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Spectrum of a class of fourth order left-definite differential operators

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 51-56页

作者： GAO Yun-lan sun jiong Dept. of Math. Inner Mongolia Univ. of Tech. Hohhot 010051 China. Dept. of Math. Inner Mongolia Univ. Hohhot 010021 China.

The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…

关键词： left-definite differential operator right-definite differential operator Krein space spectrum,eigenvalue.

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

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 1001-1012页

作者： GUI-XIA WANG jiong sun College of Mathematics science Inner Mongolia Normal University Mathematics Department Inner Mongolia University

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.

关键词： self-adjoint Sturm-Liouville problems indices of eigenvalues coupled boundary conditions Priiferangle Interlacing Eigenvalue Intervals numerical computations.

Green Function of Fourth-order Differential Operator with Eigenparameter-dependent Boundary and Transmission Conditions

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 311-326页

作者： Xin-yan ZHANG jiong sun School of Statistics and Mathematics Inner Mongolia University of Finance and Economics School of Mathematical Sciences Inner Mongolia University

We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.

关键词： fourth-order differential operator eigenparameter-dependent boundary conditions transmission conditions eigenvalues Green function

New Approach to Differential Equations with Countable Impulses

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 255-262页

作者： Hong-Kun Zhang Jin-Guo Lian jiong sun Department of Mathematics and Statistics University of Massachusetts Amherst MA 01003 USA Department of Mathematics Inner Mongolia University Hohhot Inner Mongolia 010021 China

This paper provides a new approach to study the solutions of a class of generalized Jazobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n ＋ 1. A new class of generalized differential operators is defined. We investigate the kernel of the corresponding maximal operators by applying operator theory. It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic, in which there are n dimension solutions with exponential-decaying amplitude.

关键词： countable impulses differential operator hyperbolic Jacobi fields hyperbolicity differential operators

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Journal of Hainan Medical University 2020年第17期26卷 70-72页

作者： Ding-jiong sun Hainan Provincial Hospital of traditional Chinese Medicine HaikouHainan ProvinceChina570000

In recent years,the treatment of myofascial pain trigger point is a relatively popular technology,many people regard it as"Ashi point"in meridian theory,but compared with the traditional meridian theory,the description of myofascial pain trigger point is more intuitive and easier to *** paper expounds the similarities and differences between myofascial pain trigger point and traditional meridian theory from the aspects of theory,basic research and clinical application,in order to provide a specific idea for the scientific interpretation of meridian phenomenon in traditional Chinese medicine.

关键词： Trigger point of myofascial Meridians Points Acupuncture

A DIRECT SUM DECOMPOSITION OF A CLASS OF THE INFINITELY DIFFERENTIABLE FUNCTIONS ON R^2 WITH COMPACT SUPPORT

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Annals of Differential Equations 2013年第1期29卷 68-74页

作者： Mudan Chihara Hiroyuki jiong sun Graduate School of Science and Engineering Kagoshima University Kagoshima 890-0065 Japan Dept. of Math. and Computer Science Kagoshima University Kagoshima 890-0065 Japan Inner Mongolia University

In this paper, we consider a class of the infinitely differentiable functions with compact support on R2 , and give a kind of its direct sum decomposition.

关键词： direct sum decomposition compact support

从牧童到艺术大家——中国现代雕塑家、教育家廖新学

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美术 2020年第10期634卷 52-58,F0002页

作者：孙炯中国民族哲学思想史学会云南省文化和旅游厅

他是云南边疆的一个牧童,却走向了世界。在20世纪的中国文化史上,廖新学是一位敢为天下先的云南人。云南放牛娃在20世纪40年代燃情西方艺术中心廖新学(1900—1958),云南富民县人。他出身贫寒,8岁时父母双亡,他带着自己双目失明的幼弟靠... 详细信息

他是云南边疆的一个牧童,却走向了世界。在20世纪的中国文化史上,廖新学是一位敢为天下先的云南人。云南放牛娃在20世纪40年代燃情西方艺术中心廖新学(1900—1958),云南富民县人。他出身贫寒,8岁时父母双亡,他带着自己双目失明的幼弟靠帮别人放牛才活下来。他自小酷爱绘画,更喜欢用泥土捏些小鸡、小牛、小马等小动物。1919年经人介绍辗转来到昆明,在华山南路的"如真像馆"当学徒,随同样从富民走出来的画师李鸣鹤先生修习油画。满师之后,他在昆明开设"新学美林"画馆,一面为人画像,一面传授画技。

关键词：廖新学双目失明中国文化史出身贫寒父母双亡中国现代雕塑云南边疆画技

具有内部奇异点的J-对称算子的J-自共轭延拓

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南京理工大学学报 2007年第6期31卷 673-678页

作者：王爱平孙炯内蒙古大学数学系内蒙古呼和浩特010021 天津科技大学数学系天津300457

该文所考虑的具有内部奇异点的J-对称微分算子,内部有奇异点,并且奇异点左右可以有不相同的亏指数。该文构造了相应的直和空间,并应用直和空间的相关理论及Knowles的最大算子域分解定理,在正则型域非空的情形下,利用微分方程的解给出了... 详细信息

该文所考虑的具有内部奇异点的J-对称微分算子,内部有奇异点,并且奇异点左右可以有不相同的亏指数。该文构造了相应的直和空间,并应用直和空间的相关理论及Knowles的最大算子域分解定理,在正则型域非空的情形下,利用微分方程的解给出了此类J-对称算子的J-自共轭延拓的完全解析描述,并且确定其边界条件的矩阵仅由微分方程的解在正则点的初始值决定。

关键词： J-对称算子 J-自共轭延拓内部奇异点

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一类极限点型的J-对称微分算子

数学学报（中文版） 2000年第3期43卷 481-486页

作者：王忠孙炯内蒙古大学数学系内蒙古呼和浩特010021

本文利用纳依玛克「１」的方法研究了２ｎ阶非对称微分算子（Ｊ－对称微分算子），得到一类极限点限点型的非对称微分算子（Ｊ－对称微分算子）．

关键词： J-对称微分算子亏指数极限点型极限圆型