a novel numerical method for solving two-sided space fractional partial differential equation in two dimensional case. The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order $O(h^{3- \alpha})$, where $h$ is the space step size and $\alpha\in (1, 2)$ is the order of Riemann-Liouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equation. We obtained the error estimates with the convergence orders $O(\tau +h^{3-\alpha}+ h^{\beta})$, where $\tau$ is the time step size and $\beta >0$ is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equation constructed by using the standard shifted Gr\"unwald-Letnikov formula or higher order Lubich'e methods which require the solution of the equation satisfies the homogeneous Dirichlet boundary condition in order to get the first order convergence, the numerical method for solving space fractional partial differential equation constructed by using Hadamard finite-part integral approach does not require the solution of the equation satisfies the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained by using the Hadamard finite-part integral approach for solving space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained by using the numerical methods constructed with the standard shifted Gr\"unwald-Letnikov formula or Lubich's higer order approximation schemes

Bi-LRFusion: Bi-Directional LiDAR-Radar Fusion for 3D Dynamic Object Detection

LiDAR and Radar are two complementary sensing approaches in that LiDAR specializes in capturing an object's 3D shape while Radar provides longer detection ranges as well as velocity hints. Though seemingly natural, how to efficiently combine them for improved feature representation is still unclear. The main challenge arises from that Radar data are extremely sparse and lack height information. Therefore, directly integrating Radar features into LiDAR-centric detection networks is not optimal. In this work, we introduce a bi-directional LiDAR-Radar fusion framework, termed Bi-LRFusion, to tackle the challenges and improve 3D detection for dynamic objects. Technically, Bi-LRFusion involves two steps: first, it enriches Radar's local features by learning important details from the LiDAR branch to alleviate the problems caused by the absence of height information and extreme sparsity; second, it combines LiDAR features with the enhanced Radar features in a unified bird's-eye-view representation. We conduct extensive experiments on nuScenes and ORR datasets, and show that our Bi-LRFusion achieves state-of-the-art performance for detecting dynamic objects. Notably, Radar data in these two datasets have different formats, which demonstrates the generalizability of our method. Codes are available at https://github.com/JessieW0806/BiLRFusion.Comment: accepted by CVPR202

Protective Effects of Hydrogen against Low-Dose Long-Term Radiation-Induced Damage to the Behavioral Performances, Hematopoietic System, Genital System, and Splenic Lymphocytes in Mice

Molecular hydrogen (H2) has been previously reported playing an important role in ameliorating damage caused by acute radiation. In this study, we investigated the effects of H2 on the alterations induced by low-dose long-term radiation (LDLTR). All the mice in hydrogen-treated or radiation-only groups received 0.1 Gy, 0.5 Gy, 1.0 Gy, and 2.0 Gy whole-body gamma radiation, respectively. After the last time of radiation exposure, all the mice were employed for the determination of the body mass (BM) observation, forced swim test (FST), the open field test (OFT), the chromosome aberration (CA), the peripheral blood cells parameters analysis, the sperm abnormality (SA), the lymphocyte transformation test (LTT), and the histopathological studies. And significant differences between the treatment group and the radiation-only groups were observed, showing that H2 could diminish the detriment induced by LDLTR and suggesting the protective efficacy of H2 in multiple systems in mice against LDLTR

Evaluation of the antibacterial activity of Elsholtzia ciliate essential oil against halitosis-related Fusobacterium nucleatum and Porphyromonas gingivalis

The broad-spectrum antimicrobial activity of Elsholtzia ciliate essential oil (ECO) has been previously reported, but its effectiveness against halitosis-causing bacteria such as Fusobacterium nucleatum and Porphyromonas gingivalis is not well understood. In this study, we investigated the bacteriostatic activity of ECO against planktonic cells and biofilms of F. nucleatum and P. gingivalis, as well as its ability to inhibit bacterial metabolism and production of volatile sulfur compounds (VSCs) at sub-lethal concentrations. Our findings revealed that ECO exhibited comparable activities to chlorhexidine against these oral bacteria. Treatment with ECO significantly reduced the production of VSCs, including hydrogen sulfide, dimethyl disulfide, and methanethiol, which are major contributors to bad breath. As the major chemical components of ECO, carvacrol, p-cymene, and phellandrene, were demonstrated in vitro inhibitory effects on F. nucleatum and P. gingivalis, and their combined use showed synergistic and additive effects, suggesting that the overall activity of ECO is derived from the cumulative or synergistic effect of multiple active components. ECO was found to have a destructive effect on the bacterial cell membrane by examining the cell morphology and permeability. Furthermore, the application of ECO induced significant changes in the bacterial composition of saliva-derived biofilm, resulting in the elimination of bacterial species that contribute to halitosis, including Fusobacterium, Porphyromonas, and Prevotella. These results provide experimental evidence for the potential clinical applications of ECOs in the prevention and treatment of halitosis

Double-edged sword: China’s free trade agreements reinforces embodied greenhouse gas transfers in agricultural products

Abstract China, as the world’s largest importer, heavily relies on agricultural products. However, the impact of China’s free trade agreements (FTAs) on greenhouse gas (GHG) emissions embodied in agricultural product imports has been overlooked. It’s crucial to analyze changes in embodied GHG emissions resulting from FTAs. We categorize 367 agricultural products into 15 categories and construct a dataset on the embodied GHG emissions of these products imported by China from 119 countries between 2000 and 2015. Using the Propensity Score Matching (PSM)-progressive difference-in-differences (DID) method, our findings indicate that China’s FTAs have double-edged impact on agricultural product imports. It has positively influenced imports, with a 12.22% annual growth rate, promoting economic integration. However, it has negatively affected GHG emissions, leading to a 53.00% increase in emissions from agricultural imports. These findings highlight the importance of addressing production and consumption in reducing GHG strategies with agricultural products

Diagnostic Ability of Magnifying Narrow-Band Imaging for the Extent of Early Gastric Cancer: A Systematic Review and Meta-Analysis

Background. Accurate delineation of tumor margin is essential for complete resection of early gastric cancer (EGC). The objective of this study is to assess the performance of magnifying endoscopy with narrow-band imaging (ME-NBI) for the accurate demarcation of EGC margins. Methods. We searched PubMed, EMBASE, Web of Science, and Cochrane Library databases up to March 2020 to identify eligible studies. The diagnostic accuracy of ME-NBI for EGC margins was calculated, and subgroup analyses were performed based on tumor size, depth of tumor invasion, tumor-occupied site, macroscopic type, histological type, Helicobacter pylori (H. pylori), and endoscopists’ experience. Besides, we also evaluated the negative and positive resection rates of the horizontal margin (HM) of EGC after endoscopic submucosal dissection (ESD) and surgery. Results. Ten studies comprising 1018 lesions were eligible in the databases. The diagnostic accuracy of ME-NBI for the demarcation of EGC margins was 92.4% (95% confidence interval (CI): 86.7%-96.8%). According to ME-NBI subgroup analyses, the rate of accurate evaluation of EGC margins was not associated with H. pylori infection status, tumor size, depth of tumor invasion, tumor-occupied site, macroscopic type, histological type, and endoscopists’ experience, and no statistical differences were found in subgroup analyses. Moreover, the negative and positive resection rates of HM after ESD and surgery were 97.4% (95% CI: 92.1%-100%) and 2.6% (95% CI: 0.02%-7.9%), respectively. Conclusions. ME-NBI enables a reliable delineation of the extent of EGC