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双语推荐：Sturm

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本文研究具有混合型边界条件的左定Sturm-Liouvile问题特征值的下标计算问题.首先给出具有分离型边界条件和混合型边界条件的左定Sturm-Liouville问题的特征值之间的不等式;然后利用这个结果给出一种计算混合型边界条件下左定Sturm-Liouville问题特征值下标的方法.
In this paper,we study the indices of left-definite regular self-adjoint Sturm-Liouville problems with coupled boundary conditions.Firstly,we establish a sequence of inequalities among the eigenvalues for Sturm-Liouville problems with separated and coupled boundary conditions.And then,using these results,we construct an algorithm for computing the indices of eigenvalues for the Sturm-Liouville problems.

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为了更精确地研究Sturm?Liouville问题第一特征值，本文主要讨论一类特殊的Sturm?Liouville问题第一特征值关于势函数的依赖性。应用变分原理，估计了此类特殊的Sturm?Liouville问题第一特征值在不同参数值下的界限，并证明出其中的一些界限是可以达到的，为Sturm?Liouville问题第一特征值的逼近提供了更好的理论基础。
In order to study the first eigenvalue of the Sturm-Liouvil e problem more precisely, in this paper, a special Sturm-Liouvil e problem is considered and the dependence of the first eigenvalue on the potential is studied. The boundary of the first eigenvalue with different values of the parameter is estimated and some of them can be get based on the variational principle.It provides a better theoretical basis for the first eigenvalue approximation problem.

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本文讨论边界条件中含有谱参数的Sturm-Liouville算子的逆问题，并且建立了这个算子的惟一性定理．利用Hochstadt—Lieberman的方法及整函数的性质，我们证明对固定的非负整数n，如果测得一组不同参数边界条件下Sturm—Liouville算子的第n个特征值的无穷集合，则组谱集合能够惟一确定区间[0，π]上的势函数q（x）及边界条件中的系数h．
The inverse problem of Sturm-Liouville operators with boundary condition depen-dent on the spectral parameter is considered and a uniqueness theorem for the Sturm-Liouville operator is established in this paper. Applying the Hochstadt-Lieberman’s method and prop-erties of entire functions, we verify that if the infinite set of the n-th eigenvalues for the Sturm-Liouville operator of the different boundary conditions can be measured for a fixed non-negative integer n, then this spectral set is sufficient to determine the potential q(x) on the interval [0,π] and the coefficient h of the boundary condition.

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利用锥上的不动点定理,讨论带 p‐Laplacian算子Sturm‐Liouville型边值问题正解的存在性,推广了已有结果.
@@@@We use compression‐stretching theorem in cones to study a kind of three point Sturm‐Liouville boundary value problem with p‐laplacian ,and obtain the existence of positive solutions .Some previous existence results are generalized .

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利用拟上下解方法和混合单调迭代法，研究了Banach空间中含间断项的非线性Sturm-liouville问题解的存在唯一性，并给出逼近解迭代序列的误差估计．
By using the method of quasi-upper and lower solutions and the mixed monotone iterative technique, the existence and unique solution of nonlinear Sturm-Liouville problems with discontinuous terms in Banach spaces are obtained. The error estimate of the iterative sequences of approximation solutions is given.

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本文利用两个柯西问题的渐近解及一些同阶无穷小的比较，给出权函数w厨1时分离边界条件下右定Sturm-Liouville问题特征值较精细的渐近估计。
In this paper , the right-definite Sturm-Liouville problem with separated boundary conditions whose weight function w?1 is studied .The more precise asymptotic formulas of eigenvalues of this problem are obtained by the asymptotic solutions of two Cauchy problems and the comparison of the same order infinitesimal.

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本文围绕不连续奇异微分算子的自共轭性进行研究，微分算子的自共轭性是线性算子理论中十分重要的问题。文章主要研究了定义在一个新的完备的不定度规空间下的带有转移条件的Sturm －Liouville问题，最终证明了算子在不定度规空间下的自共轭性。
In this paper ,we study the self -adjointness of discontinuous differential operators . Self -adjointness is important for linear differential operator problems .This paper mainly studies a sort of Sturm -Liouville operators with transferring conditions which are defined in a complete Krein space .The operators are proved to be of self -adjointness when the problem is conditioned in a Krein space .

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将处理Sturm-Liouville算子的一些方法用于处理一类特殊边值条件Jacobi算子,并通过对一类特殊边值条件Jacobi算子特征值的性质进行探讨,经过证明,得出了一类特殊边值条件Jacobi算子的特征值对其系数具有连续依赖性的结论.
This paper looks into some properties of eigenvalues to Jacobi operators with a special class of boundary condi-tions.A few methods for treating the Sturm-Liouville operators are adopted for processing the Jacobi operators with a special class of boundary value conditions.And through the investigation of the properties of eigenvalues to Jacobi operators with a special class of boundary value conditions and through strict mathematical proof,the conclusion is reached that the Eigenvalues to the Jacobi operators with a special class of boundary value conditions are found to have continuous dependence on their coeffi-cients.

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研究了定义在[0，1]区间且在点t0∈（0，1）具有界面条件的Sturm-Liouville算子的特征值与定义在子区间[0，t0]与[t0，1]上的两个Sturum-Liouville算子的特征值分布及其逆特征值问题。利用 Weyl-Titchmarsh-m-函数的单调性态，证明了这三组谱之间具有交错性关系，并证明了若子区间上的两组谱不相交，则可由这三组谱唯一确定势函数q（x）与边值条件中的参数h和H 。
The eigenvalue and the inverse eigenvalue problems of the Sturm-Liouville operators defined respectively on[0,1][0,t0 ]and [t0 ,1]are considered.By using the monotonicity of the Weyl-Titchmarsh-m-function,it is shown that the three spectra are alternate,and the potential q (x)and the parameters h,H in the boundary conditions can be uniquely determined by the three spectra if the spectra of the operators defined on subintervals are disjoint.

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研制规则散光眼镜片矫正规则散光的光学演示模型。方法:用几何光学成像演示器直观演示规则散光成像、规则散光透镜成像、规则散光透镜矫正规则散光。结果:直接观察到规则散光和散光透镜的成像状态-散光Sturm光锥及散光透镜矫正规则散光的光学效果。结论:规则散光眼镜片矫正规则散光的光学演示模型能观察到规则散光透镜矫正规则散光的光学效果,便于准确理解规则散光成像、规则散光透镜的成像、规则散光矫正的光学原理。
Objetive:to research and develop an optical model player of regular astigmatism lens which can be used in the correction of regular astigmatism Methods:use geometrical optics imaging demonstrator to display regu-lar astigmatism imaging, regular astigmatism lens imaging, and the correction process of regular astigmatism Re-sults:the regular astigmatism and astigmatism lens imaging were well observed, and the Sturm light cone and optical results of regular astigmatism correction also could be detected Conclusion: the optical model player of regular astigmatism lens can display the optical images of astigmatism, and it is helpful to intuitively understand the optical imaging principle.

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