A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach throu...A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.展开更多
This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering a...This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.展开更多
Kirsten rat sarcoma viral oncogene homolog(KRAS)-phosphodiesterase-delta(PDEδ)is a promising target for antitumor drug discovery.Herein,highly efficient and environmentally sensitive fluorescent probes of PDEδ(DS-Pr...Kirsten rat sarcoma viral oncogene homolog(KRAS)-phosphodiesterase-delta(PDEδ)is a promising target for antitumor drug discovery.Herein,highly efficient and environmentally sensitive fluorescent probes of PDEδ(DS-Probes)were rationally designed.As compared with the reported PDEδprobes,DS-Probes showed higher binding affinity and selectivity,which were able to conveniently and efficiently label PDEδin live cells as well as tumor tissues.Therefore,these fluorescent probes are expected to facilitate PDEδ-based mechanism elucidation,drug discovery and pathologic diagnosis.展开更多
基金supported by the National Natural Science Foundations of China(Grant Nos.12372073 and U20B2013)the Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-QN-0030).
文摘A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.
基金funded by the National Key Research and Development Program of China(No.2021YFB2600704)the National Natural Science Foundation of China(No.52171272)the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).
文摘This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.
基金supported by the National Key Research and Development Program of China(No.2020YFA0509200 to C.Sheng)National Natural Science Foundation of China(Nos.81903436 to Y.Li,82204211 to W.Wang and 22077138 to S.Wu)Shanghai Rising-Star Program(No.22QA1411300 to S.Wu).
文摘Kirsten rat sarcoma viral oncogene homolog(KRAS)-phosphodiesterase-delta(PDEδ)is a promising target for antitumor drug discovery.Herein,highly efficient and environmentally sensitive fluorescent probes of PDEδ(DS-Probes)were rationally designed.As compared with the reported PDEδprobes,DS-Probes showed higher binding affinity and selectivity,which were able to conveniently and efficiently label PDEδin live cells as well as tumor tissues.Therefore,these fluorescent probes are expected to facilitate PDEδ-based mechanism elucidation,drug discovery and pathologic diagnosis.
