Rayleigh wave is an interference wave of longitudinal wave and transverse wave which propagate along the free surface of solids. There remains a dispute about the number of Rayleigh waves in viscoelastic media until n...Rayleigh wave is an interference wave of longitudinal wave and transverse wave which propagate along the free surface of solids. There remains a dispute about the number of Rayleigh waves in viscoelastic media until now, which is an essential problem of Rayleigh wave propagation. The purpose of this study is to propose a brief way of handling this essential problem within half-space Kelvin viscoelastic media. Starting from the dynamic equations of transverse wave and longitudinal wave based on Kelvin viscoelastic model, this study sets the complex wave number as a variable, introduces complex moduli and complex exponential factors, then a characteristic equation of Kelvin viscoelastic Rayleigh wave in half space is derived and simplified support for analysis of its uniqueness. After reviewing mathematical models describing phenomena of having multiple solutions but uniqueness when a natural condition is taken into account, a conjecture is given that the Rayleigh wave in Kelvin viscoelastic media must be unique if we assume a natural condition in accordance with the natural phenomena.展开更多
We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely ...We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.展开更多
文摘Rayleigh wave is an interference wave of longitudinal wave and transverse wave which propagate along the free surface of solids. There remains a dispute about the number of Rayleigh waves in viscoelastic media until now, which is an essential problem of Rayleigh wave propagation. The purpose of this study is to propose a brief way of handling this essential problem within half-space Kelvin viscoelastic media. Starting from the dynamic equations of transverse wave and longitudinal wave based on Kelvin viscoelastic model, this study sets the complex wave number as a variable, introduces complex moduli and complex exponential factors, then a characteristic equation of Kelvin viscoelastic Rayleigh wave in half space is derived and simplified support for analysis of its uniqueness. After reviewing mathematical models describing phenomena of having multiple solutions but uniqueness when a natural condition is taken into account, a conjecture is given that the Rayleigh wave in Kelvin viscoelastic media must be unique if we assume a natural condition in accordance with the natural phenomena.
文摘We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.
