A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients

In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula for the generalized Caputo fractional derivative in time discretization and the second-order weighted and shifted Gr\"{u}nwald difference (WSGD) formula in spatial discretization, respectively. Theoretical results and numerical tests are conducted to verify the $(2 - \gamma)$-order and 2-order of temporal and spatial convergence with $\gamma\in(0,1)$ the order of Caputo fractional derivative, respectively. The fast sum-of-exponential approximation of the generalized Caputo fractional derivative and Toeplitz-like coefficient matrices are also developed to accelerate the proposed implicit difference scheme. Numerical experiments show the effectiveness of the proposed numerical scheme and its good potential for large-scale simulation of GTSFDEs.Comment: 23 pages, 10 tables, 1 figure. Make several corrections again and have been submitted to a journal at Sept. 20, 2019. Version 2: Make some necessary corrections and symbols, 13 Jan. 2020. Revised manuscript has been resubmitted to journa

Comparative Study of TCM Syndrome Scale for Liver Disease and Chronic Liver Disease Questionnaire Based on Assessment of Posthepatitic Cirrhosis

Objective. To compare and analyze the relevance and applied value of chronic liver disease questionnaire (CLDQ) and Traditional Chinese Medicine liver disease questionnaire (TCMLDQ) in patients with posthepatitic cirrhosis. Methods. The data of 146 patients' scales of CLDQ and TCMLDQ which based on the characteristics of chinese medical symptoms were collected. We made comparative analysis of the relationship between these two scales by the linear regression model and canonical correlation method and evaluated the advantages and disadvantages of two scales about its items setting and dimension definition. Result. There is a negative correlation in total scores between the two scales and the linear regression equation: CLDQ = 239.38 − 1.232TCMLDQ. The further canonical correlation analysis was used to analyze the two extracted canonical correlative variables with significances (P < 0.05), and the results showed that the overall negative correlation between the two scales mainly came from contributions of both the four dimensions of TCMLDQ (CS, GSYX, GYPX, and OS) and the five dimensions of CLDQ (AS, FA, SS, AC, and EF). Conclusion. These two scales have good consistency in the evaluation of severity and life quality of liver cirrhosis patients, so we suggested that TCMLDQ can be used to evaluate the severity and life quality of patients with posthepatitic cirrhosis

Nonreciprocal ground-state cooling of multiple mechanical resonators

The simultaneous ground-state cooling of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity-field mode has become an outstanding challenge in cavity optomechanics. This is because the dark modes formed by these mechanical modes decouple from the cavity mode and prevent extracting energy from the dark modes through the cooling channel of the cavity mode. Here we propose a universal and reliable dark-mode-breaking method to realize the simultaneous ground-state cooling of two degenerate or nondegenerate mechanical modes by introducing a phasedependent phonon-exchange interaction, which is used to form a loop-coupled configuration. We find an asymmetrical cooling performance for the two mechanical modes and expound this phenomenon based on the nonreciprocal energy transfer mechanism, which leads to the directional flow of phonons between the two mechanical modes. We also generalize this method to cool multiple mechanical modes. The physical mechanism in this cooling scheme has general validity and this method can be extended to break other dark-mode and dark-state effects in physics.Comment: 42 pages, 21 figure

A Chinese Herbal Formula to Improve General Psychological Status in Posttraumatic Stress Disorder: A Randomized Placebo-Controlled Trial on Sichuan Earthquake Survivors

Introduction. Posttraumatic stress disorder (PTSD) is accompanied by poor general psychological status (GPS). In the present study, we investigated the effects of a Chinese herbal formula on GPS in earthquake survivors with PTSD. Methods. A randomized, double-blind, placebo-controlled trial compared a Chinese herbal formula, Xiao-Tan-Jie-Yu-Fang (XTJYF), to placebo in 2008 Sichuan earthquake survivors with PTSD. Patients were randomized into XTJYF (n = 123) and placebo (n = 122) groups. Baseline-to-end-point score changes in the three global indices of the Symptom Checklist-90-Revised (SCL-90-R) and rates of response in the SCL global severity index (GSI) were the primary endpoints. A subanalysis of the nine SCL factors and the sleep quality score were secondary endpoints. Results and Discussion. Compared to placebo, the XTJYF group was significantly improved in all three SCL global indices (P = 0.001~0.028). More patients in the XTJYF group reported “much improved” than the placebo group (P = 0.001). The XTJYF group performed significantly better than control in five out of nine SCL factors (somatization, obsessive-compulsive behavior, depression, anxiety, and hostility (P = 0.001~0.036)), and in sleep quality score (P < 0.001). XTJYF produced no serious adverse events. These findings suggest that XTJYF may be an effective and safe treatment option for improving GPS in patients with PTSD

Intracellular interferons in fish : a unique means to combat viral infection

Peer reviewedPublisher PD

Pilot-scale Study on NCMBR Process for Upgrading of Sewage Treatment Plant in Industrial Park

A pilot-scale research was conducted on nanostructured ceramic membrane bio-reactor (NCMBR) for treatment of comprehensive wastewater from industrial park. The quality of the effluent water was sable and good. During stable operation, the COD, NH3-N and TP concentrations of the influent water were 147-475, 42-23.5 and 0.65-0.85 mg/L, respectively, and those of the effluent water were 147-475, 0.08-0.82 and 0.18-0.26 mg/L, respectively, so the average removal rates of COD, NH3-N and TP were 82%, 97% and 72%, respectively, meeting the standard for Class-A emissions of Discharge Standard of Pollutants for Municipal Wastewater Treatment Plant (GB18918-2002). In addition, the process has certain anti-impact capacity and ability to mitigate membrane fouling, meeting the objectives of upgrading and transformation. This study will provide reference for upgrading of existing sewage treatment plants

Nonlinear Model and Dynamic Behavior of Photovoltaic Grid-Connected Inverter

A photovoltaic grid-connected inverter is a strongly nonlinear system. A model predictive control method can improve control accuracy and dynamic performance. Methods to accurately model and optimize control parameters are key to ensuring the stable operation of a photovoltaic grid-connected inverter. Based on the nonlinear characteristics of photovoltaic arrays and switching devices, we established a nonlinear model of photovoltaic grid-connected inverters using the state space method and solved its model predictive controller. Then, using the phase diagram, folded diagram, and bifurcation diagram methods, we studied the nonlinear dynamic behavior under the influence of control parameters on both fast and slow scales. Finally, we investigated the methods of parameter selection based on the characteristics of nonlinear dynamic behavior. Our research shows that the predictive controller parameters are closely related to the bifurcation and chaos behaviors of the grid-connected photovoltaic inverter. The three-dimensional bifurcation diagram can be used to observe the periodic motion region of the control parameters. After selecting the optimization target, the bifurcation diagram can be used to guide the selection of control parameters for inverter design. The research results can be used to guide the modeling, stability analysis, and optimization design of photovoltaic grid-connected inverters