The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the perfo...The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.展开更多
The airborne cross-track three apertures MilliMeter Wave (MMW) Synthetic Aperture Radar (SAR) side-looking three-Dimensional (3D) imaging is investigated in this paper. Three apertures are distributed along the cross-...The airborne cross-track three apertures MilliMeter Wave (MMW) Synthetic Aperture Radar (SAR) side-looking three-Dimensional (3D) imaging is investigated in this paper. Three apertures are distributed along the cross-track direction, and three virtual phase centers will be obtained through one-input and three-output. These three virtual phase centers form a sparse array which can be used to obtain the cross-track resolution. Because the cross-track array is short, the cross-track resolution is low. When the system works in side-looking mode, the cross-track resolution and height resolution will be coupling, and the low cross-track resolution will partly be transformed into the height uncertainty. The beam pattern of the real aperture is used as a weight to improve the Peak to SideLobe Ratio (PSLR) and Integrated SideLobe Ratio (ISLR) of the cross-track sparse array. In order to suppress the high cross-track sidelobes, a weighting preprocessing method is proposed. The 3D images of a point target and a simulation scene are achieved to verify the feasibility of the proposed method. And the imaging result of the real data obtained by the cross-track three-baseline MMW InSAR prototype is presented as a beneficial attempt.展开更多
The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficie...The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.展开更多
In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler...In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler forms, which are coupled and linear partial differentialequations, then obtain its general solution. Some special types of the localized excitations, suchas oscillating dromion, multi-solitoff, multi-dromion, multi-lump and multi-ring soliton solutionsare derived by selecting the arbitrary functions appropriately.展开更多
The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion th...The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.展开更多
A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is anal...A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is analyzed It is proved that the rectangle mark image edge of PCB has some fractal features A method of deleting unordinary curve noise and compensating the length of the fractal curve is put forward,which can get the fractal dimension value from one complex edge fractal property curve The relation between the dim ension of the fractal curve and the turning angle of image can be acquired from an equation,as a result,the angle value of the PCB image is got exactly A real image edge analysis result confirms that the method based on the fractal theory is a new powerful tool for angle locating on PCB and related image area.展开更多
Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. T...Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.展开更多
文摘The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.
基金Supported by the National Basic Research Program (973) of China (No. 2009CB72400)
文摘The airborne cross-track three apertures MilliMeter Wave (MMW) Synthetic Aperture Radar (SAR) side-looking three-Dimensional (3D) imaging is investigated in this paper. Three apertures are distributed along the cross-track direction, and three virtual phase centers will be obtained through one-input and three-output. These three virtual phase centers form a sparse array which can be used to obtain the cross-track resolution. Because the cross-track array is short, the cross-track resolution is low. When the system works in side-looking mode, the cross-track resolution and height resolution will be coupling, and the low cross-track resolution will partly be transformed into the height uncertainty. The beam pattern of the real aperture is used as a weight to improve the Peak to SideLobe Ratio (PSLR) and Integrated SideLobe Ratio (ISLR) of the cross-track sparse array. In order to suppress the high cross-track sidelobes, a weighting preprocessing method is proposed. The 3D images of a point target and a simulation scene are achieved to verify the feasibility of the proposed method. And the imaging result of the real data obtained by the cross-track three-baseline MMW InSAR prototype is presented as a beneficial attempt.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571263,11501579,11701571 and41572315)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant No.CUGW150809)
文摘The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.
文摘In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler forms, which are coupled and linear partial differentialequations, then obtain its general solution. Some special types of the localized excitations, suchas oscillating dromion, multi-solitoff, multi-dromion, multi-lump and multi-ring soliton solutionsare derived by selecting the arbitrary functions appropriately.
基金Supported by National Natural Science Foundation ofChina(No. 196 310 6 0 ) and Post Doctor Science Foun-dation of China
文摘The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.
文摘A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is analyzed It is proved that the rectangle mark image edge of PCB has some fractal features A method of deleting unordinary curve noise and compensating the length of the fractal curve is put forward,which can get the fractal dimension value from one complex edge fractal property curve The relation between the dim ension of the fractal curve and the turning angle of image can be acquired from an equation,as a result,the angle value of the PCB image is got exactly A real image edge analysis result confirms that the method based on the fractal theory is a new powerful tool for angle locating on PCB and related image area.
基金supported by the national natural foundationof China (70871104)the key research base for humanities and social sciences of Zhejiang Provincial high education talents (Statistics of Zhejiang Gongshang University)
文摘Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.
