The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the correspondi...The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.展开更多
Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annea...Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.展开更多
The back propagation(BP)neural network method is widely used in bathymetry based on multispectral satellite imagery.However,the classical BP neural network method faces a potential problem because it easily falls into...The back propagation(BP)neural network method is widely used in bathymetry based on multispectral satellite imagery.However,the classical BP neural network method faces a potential problem because it easily falls into a local minimum,leading to model training failure.This study confirmed that the local minimum problem of the BP neural network method exists in the bathymetry field and cannot be ignored.Furthermore,to solve the local minimum problem of the BP neural network method,a bathymetry method based on a BP neural network and ensemble learning(BPEL)is proposed.First,the remote sensing imagery and training sample were used as input datasets,and the BP method was used as the base learner to produce multiple water depth inversion results.Then,a new ensemble strategy,namely the minimum outlying degree method,was proposed and used to integrate the water depth inversion results.Finally,an ensemble bathymetric map was acquired.Anda Reef,northeastern Jiuzhang Atoll,and Pingtan coastal zone were selected as test cases to validate the proposed method.Compared with the BP neural network method,the root-mean-square error and the average relative error of the BPEL method can reduce by 0.65–2.84 m and 16%–46%in the three test cases at most.The results showed that the proposed BPEL method could solve the local minimum problem of the BP neural network method and obtain highly robust and accurate bathymetric maps.展开更多
This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is establish...This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is established. Furthermore, the blow-up criterion for the solutions of the hyperelastic rots equation is derived.展开更多
In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilin...In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.展开更多
In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed proble...In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.展开更多
In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining fu...In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.展开更多
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally f...Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.展开更多
The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v ...The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.展开更多
文摘The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.
基金the National Natural Science Foundation of China (60373089, 60674106, and 60533010)the National High Technology Research and Development "863" Program (2006AA01Z104)
文摘Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.
基金The National Natural Science Foundation of China under contract No.42001401the China Postdoctoral Science Foundation under contract No.2020M671431+1 种基金the Fundamental Research Funds for the Central Universities under contract No.0209-14380096the Guangxi Innovative Development Grand Grant under contract No.2018AA13005.
文摘The back propagation(BP)neural network method is widely used in bathymetry based on multispectral satellite imagery.However,the classical BP neural network method faces a potential problem because it easily falls into a local minimum,leading to model training failure.This study confirmed that the local minimum problem of the BP neural network method exists in the bathymetry field and cannot be ignored.Furthermore,to solve the local minimum problem of the BP neural network method,a bathymetry method based on a BP neural network and ensemble learning(BPEL)is proposed.First,the remote sensing imagery and training sample were used as input datasets,and the BP method was used as the base learner to produce multiple water depth inversion results.Then,a new ensemble strategy,namely the minimum outlying degree method,was proposed and used to integrate the water depth inversion results.Finally,an ensemble bathymetric map was acquired.Anda Reef,northeastern Jiuzhang Atoll,and Pingtan coastal zone were selected as test cases to validate the proposed method.Compared with the BP neural network method,the root-mean-square error and the average relative error of the BPEL method can reduce by 0.65–2.84 m and 16%–46%in the three test cases at most.The results showed that the proposed BPEL method could solve the local minimum problem of the BP neural network method and obtain highly robust and accurate bathymetric maps.
基金Supported by the National Natural Science Foundation of China(Grant No.11001107)
文摘This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is established. Furthermore, the blow-up criterion for the solutions of the hyperelastic rots equation is derived.
文摘In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.
文摘In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.
基金Supported by the Scientific Research Foundation for the Doctor,Nanjing University of Aeronautics and Astronautics(No.1008-907359)
文摘In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.
文摘Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
文摘The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.
