For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initi...For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.展开更多
A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved...A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.展开更多
We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a ...We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.展开更多
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti...First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.展开更多
Let the linear system Ax=b where the coefficient matrix A=(a<sub>ij</sub>)∈R<sup>m,n</sup> is an L-ma-trix(that is,a<sub>ij</sub>】0 （?） i and a<sub>ij</sub>≤0 （?...Let the linear system Ax=b where the coefficient matrix A=(a<sub>ij</sub>)∈R<sup>m,n</sup> is an L-ma-trix(that is,a<sub>ij</sub>】0 （?） i and a<sub>ij</sub>≤0 （?） i≠j),A=I-L-U,I is the identity matrix,-L and-U are,respectively,strictly lower and strictly upper triangular parts of A.In[1]theauthors considered two preconditioned linear systems?x=（?） and ?x=（?）展开更多
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the m...A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.展开更多
A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper...A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.展开更多
In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence ...In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.展开更多
A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling ...A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is chosen as coarse mesh H-square, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.展开更多
Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuo...Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuous feedback associative memory neural networks. The neural network synthesis procedure ensured the gain of large exponential convergence rate without reduction of the attraction domain.展开更多
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ...The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.展开更多
This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of init...This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.展开更多
A series of novel ester-capped carbosilane dendrimers（G0-COOCH3–G2-COOCH3） were designed and successfully synthesized via a hybrid divergent–convergent method through a facile hydrosilylation reaction. The structu...A series of novel ester-capped carbosilane dendrimers（G0-COOCH3–G2-COOCH3） were designed and successfully synthesized via a hybrid divergent–convergent method through a facile hydrosilylation reaction. The structures of these dendrimers were confirmed by FTIR,1H NMR, and HRMS analyses.展开更多
We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Po...This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise....In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).展开更多
The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. Howev...The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC3D. It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.展开更多
基金Project(2021JLM-49) supported by Natural Science Basic Research Program of Shaanxi-Joint Fund of Hanjiang to Weihe River Valley Water Diversion Project,ChinaProject(42077248) supported by the National Natural Science Foundation of China
文摘For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.
文摘A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.
文摘We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.
文摘First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.
文摘Let the linear system Ax=b where the coefficient matrix A=(a<sub>ij</sub>)∈R<sup>m,n</sup> is an L-ma-trix(that is,a<sub>ij</sub>】0 （?） i and a<sub>ij</sub>≤0 （?） i≠j),A=I-L-U,I is the identity matrix,-L and-U are,respectively,strictly lower and strictly upper triangular parts of A.In[1]theauthors considered two preconditioned linear systems?x=（?） and ?x=（?）
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
基金Supported by the National Natural Science Foundation of China(1 980 1 0 0 9) and by the Natural Sci-ence Foundation of Guangxi
文摘A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.
基金This work was supported by the National Natural Science Foundation of China (10201001, 70471008)
文摘A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
文摘In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.
文摘A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is chosen as coarse mesh H-square, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.
文摘Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuous feedback associative memory neural networks. The neural network synthesis procedure ensured the gain of large exponential convergence rate without reduction of the attraction domain.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304074,61475042,and 11274088)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2015202320 and GCC2014048)the Key Subject Construction Project of Hebei Province University,China
文摘The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
文摘This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.
基金support by the National Natural Science Foundation of China(No.21307053)China Postdoctoral Science Foundation Funded Project(No.2013M541911)+1 种基金Promotive Research Fund for Excellent Young and Middle-Aged Scientists of Shandong Province(No.BS2013CL044)Natural Science Foundation of Ludong University(No.LY2011004)
文摘A series of novel ester-capped carbosilane dendrimers（G0-COOCH3–G2-COOCH3） were designed and successfully synthesized via a hybrid divergent–convergent method through a facile hydrosilylation reaction. The structures of these dendrimers were confirmed by FTIR,1H NMR, and HRMS analyses.
文摘We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
基金Supported by the National Natural Science Foundation of China(1 0 1 6 1 0 0 2 ) and Guangxi Natural Sci-ence Foundation (0 1 3 5 0 0 4 )
文摘This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).
基金supported by National Natural Science Foundation of China(61573194,61374180,61573096)China Postdoctoral Science Foundation Funded Project(2013M530229)+3 种基金China Postdoctoral Science Special Foundation Funded Project(2014T70463)Six Talent Peaks High Level Project of Jiangsu Province(ZNDW-004)Science Foundation of Nanjing University of Posts and Telecommunications(NY213095)Australian Research Council(DP120104986)
基金The author gratefully acknowledges the financial support and affiliation from the University of Adelaide.
文摘The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC3D. It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.
