High-order Compact Difference Schemes for the Modified Anomalous Subdiffusion Equation

In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference operator. We apply these methods to fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability and convergence analysis of these difference schemes are studied by Fourier method in details. The convergence orders of these numerical schemes are $\mathcal {O}(\tau^2+h^6)$ and $\mathcal {O}(\tau^2+h^8)$, respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.Comment:

Gödel Fuzzy Argumentation Frameworks

Acknowledgements This work is supported by the Excellent Young Scholars Research Fund of Shandong Normal University. This research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF-06-3-0001.Publisher PD

High-Order Algorithms for Riesz Derivative and Their Applications (

We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth-order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first-order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis

Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative

Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the pth order schemes (p=2,3,4,5,6) for the αth order Riemann-Liouville integral and αth order Riemann-Liouville derivative. In this paper, we study such a problem and develop recursion formulas to compute these coefficients in the higher-order schemes. The coefficients of higher-order schemes (p=7,8,9,10) are also obtained. We first find that these coefficients are oscillatory, which is similar to Runge’s phenomenon. So, they are not suitable for numerical calculations. Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for p=3,…,6

The Synthetic Compound Norcantharidin Induced Apoptosis in Mantle Cell Lymphoma In Vivo and In Vitro through the PI3K-Akt-NF- κ

This study aimed to elucidate the antitumor activity of norcantharidin (NCTD) against human mantle cell lymphoma (MCL). Cell proliferation and apoptosis were examined by MTS and flow cytometry. Caspase-3, -8, and -9 activities were detected with a colorimetric caspase protease assay. Apoptotic proteins—including PARP, cyclin D1, Bcl-2 family proteins, XIAP, and cIAP I—were studied by western blot. The phosphoinositide 3 kinase (PI3K) inhibitor LY294002 was used to investigate the involvement of the PI3K/Akt signaling pathway. In vivo studies were performed using Z138 cell xenografts in nude mice. NCTD inhibited proliferation and induced apoptosis of Z138 and Mino cells, both in vitro and in vivo. PI3Kp110α and p-Akt expressions were downregulated by NCTD treatment. NCTD downregulated NF-κB activity by preventing NF-κB phosphorylation and nuclear translocation. This effect was correlated with the suppression of NF-κB-regulated gene products, such as cyclin D1, BAX, survivin, Bcl-2, XIAP, and cIAP. This phenomenon was blocked by the PI3K inhibitor LY294002. Our results demonstrated that NCTD can induce growth arrest and apoptosis in MCL cells and that the mechanism may involve the PI3K/Akt/NF-κB signaling pathway. NCTD may have therapeutic and/or adjuvant therapeutic applications in the treatment of MCL

Synthesis and Properties of Magnetic Carbon Nanocages Particles for Dye Removal

Magnetic carbon nanocages (MCNCs) with multiform pore structure have been synthesized by a simple low temperature carbonization process. Biorenewable lignin was used as a cheap and carbon-rich precursor for the first time. The products were characterized by X-ray diffraction (XRD), nitrogen adsorption-desorption, energy dispersive X-ray spectroscopy (EDS), vibrating sample magnetometer (VSM), transmission electron microscopy (TEM), and Raman spectrum. XRD pattern and Raman spectrum showed that the product has a high degree of graphitization crystallinity. TEM micrograph indicated that the synthesized MCNCs have the hierarchical pore and cage structure. Due to these characteristics, the obtained magnetic carbon nanocages can be used as efficient and recycled adsorbents in the removal of dye staff from textile wastewater

An Imprecise Probability Approach for Abstract Argumentation based on Credal Sets

Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making.Comment: 8 pages, 2 figures, Accepted in The 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019