查询词典 adjoint differential expression

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

We also give all positive self-adjoint extensions ofsingular differential operators,and all positive self-adjoint operators generated by theproducts of differential expressions 〓,where l is an nth order differentialexpression.The result that each positive self-adjoint operator is not necessarily theform of operator product 〓.This answers an open problem proposed by theauthors recently.

我们也给出了奇型微分算子的所有正自伴扩张形式及乘积微分算式〓所诱导的所有正自伴算子形式，证明〓所诱出的正自伴算子不必须是由算子乘积〓为l所生成的算子）的形式，从而回答了作者新近提出的一个公开问题。

How to establish the adjoint medel is discussed by using the Gateaux differential of function and the concepts of the adjoint operators in Hibert space. At the same time it is verified that selecting proper finite difference scheme can ensure discrete form remaining the same adjoint r...

文中利用泛函的Gateaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立，并通过选择适当的差分格式离散伴随模型，使其保持连续时的伴随关系，同时给出了水温初始场最优化过程及相应的同化试验数值结果。

This article starts with a review of the history of the "Expression" conception in the Occident literature tradition,from which to conclude the base connotation of modern "Expression" conception in occident.Relying on this springboard,we analyses the history of the occidental modern plastic arts gradually ,then the naissance and development of the occidental modern plastic arts may boil down to a going-deep course driven by the "Expression" conception:the impressionism which had been pursuing sensual reality brought out a turning point from Representation to expression;Faurism accomplished the consciousness of Expression based on inheriting and criticizing Post-Impressionisme, and resisted the suppressant on Expression by Physical Image; the German Expressionism and Surrealism uplifted Expression at the same time they resisted Physical Image by "Nugatory Physical image"; From the apocalypse of Cubism,Suprematism and De Stijl tended towards Pure Plastic which excluded Physical Image completely,meaning that it had realized absolute Expression in the range of plastic;After WW II,artsists in western detected that Pure Plastic had actually suppressed Expression newly,as a result of Abstract-Expressionism and Mirnirnaliam Art,Expression broke away from Pure Plastic gradually to seek some new possibilities other than plastic.

本文从对西方文艺传统中的"表现"观念的历史考察着手，归纳出西方现代"表现"观念的核心内涵，以此为基点来逐步分析西方现代造型艺术史，进而将西方现代造型艺术的产生与发展归结为在"表现"观念驱动下不断递进的历史进程：印象主义对感觉真实的追求为造型艺术由再现走向表现打开了缺口；野兽派在继承和批判后印象主义的基础上首次实现了表现的自觉，并在艺术中反抗物象对表现的压迫；德国表现主义与超现实主义以不彻底的"否定性物象"来张扬表现反抗物象；至上主义、风格派等则在立体主义的启示下走向完全排斥物象的纯粹造型，在造型的范围内实现彻底的表现；二战后的西方艺术家们察觉到纯粹造型已经掉转头来形成新的对表现的压制；经由抽象表现主义、最低限艺术，表现逐步摆脱了纯粹造型，寻求造型之外的新的表现可能。

This article starts with a review of the history of the "Expression" conception in the Occident literature tradition,from which to conclude the base connotation of modern "Expression" conception in occident.Relying on this springboard,we analyses the history of the occidental modern plastic arts gradually ,then the naissance and development of the occidental modern plastic arts may boil down to a going-deep course driven by the "Expression" conception:the impressionism which had been pursuing sensual reality brought out a turning point from Representation to expression;Faurism accomplished the consciousness of Expression based on inheriting and criticizing Post-Impressionisme, and resisted the suppressant on Expression by Physical Image; the German Expressionism and Surrealism uplifted Expression at the same time they resisted Physical Image by "Nugatory Physical image"; From the apocalypse of Cubism,Suprematism and De Stijl tended towards Pure Plastic which excluded Physical Image completely,meaning that it had realized absolute Expression in the range of plastic;After WW II,artsists in western detected that Pure Plastic had actually suppressed Expression newly,as a result of Abstract-Expressionism and Mirnirnaliam Art,Expression broke away from Pure Plastic gradually to seek some new possibilities other than plastic.

本文从对西方文艺传统中的&表现&观念的历史考察着手，归纳出西方现代&表现&观念的核心内涵，以此为基点来逐步分析西方现代造型艺术史，进而将西方现代造型艺术的产生与发展归结为在&表现&观念驱动下不断递进的历史进程：印象主义对感觉真实的追求为造型艺术由再现走向表现打开了缺口；野兽派在继承和批判后印象主义的基础上首次实现了表现的自觉，并在艺术中反抗物象对表现的压迫；德国表现主义与超现实主义以不彻底的&否定性物象&来张扬表现反抗物象；至上主义、风格派等则在立体主义的启示下走向完全排斥物象的纯粹造型，在造型的范围内实现彻底的表现；二战后的西方艺术家们察觉到纯粹造型已经掉转头来形成新的对表现的压制；经由抽象表现主义、最低限艺术，表现逐步摆脱了纯粹造型，寻求造型之外的新的表现可能。

Furthermore data assimilation experiments are conducted with MM5 Adjoint-model Assimilation System made by adjoint codes. With a case of heavy rainfall taking place from 00h July 23 to 00h July 24,2002, several numerical simulation experiments of different schemes are performed. The results are as follows. MM5 Adjoint-model Assimilation System not only can improve the initial field effectively and promote the coordination with the model but also can enhance the forecast on the precipitation and other elements. The assimilation of CDW has an improvement on quality of upper wind. The effect of direct numerical simulation with utilizing the CDW to amend the initial field gains the advantage over the one not.

结果表明，MM5伴随模式同化系统能有效改善初始场与模式的协调能力，提高模式对于降水场和其它要素场的预报；使用云导风资料修正初始场后直接模拟的效果比未使用时直接模拟的效果要好，对部分区域的强降水预报精度有一定程度的改善；使用伴随模式同化系统后，加入云导风资料的同化试验对其它要素的改善与直接同化常规资料的效果相比，改善优势不明显，但从各要素的误差来看，对于风场的改善最好。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同，当微分算子在端点处的亏指数均取(2， 2)时，通过构造商空间，应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题，并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

We discuss a class of second order self-adjoint matrix differential systems with damping term and self-adjoint Hamiltonian matrix differential systems, etc.

在第五、六章中，考虑一类线性泛函g和一类对s偏导数不一定非正的Hk型函数，分别研究了自伴的带有阻尼项的二阶矩阵微分系统和自共轭的Hamilton矩阵微分系统。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

Core, self psychology is psychoanalytic, but there are crucial differences in how the patient-therapist relationship is viewed.

自体心理学的核心是精神分析，但在如何看待患者-治疗师关系方面，自体心理学和精神分析有着根本性的不同。

High-performance cars brake drum production costs increase less than 10%.

高性能汽车刹车鼓的生产成本增加小于10％。