This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are ...This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the secondnorm of estimated parameter’s total error.展开更多
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an a...Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.展开更多
The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylin...The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.展开更多
Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in ter...Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.展开更多
Laboratory experiments are performed to explore the response rule of a sandy beach profile under plunging wave on a non-uniform sediment-bed slope. The initial beach slope of combination of 1/10 and 1/20 is exposed to...Laboratory experiments are performed to explore the response rule of a sandy beach profile under plunging wave on a non-uniform sediment-bed slope. The initial beach slope of combination of 1/10 and 1/20 is exposed to regular waves and cnoidal waves respectively. The free surface elevation, process of wave propagation, wave breaking, uprush and backwash and the change of a cross-shore beach profile are measured and recorded. The beach profile under the regular waves action exhibits two parts： a sandbar profile and a beach berm profile, and only one typical profile transformation under the cnoidal waves action is obtained, which is the beach berm profile. In the laboratory experiments, it is found that the beach states under wave action related to the previous factors. In addition, they are related to the characteristic of breaking waves such as the breaking intensity of the plunging wave. A concept about the characteristic angle of the plunging wave has been put forward through the observation and analysis of the phenomenon of the laboratory experiment. A qualitative analysis about the sediment transport carrying by currents generated from the plunging wave and the state of beach profile under the wave action has been done. The quantitative analysis about the relationship between the characteristic angle and Irribarren number has been done. An available formula of equilibrium states for the sandy beach induced by the plunging wave has been established based on the relationship between Irribarren number and the beach profile. By fitting these experimental results and others＇ experimental results to three lines, the three fitting coefficients can be calculated in their formula respectively. The recommended empirical formulas can divide three states of a beach morphology profile obviously, which include a depositive beach, an erosive beach and an intermediate beach.展开更多
文摘This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the secondnorm of estimated parameter’s total error.
基金The project was supported by the Natural Science Foundation of Fujian Province of China (Z0511002)the National Science Foundation of China (10271097,10571144)+1 种基金Foundation of Tianyuan (10526033)Chen L P, the Corresponding author
文摘Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.11632012 and 41861144024)the National Basic Research Program of China(973 Program,Grant No.2014CB046203)
文摘The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.
基金National Natural Science Foundation of China(No.11371086)the Fund of Science and Technology Commission of Shanghai Municipality,China(No.13ZR1400100)
文摘Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
基金The National Natural Science Foundation of China under contract Nos 51239001,51179015,51409022 and 51509023the Hunan Provincial Innovation Foundation for Postgraduate under contract No.CX2015B348
文摘Laboratory experiments are performed to explore the response rule of a sandy beach profile under plunging wave on a non-uniform sediment-bed slope. The initial beach slope of combination of 1/10 and 1/20 is exposed to regular waves and cnoidal waves respectively. The free surface elevation, process of wave propagation, wave breaking, uprush and backwash and the change of a cross-shore beach profile are measured and recorded. The beach profile under the regular waves action exhibits two parts： a sandbar profile and a beach berm profile, and only one typical profile transformation under the cnoidal waves action is obtained, which is the beach berm profile. In the laboratory experiments, it is found that the beach states under wave action related to the previous factors. In addition, they are related to the characteristic of breaking waves such as the breaking intensity of the plunging wave. A concept about the characteristic angle of the plunging wave has been put forward through the observation and analysis of the phenomenon of the laboratory experiment. A qualitative analysis about the sediment transport carrying by currents generated from the plunging wave and the state of beach profile under the wave action has been done. The quantitative analysis about the relationship between the characteristic angle and Irribarren number has been done. An available formula of equilibrium states for the sandy beach induced by the plunging wave has been established based on the relationship between Irribarren number and the beach profile. By fitting these experimental results and others＇ experimental results to three lines, the three fitting coefficients can be calculated in their formula respectively. The recommended empirical formulas can divide three states of a beach morphology profile obviously, which include a depositive beach, an erosive beach and an intermediate beach.
