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
The aim of this paper is to derive a numerical scheme for Troesch’s problem and to overcome the difficulty which faces the existing numerical methods when considering the Troesch’s problem with large values of λ. A...The aim of this paper is to derive a numerical scheme for Troesch’s problem and to overcome the difficulty which faces the existing numerical methods when considering the Troesch’s problem with large values of λ. A logarithmic finite difference method is derived for solving the Troesch’s problem. The method is very simple and works well for arbitrarily large values of the Troesch’s parameter. To test the proposed method, we have used a wide range of the Troesch’s parameter λ. A comparison with some existing methods is given. The numerical results show the robustness and the superiority of the proposed scheme over most of the existing numerical methods for the Troesch’s problem.展开更多
It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique...It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is continuous in a domain , where is Hausdorff space and connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is fixed and is stable;for what in this case, the inverse problem turns out to be well-posed.展开更多
We introduce a primitive class of analytic functions,by specializing in many well-known classes,classify Ma-Minda functions based on its conditions and their interesting geomet-rical aspects.Further,study a newly de n...We introduce a primitive class of analytic functions,by specializing in many well-known classes,classify Ma-Minda functions based on its conditions and their interesting geomet-rical aspects.Further,study a newly de ned subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results.We also establish some majorization,Bloch function norms,and other related problems for the same class.展开更多
In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mat...In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.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.
文摘The aim of this paper is to derive a numerical scheme for Troesch’s problem and to overcome the difficulty which faces the existing numerical methods when considering the Troesch’s problem with large values of λ. A logarithmic finite difference method is derived for solving the Troesch’s problem. The method is very simple and works well for arbitrarily large values of the Troesch’s parameter. To test the proposed method, we have used a wide range of the Troesch’s parameter λ. A comparison with some existing methods is given. The numerical results show the robustness and the superiority of the proposed scheme over most of the existing numerical methods for the Troesch’s problem.
文摘It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is continuous in a domain , where is Hausdorff space and connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is fixed and is stable;for what in this case, the inverse problem turns out to be well-posed.
文摘We introduce a primitive class of analytic functions,by specializing in many well-known classes,classify Ma-Minda functions based on its conditions and their interesting geomet-rical aspects.Further,study a newly de ned subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results.We also establish some majorization,Bloch function norms,and other related problems for the same class.
基金The National Natural Science Foundation of China(No60402019)the Science Research Program of Education Bureau of Hubei Province (NoQ200629001)
文摘In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.
