In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem an...In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.展开更多
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which adm...This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This...Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This paper presents context-aware conditional functional dependencies（CCFDs） which contribute to provide reasonable values and detect po- tential errors. Especially, we focus on automatically discov- ering minimal CCFDs. In this paper, we present context rela- tivity to measure the relationship of CFDs. The overlap of the related CFDs can provide reasonable values which result in more accuracy consistency repairing, and some related CFDs are combined into CCFDs. Moreover, we prove that discover- ing minimal CCFDs is NP-complete and we design the pre- cise method and the heuristic method. We also present the dominating value to facilitate the process in both the precise method and the heuristic method. Additionally, the context relativity of the CFDs affects the cleaning results. We will give an approximate threshold of context relativity accord- ing to data distribution for suggestion. The repairing results are approved more accuracy, even evidenced by our empirical evaluation.展开更多
文摘In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10371098, 10447007 and 10475055）, the Natural Science Foundation of Shaanxi Province of China （Grant No 2005A13）.
文摘This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
文摘Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This paper presents context-aware conditional functional dependencies（CCFDs） which contribute to provide reasonable values and detect po- tential errors. Especially, we focus on automatically discov- ering minimal CCFDs. In this paper, we present context rela- tivity to measure the relationship of CFDs. The overlap of the related CFDs can provide reasonable values which result in more accuracy consistency repairing, and some related CFDs are combined into CCFDs. Moreover, we prove that discover- ing minimal CCFDs is NP-complete and we design the pre- cise method and the heuristic method. We also present the dominating value to facilitate the process in both the precise method and the heuristic method. Additionally, the context relativity of the CFDs affects the cleaning results. We will give an approximate threshold of context relativity accord- ing to data distribution for suggestion. The repairing results are approved more accuracy, even evidenced by our empirical evaluation.
