In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theo...In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.展开更多
In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite differ...In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.展开更多
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr...This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.展开更多
The laws of motion of particle groups in a jigging process are studied. These describe the macroscopic phenomena that occur during jigging. During jigging the heavier and bigger particles concentrate at the bed bottom...The laws of motion of particle groups in a jigging process are studied. These describe the macroscopic phenomena that occur during jigging. During jigging the heavier and bigger particles concentrate at the bed bottom while lighter and smaller particles move to the upper part of the bed. Particles with equivalent properties tend to concentrate at a certain position centered around the inherent height of their distribution. The particle distribution variance gradually diminishes to some asymptotic value. The state equation group of the jigging bed is deduced and a calculation method, called the λ value judgment method, is proposed. The method is used to calculate the layer number and the inherent height of each particle group. A mathematical expression for the particle distribution variance is also given.展开更多
Deformation modulus is the important parameter in stability analysis of tunnels, dams and mining struc- tures. In this paper, two predictive models including Mamdani fuzzy system （MFS） and multivariable regression a...Deformation modulus is the important parameter in stability analysis of tunnels, dams and mining struc- tures. In this paper, two predictive models including Mamdani fuzzy system （MFS） and multivariable regression analysis （MVRA） were developed to predict deformation modulus based on data obtained from dilatometer tests carried out in Bakhtiary dam site and additional data collected from longwall coal mines. Models inputs were considered to be rock quality designation, overburden height, weathering, unconfined compressive strength, bedding inclination to core axis, joint roughness coefficient and fill thickness. To control the models performance, calculating indices such as root mean square error （RMSE）, variance account for （VAF） and determination coefficient （R^2） were used. The MFS results show the significant prediction accuracy along with high performance compared to MVRA results. Finally, the sensitivity analysis of MFS results shows that the most and the least effective parameters on deformation modulus are weatherin~ and overburden height, respectively.展开更多
文摘In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.
文摘In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.
文摘This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
基金Project 50474065 supported by the National Natural Science Foundation of China
文摘The laws of motion of particle groups in a jigging process are studied. These describe the macroscopic phenomena that occur during jigging. During jigging the heavier and bigger particles concentrate at the bed bottom while lighter and smaller particles move to the upper part of the bed. Particles with equivalent properties tend to concentrate at a certain position centered around the inherent height of their distribution. The particle distribution variance gradually diminishes to some asymptotic value. The state equation group of the jigging bed is deduced and a calculation method, called the λ value judgment method, is proposed. The method is used to calculate the layer number and the inherent height of each particle group. A mathematical expression for the particle distribution variance is also given.
文摘Deformation modulus is the important parameter in stability analysis of tunnels, dams and mining struc- tures. In this paper, two predictive models including Mamdani fuzzy system （MFS） and multivariable regression analysis （MVRA） were developed to predict deformation modulus based on data obtained from dilatometer tests carried out in Bakhtiary dam site and additional data collected from longwall coal mines. Models inputs were considered to be rock quality designation, overburden height, weathering, unconfined compressive strength, bedding inclination to core axis, joint roughness coefficient and fill thickness. To control the models performance, calculating indices such as root mean square error （RMSE）, variance account for （VAF） and determination coefficient （R^2） were used. The MFS results show the significant prediction accuracy along with high performance compared to MVRA results. Finally, the sensitivity analysis of MFS results shows that the most and the least effective parameters on deformation modulus are weatherin~ and overburden height, respectively.
