In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related ...In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related to the Fourier integral of slowly growing functions. The part of the Fourier ex- ponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines. First. it allows us to con- struct a rich library of splines possessing the property that translations of any such spline form a ba- sis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline spaces and of spline interpolation of growing func- tion. We derive formulas for approximate evaluation of splines projecting a function onto the spline space and establish therewith exact estimations of the approximation errors.展开更多
The Median Tectonic Line(MTL)is the largest active fault system on the Japan Islands and underlies many densely populated areas.To understand the seismotectonics and to reduce seismic hazard in the MTL region,we deter...The Median Tectonic Line(MTL)is the largest active fault system on the Japan Islands and underlies many densely populated areas.To understand the seismotectonics and to reduce seismic hazard in the MTL region,we determined a detailed 3-D crustal structure under the region using a large number of arrival times of the first P-waves and Moho-reflected waves(PmP).Results of detailed resolution tests show that the addition of PmP data can significantly improve the resolution of the lower crustal structure and the entire crustal structure can be imaged better than that by using P-wave data alone.The展开更多
Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structure...Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structured light image, a ranked-order based adaptively extremum median （RAEM） filter algorithm on salt and pepper noise is presented. In the algorithm, firstly effective points and noise points in a filtering window are differentiated; then the gray values of noise points are replaced by the medium of gray values of the effective pixels, with the efficient points＇ gray values unchanged; in the end this algorithm is proved to be efficient by experiments. Experimental resuits demonstrate that the image blur, resulting into proposed algorithm can remove noise points effectively and minimize the protecting the edge information as much as possible.展开更多
文摘In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related to the Fourier integral of slowly growing functions. The part of the Fourier ex- ponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines. First. it allows us to con- struct a rich library of splines possessing the property that translations of any such spline form a ba- sis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline spaces and of spline interpolation of growing func- tion. We derive formulas for approximate evaluation of splines projecting a function onto the spline space and establish therewith exact estimations of the approximation errors.
文摘The Median Tectonic Line(MTL)is the largest active fault system on the Japan Islands and underlies many densely populated areas.To understand the seismotectonics and to reduce seismic hazard in the MTL region,we determined a detailed 3-D crustal structure under the region using a large number of arrival times of the first P-waves and Moho-reflected waves(PmP).Results of detailed resolution tests show that the addition of PmP data can significantly improve the resolution of the lower crustal structure and the entire crustal structure can be imaged better than that by using P-wave data alone.The
基金Supported by the National Natural Science Foundation of China(61273346)the National Defense Key Fundamental Research Program of China(A20130010)the Program for the Fundamental Research of Beijing Institute of Technology(2016CX02010)
文摘Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structured light image, a ranked-order based adaptively extremum median （RAEM） filter algorithm on salt and pepper noise is presented. In the algorithm, firstly effective points and noise points in a filtering window are differentiated; then the gray values of noise points are replaced by the medium of gray values of the effective pixels, with the efficient points＇ gray values unchanged; in the end this algorithm is proved to be efficient by experiments. Experimental resuits demonstrate that the image blur, resulting into proposed algorithm can remove noise points effectively and minimize the protecting the edge information as much as possible.
