This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouvill...This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.展开更多
In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finit...Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finite-dim ensionalsubspaces,a stabilization form ulation is pre- sented for the Stokes problem by em ploying nonconform ing elem ents.This form ulation is uni- form ly coercive and notsubject to the Babus ka-Brezzicondition,and the resulted linear algebraic system is positive definitew ith the spectralcondition num berO(h- 2 ). Quasi-optim alerrorbounds are obtained,which is consistentwith the interpola- tion properties ofthe finite elem entsused.展开更多
THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ ...THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).展开更多
The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity ...The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity function of TLA is presented in this paper. An algorithm for precisely determning the coordinates of each element by means of the inverse elliptic function is derived. A fast approximation of recursive formula for solving distorted array shape is given. According to the comparison between ideal directivity and the directivity of distorted array, the criterion for making decision of operational mode of TLA sonar is presented. So that the performance prediction problem in TLA is solved. The results of system simulation in computer show a good agreement with the theoretical analysis.展开更多
In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the H...In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.展开更多
基金partially supportedby Ministerio de Ciencia e Innovacion-SPAINFEDER,project MTM2010-15314supported by the Ministry of Science and Education of the Republic of Kazakhstan through the Project No.0713 GF
文摘This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
文摘Follow ing the fram ew ork of the finite elem ent m ethods based on Riesz-representing operators developed by Duan Huoyuan in 1997,through discreteRieszrepresenting-operators on som e virtual(non-) conform ing finite-dim ensionalsubspaces,a stabilization form ulation is pre- sented for the Stokes problem by em ploying nonconform ing elem ents.This form ulation is uni- form ly coercive and notsubject to the Babus ka-Brezzicondition,and the resulted linear algebraic system is positive definitew ith the spectralcondition num berO(h- 2 ). Quasi-optim alerrorbounds are obtained,which is consistentwith the interpola- tion properties ofthe finite elem entsused.
文摘THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).
文摘The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity function of TLA is presented in this paper. An algorithm for precisely determning the coordinates of each element by means of the inverse elliptic function is derived. A fast approximation of recursive formula for solving distorted array shape is given. According to the comparison between ideal directivity and the directivity of distorted array, the criterion for making decision of operational mode of TLA sonar is presented. So that the performance prediction problem in TLA is solved. The results of system simulation in computer show a good agreement with the theoretical analysis.
文摘In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.
