The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on...The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.展开更多
The bio-clogging using bacteria can be an eco-friendly and sustainable alternative to conventional grouting methods for seepage control.However,it remains unclear to date how the dilute concentration of bacterium and ...The bio-clogging using bacteria can be an eco-friendly and sustainable alternative to conventional grouting methods for seepage control.However,it remains unclear to date how the dilute concentration of bacterium and medium during field installation can affect the setting time of bacterium and its correlation with permeability reduction.In this study,the setting time of bacterium and its effectiveness in permeability reduction were addressed through experimental and theoretical investigations.A series of sand column was cultivated using different concentrations of Leuconostoc mesenteroides and culture medium.The distribution and composition of the bacterial product(i.e.dextran)were observed by refractometer,scanning electron microscope(SEM),and energy dispersive X-ray spectroscopy(EDS).Soil permeability was recorded using a constant head test.The results revealed that bacterium was effective to produce dextran at the setting time of about 5 d after installation.This dextran can reduce the permeability of bio-mediated soil by two orders of magnitude,even without culture medium supply.In general,the dextran production decreased proportionally with increase of bacterium and medium concentration.However,at 50%bacterium and medium concentration by weight,it still has a significant influence on permeability reduction with similar setting time,compared to 100%concentration.展开更多
This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the F...This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.展开更多
基金supported by the National Natural Science Foundation of China(62176218,62176027)the Fundamental Research Funds for the Central Universities(XDJK2020TY003)the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。
文摘The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.
基金This work is supported by King Mongkut’s Institute of Technology Ladkrabang(Grant No.2563-02-01-014).
文摘The bio-clogging using bacteria can be an eco-friendly and sustainable alternative to conventional grouting methods for seepage control.However,it remains unclear to date how the dilute concentration of bacterium and medium during field installation can affect the setting time of bacterium and its correlation with permeability reduction.In this study,the setting time of bacterium and its effectiveness in permeability reduction were addressed through experimental and theoretical investigations.A series of sand column was cultivated using different concentrations of Leuconostoc mesenteroides and culture medium.The distribution and composition of the bacterial product(i.e.dextran)were observed by refractometer,scanning electron microscope(SEM),and energy dispersive X-ray spectroscopy(EDS).Soil permeability was recorded using a constant head test.The results revealed that bacterium was effective to produce dextran at the setting time of about 5 d after installation.This dextran can reduce the permeability of bio-mediated soil by two orders of magnitude,even without culture medium supply.In general,the dextran production decreased proportionally with increase of bacterium and medium concentration.However,at 50%bacterium and medium concentration by weight,it still has a significant influence on permeability reduction with similar setting time,compared to 100%concentration.
基金supported by the Mathematical Tianyuan Foundation (No. 10826078)the National Natural Science Foundation of China (No. 60874006)
文摘This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.
