In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these t...In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.展开更多
Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate ...Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al.(2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.展开更多
文摘In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.
基金supported by National Science Foundation of USA (Grant Nos. DMS1209191 and DMS-1507511)
文摘Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al.(2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.
