Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results.

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

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.

STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

The purpose of this article is to extend some spectral properties of regular Sturm- Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green＇s function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L2[a, b].

SPECTRAL PROPERTIES OF DISCRETE STURM-LIOUVILLE PROBLEMS WITH TWO SQUARED EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS

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.

Left-definite boundary conditions of Sturm-Liouville problems when the interval shrinks to a point

On the condition that the interval of the problem shrinks to a point, we investigated the separated boundary conditions Sα,β of left-definite Sturm-Liouville problem, and answered the following question： Is there a co ∈ J such that Sα,β is always left-definite or semi-left-definite for the Sturm-Liouville equation for each c ∈ （a, co）？

Inverse Nodal Problems for the Sturm-Liouville Operator with Some Nonlocal Integral Conditions

In this paper, we study three inverse nodal problems for the Sturm-Liouville operator with different nonlocal integral conditions. We get the conclusion that the potential function can be determined by a dense nodal subset uniquely. And we present some constructive procedures to solve the inverse nodal problems.

Inverse nodal problem for the Sturm-Liouville operator with a weight

In this work,we consider the inverse nodal problem for the Sturm-Liouville problem with a weight and the jump condition at the middle point.It is shown that the dense nodes of the eigenfunctions can uniquely determine the potential on the whole interval and some parameters.

Eigenvalue Computation of Regular 4th Order Sturm-Liouville Problems

In this paper we present and test a numerical method for computing eigenvalues of 4th order Sturm-Liouville (SL) differential operators on finite intervals with regular boundary conditions. This method is a 4th order shooting method based on Magnus expansions (MG4) which use MG4 shooting as the integrator. This method is similar to the SLEUTH (Sturm-Liouville Eigenvalues Using Theta Matrices) method of Greenberg and Marletta which uses the 2nd order Pruess method (also known as the MG2 shooting method) for the integrator. This method often achieves near machine precision accuracies, and some comparisons of its performance against the well-known SLEUTH software package are presented.

一类带转移条件Sturm-Liouville问题特征值的性质

把正则Sturm-Liouville问题关于特征值的性质推广到一类带转移条件的Sturm-Liouville问题中,利用prüfer变换证明了具有分离边界条件的这类问题有无穷多个实特征值,且特征值是下方有界的.

具有转移条件的Sturm-Liouville问题的Green函数

考虑了具有转移条件的Sturm-Liouville问题,即在有限区间上具有转移条件的问题,并给出了具有转移条件的Sturm-Liouville问题的Green函数.

一类具有转移条件的Sturm-Liouville问题的特征值(英文)

利用正规取样的方法,计算带有转移条件的不连续S turm-Liouville算子的特征值.

边界条件中带有谱参数且具有k点不连续的Sturm-Liouville问题

Kadakal,Altinisik,Mukhtarov等已对边界条件带有谱参数且分别在一点和两点不连续的Sturm-Liouville问题的特征值和特征函数的渐近式作了研究.在其基础上,先是定义了新内积、讨论了算子的自伴性,然后研究了边界条件中带有谱参数且在k个点不连续的Sturm-Li-ouville特征问题及其特征值和特征函数的渐近式.

AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS

In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.

Reconstruction of the Sturm-Liouville operator with discontinuities from a particular set of eigenvalues

Sturm-Liouville operators on a finite interval with discontinuities are considered. We give a uniqueness theorem for determining the potential and the parameters in boundary and under discontinuous conditions from a particular set of eigenvalues, and provide corresponding reconstruction algorithm, which can be applicable to McLaughlin-Rundell＇s uniqueness theorem （see J. Math. Phys. 28, 1987）.

A New Method of Solving the Index Problem for Sturm-Liouville Eigenvalues

Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.

青藏500kV输电工程沿线冻土工程特性及其对策探讨

根据青海-西藏500 kV直流联网工程输电线路沿线多年冻土区已有研究成果及现场实际勘察结果,结合输电线路工程特点对沿线冻土工程地质条件、存在的冻土工程问题,以及对策进行了较为系统研究。研究表明:输电线路沿线跨越540 km的连续片状多年冻土区和80 km的岛状多年冻土区,其中高含冰量冻土区占一半左右,低含冰量冻土区占25%;工程稳定性差的冻土地温带分布广;沿线的工程地质问题普遍存在,冻胀融沉是输电线路塔基失稳的主要原因,其中冻拔问题将是输电线路工程面临的新问题;不良冻土现象广泛分布于沿线,对线路构成较大危害;在气候变暖条件下,冻土退化较为显著,对输电线路的长期稳定性产生负面影响。同时,结合地下冰发育规律和工程特点,提出了输电线路选线选位的原则,以及塔基设计建议方案,并针对可能存在的工程问题给出施工建议。其研究成果将为输电线路的施工建设提供科学依据。

填充介质的厚屏频率选择表面传输特性

为了改善厚屏频率选择表面(FSS)的滤波特性,实现FSS在雷达天线罩上的应用,设计了具有圆孔单元的厚屏FSS结构,并将其单元内填充介质,制备出了相应的实验件。理论分析时,首先建立等效问题;接着用Floquet定理将无限大厚屏FSS上所有阵列单元的场展开为无穷多个平面电磁波;然后在单元边界处强加边界条件;最后用矩量法求解等效的磁场积分方程。在微波暗室测试后,发现测试值与计算值基本一致。结果表明:中心频率的变化主要取决于单元间距、入射角和介电常数等3个参数;其中,当单元间距由30mm增加到36mm,电磁波的入射角由10°增加到30°,填充介质的介电常数由2.5增加到7.0时,中心频率分别减小了2.1,1.5,1.9GHz;另外,单元直径增大使得带宽增加,当单元直径由14mm增加到17mm,带宽增加了1.2GHz。可以看出,改善厚屏FSS的传输特性是多参数优化的问题,如果合理选择填充介质并适当选取其他参数,能够获得理想的传输特性。

具有转移条件且边界条件含特征参数的奇异微分算子的谱分析(英文)

考虑了有限区间内一类边界条件含特征参数且在一内点处具有转移条件的奇异Sturm-Liouville问题,构造了其基础解系,考察了该问题特征值的性质,给出了其基本解的渐进估计.

一类具有耦合转移条件Sturm-Liouville问题的逆问题

考虑了具有耦合转移条件Sturm-Liouville(简称S-L)问题的逆问题,在一定条件下,通过利用S-L方程右边的函数f_j(x)确定方程的解,并由数据{u_j(x_0)}_j~∞=i或{p(x_0)(du_j(x_0))-(dx)}_j~∞=1唯一确定S-L算子中的系数p(x)和q(x).其中u_j(x)满足S-L方程,分离边界条件和耦合转移条件,而{f_j(x)}_(j-i)~∞构成L^2(I)的一个基.