Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + ...Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.展开更多
In present paper, we study precisely the growth of analytic functions defined by zero order Laplace-Stieltjes transformation converging in right plane. The coefficient characterizations of generalized logarithmic p-ty...In present paper, we study precisely the growth of analytic functions defined by zero order Laplace-Stieltjes transformation converging in right plane. The coefficient characterizations of generalized logarithmic p-type and generalized lower logarithmic p-type are obtained, which improve the results of logarithmic type and lower logarithmic type.展开更多
A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and ...A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and scaling attacks, and the odd-even quantization algorithm is used to embed watermark so it can be extracted without the original host image. The experiments show that the proposed algorithm not only resists various geomet- ric attacks but also is robust enough to the common signal processing.展开更多
文摘Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.
基金Supported by the Technology Project of Jiangxi Provincial Education Department(Grant No.GJJ13788)
文摘In present paper, we study precisely the growth of analytic functions defined by zero order Laplace-Stieltjes transformation converging in right plane. The coefficient characterizations of generalized logarithmic p-type and generalized lower logarithmic p-type are obtained, which improve the results of logarithmic type and lower logarithmic type.
基金Supported by the National Natural Science Foundation of China (60842006)
文摘A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and scaling attacks, and the odd-even quantization algorithm is used to embed watermark so it can be extracted without the original host image. The experiments show that the proposed algorithm not only resists various geomet- ric attacks but also is robust enough to the common signal processing.
基金国家电网公司科技项目(<提高特高压互感器可靠性技术研究>)(合同编号EPRIGYKJ[2012]4939号)Science and Technology Project of the State Grid Corporation of China("Research to Improve the Reliability of UHV Instrument Transformer")(No.EPRIGYKJ[2012]4939)
