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
Current Conditional Functional Dependency(CFD)discovery algorithms always need a well-prepared training dataset.This condition makes them difficult to apply on large and low-quality datasets.To handle the volume issue...Current Conditional Functional Dependency(CFD)discovery algorithms always need a well-prepared training dataset.This condition makes them difficult to apply on large and low-quality datasets.To handle the volume issue of big data,we develop the sampling algorithms to obtain a small representative training set.We design the fault-tolerant rule discovery and conflict-resolution algorithms to address the low-quality issue of big data.We also propose parameter selection strategy to ensure the effectiveness of CFD discovery algorithms.Experimental results demonstrate that our method can discover effective CFD rules on billion-tuple data within a reasonable period.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.
基金partially supported by the National Key R&D Program of China(No.2018YFB1004700)the National Natural Science Foundation of China(Nos.U1509216,U1866602,and 61602129)Microsoft Research Asia.
文摘Current Conditional Functional Dependency(CFD)discovery algorithms always need a well-prepared training dataset.This condition makes them difficult to apply on large and low-quality datasets.To handle the volume issue of big data,we develop the sampling algorithms to obtain a small representative training set.We design the fault-tolerant rule discovery and conflict-resolution algorithms to address the low-quality issue of big data.We also propose parameter selection strategy to ensure the effectiveness of CFD discovery algorithms.Experimental results demonstrate that our method can discover effective CFD rules on billion-tuple data within a reasonable period.
