Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positiv...Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unciear what kind of initial state shares an affine map. In this study, we give a sumcient condition of initial states, in which the reduced dynamics can always be described by an affihe map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map.展开更多
In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there hav...In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.展开更多
A new image warping method is proposed in this letter, which can warp a given image by some manual defined features. Based on the radial basis interpolation function algorithm, the proposed method can transform the or...A new image warping method is proposed in this letter, which can warp a given image by some manual defined features. Based on the radial basis interpolation function algorithm, the proposed method can transform the original optimized problem into nonsingular linear problem by adding one-order term and affine differentiable condition. This linear system can get the steady unique solution by choosing suitable kernel function. Furthermore, the proposed method demonstrates how to set up the radial basis function in the target image so as to achieve supports to adopt the backward re-sampling technology accordingly which could gain the very slippery warping image. Theexperimental result shows that the proposed method can implement smooth and gradual image warping with multi-anchor points' accurate interpolation.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11175105
文摘Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unciear what kind of initial state shares an affine map. In this study, we give a sumcient condition of initial states, in which the reduced dynamics can always be described by an affihe map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map.
基金Supported by University Grants Commission, India(F. 30-238/2004(SR))
文摘In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.
基金Supported by the National Natural Science Foundation of China (No.60141002).
文摘A new image warping method is proposed in this letter, which can warp a given image by some manual defined features. Based on the radial basis interpolation function algorithm, the proposed method can transform the original optimized problem into nonsingular linear problem by adding one-order term and affine differentiable condition. This linear system can get the steady unique solution by choosing suitable kernel function. Furthermore, the proposed method demonstrates how to set up the radial basis function in the target image so as to achieve supports to adopt the backward re-sampling technology accordingly which could gain the very slippery warping image. Theexperimental result shows that the proposed method can implement smooth and gradual image warping with multi-anchor points' accurate interpolation.
