In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.T...With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L_(∞)-norm,respectively,where1<γ<2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.展开更多
In July, construction began on the Shanghai International Motorcycle Race Field. Main construction should be completed in March 2004 and Fl Formula China Championships could be held that year.Located in the suburban J...In July, construction began on the Shanghai International Motorcycle Race Field. Main construction should be completed in March 2004 and Fl Formula China Championships could be held that year.Located in the suburban Jiading District of Shanghai, the International Motorcycle Race Field will occupy an area of 5.3 square kilometers. It consists of a race area, a business and exhibition area, an entertainment area and a reserved area.展开更多
Objective:Qu Du Qiang Fei 1 Hao Fang(QDQF1)is a novel Chinese herbal medicine formula used to treat coronavirus disease 2019(COVID-19).However,the pharmacological mechanisms of action of QDQF1 remain unclear.The objec...Objective:Qu Du Qiang Fei 1 Hao Fang(QDQF1)is a novel Chinese herbal medicine formula used to treat coronavirus disease 2019(COVID-19).However,the pharmacological mechanisms of action of QDQF1 remain unclear.The objective of this study was to identify the effective ingredients and biological targets of QDQF1 for COVID-19 treatment.Materials and Methods:The effective ingredients and mechanisms of action of QDQF1 were analyzed by using network pharmacology methods,which included an analysis of the effective ingredients and corresponding targets,COVID-19-related target acquisition,compound-target network analyses,protein-protein interaction network analysis,Kyoto Encyclopedia of Genes and Genomes(KEGG)and Gene Ontology(GO)enrichment analyses,and molecular docking studies.Results:In total,288 effective QDQF1 ingredients were identified.We identified 51 core targets from the 148 targets through an overlap between putative QDQF1 targets and COVID-19-related targets.Six key components,including formononetin,kaempferol,luteolin,naringenin,quercetin,and wogonin were identified through component-target network analyses.GO functional enrichment analysis of the core targets revealed 1296 items,while KEGG pathway enrichment analysis identified 148 signaling pathways.Nine central targets(CCL2,CXCL8,IL1B,IL6,MAPK1,MAPK3,MAPK8,STAT3,and TNF)related to the COVID-19 pathway were identified in the KEGG pathway enrichment analysis.Furthermore,molecular docking analysis suggested that the docking scores of the six key components to the nine central targets were better than those to remdesivir.Conclusions:QDQF1 may regulate multiple immune-and inflammation-related targets to inhibit the progression of severe acute respiratory syndrome coronavirus 2,and thus,may be suitable for the treatment of COVID-19.展开更多
OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels i...OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels in a rat model of osteoarthritis(OA).METHODS:Sprague-Dawley rats were used to establish an OA model and subjected to various treatments over 6 weeks.Rats were treated with BHF,glucosamine sulfate(G5),or starch as a control.Serum levels of IL-1β and MMP-1 and joint fluid levels of IL-1 β were determined by means of ELISAs.We used immunohistochemistry to determine DDR2 levels in knee cartilage.Gene expression levels of MMP-1 in joint synovial tissue were assessed using reverse transcription polymerase chain reaction assays.RESULTS:Serum IL-1β levels were unchanged throughout the study.Levels of IL-1β in joint fluid and MMP-1 in sera from the BHF- and GS-treated groups were significantly reduced.DDR2 levels in knee cartilage were also significantly reduced in the BHF group.Expression of the MMP-1 gene was significantly reduced by BHF treatment.CONCLUSION:BHF might be beneficial in the inhibition and alleviation of local inflammatory responses and cartilage degeneration in OA.展开更多
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
基金supported by the National Natural Science Foundation of China(grant number 11671081).
文摘With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L_(∞)-norm,respectively,where1<γ<2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.
文摘In July, construction began on the Shanghai International Motorcycle Race Field. Main construction should be completed in March 2004 and Fl Formula China Championships could be held that year.Located in the suburban Jiading District of Shanghai, the International Motorcycle Race Field will occupy an area of 5.3 square kilometers. It consists of a race area, a business and exhibition area, an entertainment area and a reserved area.
基金funded by the National Natural Science Foundation of China(81973543)the Shanghai Sailing Program(No.22YF1449800),China。
文摘Objective:Qu Du Qiang Fei 1 Hao Fang(QDQF1)is a novel Chinese herbal medicine formula used to treat coronavirus disease 2019(COVID-19).However,the pharmacological mechanisms of action of QDQF1 remain unclear.The objective of this study was to identify the effective ingredients and biological targets of QDQF1 for COVID-19 treatment.Materials and Methods:The effective ingredients and mechanisms of action of QDQF1 were analyzed by using network pharmacology methods,which included an analysis of the effective ingredients and corresponding targets,COVID-19-related target acquisition,compound-target network analyses,protein-protein interaction network analysis,Kyoto Encyclopedia of Genes and Genomes(KEGG)and Gene Ontology(GO)enrichment analyses,and molecular docking studies.Results:In total,288 effective QDQF1 ingredients were identified.We identified 51 core targets from the 148 targets through an overlap between putative QDQF1 targets and COVID-19-related targets.Six key components,including formononetin,kaempferol,luteolin,naringenin,quercetin,and wogonin were identified through component-target network analyses.GO functional enrichment analysis of the core targets revealed 1296 items,while KEGG pathway enrichment analysis identified 148 signaling pathways.Nine central targets(CCL2,CXCL8,IL1B,IL6,MAPK1,MAPK3,MAPK8,STAT3,and TNF)related to the COVID-19 pathway were identified in the KEGG pathway enrichment analysis.Furthermore,molecular docking analysis suggested that the docking scores of the six key components to the nine central targets were better than those to remdesivir.Conclusions:QDQF1 may regulate multiple immune-and inflammation-related targets to inhibit the progression of severe acute respiratory syndrome coronavirus 2,and thus,may be suitable for the treatment of COVID-19.
基金Supported by the Shandong Provincial Department of Education(Mechanism of Bushenhuoxue Formula Protecting Chondrocytes of Osteoarthritis,No.J07YD08)the Shandong Provincial Administration of Traditional Chinese Medicine(Relationship between Bushenhuoxue Formula and the Osteoarthritis Signaling Molecule DDR2,No.2007-027)
文摘OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels in a rat model of osteoarthritis(OA).METHODS:Sprague-Dawley rats were used to establish an OA model and subjected to various treatments over 6 weeks.Rats were treated with BHF,glucosamine sulfate(G5),or starch as a control.Serum levels of IL-1β and MMP-1 and joint fluid levels of IL-1 β were determined by means of ELISAs.We used immunohistochemistry to determine DDR2 levels in knee cartilage.Gene expression levels of MMP-1 in joint synovial tissue were assessed using reverse transcription polymerase chain reaction assays.RESULTS:Serum IL-1β levels were unchanged throughout the study.Levels of IL-1β in joint fluid and MMP-1 in sera from the BHF- and GS-treated groups were significantly reduced.DDR2 levels in knee cartilage were also significantly reduced in the BHF group.Expression of the MMP-1 gene was significantly reduced by BHF treatment.CONCLUSION:BHF might be beneficial in the inhibition and alleviation of local inflammatory responses and cartilage degeneration in OA.
