The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction pr...The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.展开更多
Sideways fall has been identified as the most critical situation for the elderly to develop hip fractures. The impact force onto the greater trochanter is the key factor for predicting fracture risk. For the elderly, ...Sideways fall has been identified as the most critical situation for the elderly to develop hip fractures. The impact force onto the greater trochanter is the key factor for predicting fracture risk. For the elderly, the impact force can only be determined by dynamics simulations, and the dynamics model must be first validated by experiments before it can be applied in clinic. In this study, subject-specific whole-body dynamics models constructed from dual energy X-ray absorptiometry (DXA) images of the subjects were validated by controlled and protected fall tests using young volunteers. The validation results suggested that subject-specific dynamics model is much more accurate in predicting impact force induced in sideways fall than conventional non-subject-specific dynamics model. Therefore, subject-specific dynamics model can be applied in clinic to improve the accuracy of assessing hip fracture risk.展开更多
We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can prod...We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can produce a big alteration on its solution （if it exists）. We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren＇t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].展开更多
Abstract In this paper, we introduce a modified Landweber iteration to solve the sideways parabolic equation, which is an inverse heat conduction problem （IHCP） in the quarter plane and is severely ill-posed. We sha...Abstract In this paper, we introduce a modified Landweber iteration to solve the sideways parabolic equation, which is an inverse heat conduction problem （IHCP） in the quarter plane and is severely ill-posed. We shall show that our method is of optimal order under both a priori and a posteriori stopping rule. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound. Numerical examples show that the computation effect is satisfactory.展开更多
文摘The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.
文摘Sideways fall has been identified as the most critical situation for the elderly to develop hip fractures. The impact force onto the greater trochanter is the key factor for predicting fracture risk. For the elderly, the impact force can only be determined by dynamics simulations, and the dynamics model must be first validated by experiments before it can be applied in clinic. In this study, subject-specific whole-body dynamics models constructed from dual energy X-ray absorptiometry (DXA) images of the subjects were validated by controlled and protected fall tests using young volunteers. The validation results suggested that subject-specific dynamics model is much more accurate in predicting impact force induced in sideways fall than conventional non-subject-specific dynamics model. Therefore, subject-specific dynamics model can be applied in clinic to improve the accuracy of assessing hip fracture risk.
基金Supported by Beijing Natural Science Foundation (Grant Nos. 1092003 and 1082003)National Natural Science Foundation of China (Grant No. 10871012)+1 种基金Beijing Educational Committee Foundation (Grant No. 00600054R1002)Science and Technology Innovation Foundation of Beijing Educational Committee (Grant No. 00600054K2009)
文摘We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can produce a big alteration on its solution （if it exists）. We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren＇t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].
基金Supported by the National Natural Science Foundation of China (No. 10971019)Scientific Research Fund of Guangxi Education Department Grant No. 201012MS067
文摘Abstract In this paper, we introduce a modified Landweber iteration to solve the sideways parabolic equation, which is an inverse heat conduction problem （IHCP） in the quarter plane and is severely ill-posed. We shall show that our method is of optimal order under both a priori and a posteriori stopping rule. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound. Numerical examples show that the computation effect is satisfactory.
