In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their c...A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.展开更多
In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain th...In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.展开更多
In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a cla...In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.展开更多
The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this pa...The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.展开更多
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived ...The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints.展开更多
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a ...Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.展开更多
In this paper we show that a class of superlinear boundary value problems in annular domains have infinitely many radially symmetric solutions. The result is obtained without other restrictions on the growth of the no...In this paper we show that a class of superlinear boundary value problems in annular domains have infinitely many radially symmetric solutions. The result is obtained without other restrictions on the growth of the nonlinearities. Our methods rely on the energy analysis and the phase plane angle analysis of the solutions for the associated ordinary differential equations.展开更多
A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted...A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted structured total least squares(WSTLS)framework and improved based on the robust estimation theory.Moreover, the improved Danish weight function is proposed according to the robust extremal function of the WSTLS, so that the new algorithm can detect outliers based on residuals and reduce the weights of outliers automatically. Finally, the inverse iteration method is discussed to deal with the RSTLS problem. Simulations show that when outliers appear, the result of the proposed algorithm is still accurate and robust, whereas that of the conventional algorithms is distorted seriously.展开更多
In this paper,we solve the optimal constant problem in the setting of Ohsawa’s generalized L2extension theorem.As applications,we prove a conjecture of Ohsawa and the extended Suita conjecture,we also establish some ...In this paper,we solve the optimal constant problem in the setting of Ohsawa’s generalized L2extension theorem.As applications,we prove a conjecture of Ohsawa and the extended Suita conjecture,we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.展开更多
In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate opti...In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.展开更多
This note gives two examples of surfaces with normal crossing singularities.In the first example the canonical ring is not finitely generated.In the second,the canonical line bundle is not ample but its pull back to t...This note gives two examples of surfaces with normal crossing singularities.In the first example the canonical ring is not finitely generated.In the second,the canonical line bundle is not ample but its pull back to the normalization is ample.The latter answers in the negative a problem left unresolved in Ⅲ.2.6.2 of lments de gometrie algbrique,1961,and raised again by Viehweg.展开更多
The author studies the technique of paradifferential operator defined on a space of conormaldistribution with three indeces,and then use this technique to prove that a progressing wavewhich hits the boundary is reflec...The author studies the technique of paradifferential operator defined on a space of conormaldistribution with three indeces,and then use this technique to prove that a progressing wavewhich hits the boundary is reflected according to the usual law.展开更多
This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is ...This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.展开更多
The CFD/CSD coupling method is turning into the main research direction for the static/dynamic aeroelastic analyses. If one wants to use the method for the complex engineering aeroelastic problems, he needs to investi...The CFD/CSD coupling method is turning into the main research direction for the static/dynamic aeroelastic analyses. If one wants to use the method for the complex engineering aeroelastic problems, he needs to investigate the relative aeroelasfic algorithms, such as the numerical computational method of unsteady aerodynamic forces, equivalent low-dimensional structural fi- nite element model and the solution method of structural dynamic equations, data transfer technique between fluid and structure, the moving grid method, etc. Besides, he also needs to improve the computational efficiency by such as massive parallel CFD algorithm, reduced-order model （ROM） of unsteady aerodynamic forces, etc. In this paper, based on the authors＇ recent investigations, the research progresses in computational aeroelastic methods and their applications to engineering problem are summarized.展开更多
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
文摘A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.
文摘In this paper,the fixed_point theorem is used to estimated an asymptotic solution of initial value problems for a class of third nonlinear differential equations which has double initial_layer properties. We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.
文摘In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.
文摘The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.
文摘This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
文摘The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.
文摘In this paper we show that a class of superlinear boundary value problems in annular domains have infinitely many radially symmetric solutions. The result is obtained without other restrictions on the growth of the nonlinearities. Our methods rely on the energy analysis and the phase plane angle analysis of the solutions for the associated ordinary differential equations.
基金supported by the National Natural Science Foundation of China(61202490)
文摘A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted structured total least squares(WSTLS)framework and improved based on the robust estimation theory.Moreover, the improved Danish weight function is proposed according to the robust extremal function of the WSTLS, so that the new algorithm can detect outliers based on residuals and reduce the weights of outliers automatically. Finally, the inverse iteration method is discussed to deal with the RSTLS problem. Simulations show that when outliers appear, the result of the proposed algorithm is still accurate and robust, whereas that of the conventional algorithms is distorted seriously.
基金supported by National Natural Science Foundation of China (Grant No. 11031008)
文摘In this paper,we solve the optimal constant problem in the setting of Ohsawa’s generalized L2extension theorem.As applications,we prove a conjecture of Ohsawa and the extended Suita conjecture,we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.
基金supported by the Doctoral Special Foundation of ZHJNC-ZL0904+1 种基金the National Natural Science Foundation of China under Grants Nos.10871039,10601010,and 10826077Guangdong Provincial Natural Science Foundation under Grant No.07301595
文摘In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.
基金provided by the NSF under grant number DMS-0500198
文摘This note gives two examples of surfaces with normal crossing singularities.In the first example the canonical ring is not finitely generated.In the second,the canonical line bundle is not ample but its pull back to the normalization is ample.The latter answers in the negative a problem left unresolved in Ⅲ.2.6.2 of lments de gometrie algbrique,1961,and raised again by Viehweg.
文摘The author studies the technique of paradifferential operator defined on a space of conormaldistribution with three indeces,and then use this technique to prove that a progressing wavewhich hits the boundary is reflected according to the usual law.
基金supported by National Natural Science Foundation of China (Grant Nos.91130009, 11171299 and 11041005)National Natural Science Foundation of Zhejiang Province in China (Grant Nos. Y6090091 and Y6090641)
文摘This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.
文摘The CFD/CSD coupling method is turning into the main research direction for the static/dynamic aeroelastic analyses. If one wants to use the method for the complex engineering aeroelastic problems, he needs to investigate the relative aeroelasfic algorithms, such as the numerical computational method of unsteady aerodynamic forces, equivalent low-dimensional structural fi- nite element model and the solution method of structural dynamic equations, data transfer technique between fluid and structure, the moving grid method, etc. Besides, he also needs to improve the computational efficiency by such as massive parallel CFD algorithm, reduced-order model （ROM） of unsteady aerodynamic forces, etc. In this paper, based on the authors＇ recent investigations, the research progresses in computational aeroelastic methods and their applications to engineering problem are summarized.
