In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functi...In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.展开更多
The oscillation property (OP) is a fundamental and important qualitative property for the vibrations of single span one-dimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discr...The oscillation property (OP) is a fundamental and important qualitative property for the vibrations of single span one-dimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discretized continuum model should keep the OP. In literatures, the OP of discrete beam models is discussed essentially by means of matrix factorization. The discussion is model-specific and boundary-condition- specific. Besides, matrix factorization is difficult in handling finite element (FE) models of beams. In this paper, according to a sufficient condition for the OP, a new approach to discuss the property is proposed. The local criteria on discrete displacements rather than global matrix factorizations are given to verify the OP. Based on the proposed approach, known results such as the OP for the 2-node FE beams via the Heilinger- Reissener principle (HR-FE beams) as well as the 5-point finite difference (FD) beams are verified. New results on the OP for the 2-node PE-FE beams and the FE Timoshenko beams with small slenderness are given. Through a simple manipulation, the qualitative property of discrete multibearing beams can also be discussed by the proposed approach.展开更多
In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from inf...In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.展开更多
In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of ...In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.展开更多
This paper presents a measurement-based solution for low frequency oscillation(LFO) analysis in both real time monitoring and off-line case study. An online LFO property discrimination method is developed first,which ...This paper presents a measurement-based solution for low frequency oscillation(LFO) analysis in both real time monitoring and off-line case study. An online LFO property discrimination method is developed first,which alternately uses empirical mode decomposition(EMD)/Hilbert transform(HT) and square calculation to process the measurement data. The method magnifies the variation trend of oscillating variables to accurately discriminate the property of the oscillation. Subsequently, an oscillation source locating method for the forced oscillation(FO) and a strongly correlated generator identification method for the weak damping oscillation(WDO) are proposed. Finally, numerical study results on a test system of the isolated Changdu grid in Tibet validate the proposed methods.展开更多
This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are establish...This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are established. Our results generalize the known Hille's ones.展开更多
基金The authors are supported by National Natural Sciences Foundation of China(11961060,11671322)the Key Project of Natural Sciences Foundation of Gansu Province(18JR3RA084).
文摘In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.
基金Project supported by the National Natural Science Foundation of China(Nos.10972005 and 11272011)
文摘The oscillation property (OP) is a fundamental and important qualitative property for the vibrations of single span one-dimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discretized continuum model should keep the OP. In literatures, the OP of discrete beam models is discussed essentially by means of matrix factorization. The discussion is model-specific and boundary-condition- specific. Besides, matrix factorization is difficult in handling finite element (FE) models of beams. In this paper, according to a sufficient condition for the OP, a new approach to discuss the property is proposed. The local criteria on discrete displacements rather than global matrix factorizations are given to verify the OP. Based on the proposed approach, known results such as the OP for the 2-node FE beams via the Heilinger- Reissener principle (HR-FE beams) as well as the 5-point finite difference (FD) beams are verified. New results on the OP for the 2-node PE-FE beams and the FE Timoshenko beams with small slenderness are given. Through a simple manipulation, the qualitative property of discrete multibearing beams can also be discussed by the proposed approach.
基金supported by the National Natural Science Foundation of China (11871250),Qing Lan ProjectKey (large) projects of Shandong Institute of Finance in2019 (2019SDJR31)the teaching reform project of Qilu Normal University (jg201710)
文摘In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.
基金supported by the Natural Science Foundation of China (Grant No. 10671019)Research Fund for the Doctoral Program Higher Education (No. 20050027007)Scientific Research Fund of Zhejiang Provincial Education Department (No. 20070509)
文摘In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.
基金supported in part by the National Natural Science Foundation of China(No.51177079,No.51321005)Sichuan Electric Power Company
文摘This paper presents a measurement-based solution for low frequency oscillation(LFO) analysis in both real time monitoring and off-line case study. An online LFO property discrimination method is developed first,which alternately uses empirical mode decomposition(EMD)/Hilbert transform(HT) and square calculation to process the measurement data. The method magnifies the variation trend of oscillating variables to accurately discriminate the property of the oscillation. Subsequently, an oscillation source locating method for the forced oscillation(FO) and a strongly correlated generator identification method for the weak damping oscillation(WDO) are proposed. Finally, numerical study results on a test system of the isolated Changdu grid in Tibet validate the proposed methods.
文摘This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are established. Our results generalize the known Hille's ones.