查询词典 adjoint

Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved.

针对M.E.Gurtin提出的含卷积运算的抛物型偏微分方程及其对应的泛函，运用泛函势算子理论，从理论上证明了含卷积运算的抛物型偏微分方程及其边界条件所对应的矩阵算子有势，进而给出并证明了具有普适意义的含卷积运算的变分定理及预备定理。

We have obtained the following main significant results:(1) A master constraint operator for LQG is constructed, which is shown to be self-adjoint in the diffeomorphism invariant Hilbert space. Thus it lays a foundation for the master contraint programme in LQG;(2) The Immirzi parameter ambiguity in LQG is fixed by introducing supersymmetry, which leads to the conclusion that in the case where matter fields are coupled LQG might prefer supersymmetry in low energy;(3) The current accelerating expansion of our universe is successfully explained in the context of 5-dimensional Brans-Dicke theory, which gives a natural strategy to solve the dark energy problem.

重要成果包括：(1)构造出圈量子引力的Master约束算符，并证明了其自伴性，从而为应用Master约束方法解决量子动力学的难题奠定了基础；(2)通过引入超对称合理地固定了Immirzi参数，得出了在与物质场耦合的低能情况下圈量子引力可能偏爱超对称的结论；(3)用五维Brans-Dicke理论成功地解释了当今宇宙的加速膨胀，从而给出了一个自然解决暗能量问题的方案。

In this paper, we also obtain a sufficient condition for the discreteness of spectrum of 2n-th order J-self-adjoint differential operators.

最后，本文还给出了2n阶J-自伴微分算子的谱是离散的一个充分条件。

The stability region estimation of the singularly perturbed systems can be replaced by that of the adjoint systems, and an optimization method based on linear matrix inequality was provided to reduce the conservativeness in the estimation.

将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题，利用线性矩阵不等式(Linear matrix inequality， LMI)优化方法估计伴随系统的稳定域以减少保守性。

Jacobian, Hessian Matrix Properties, Sensitivity Analysis w.r.t Design Variables, Fixed Parameters and Constraints, Normalization, Finite Difference Approximation, Automatic Differentiation, ANOVA, Adjoint Methods, Examples

Jacobian， Hessian矩阵属性，灵敏度分析w.r.t设计变量，固定参数和约束，归一化，有限差分逼近算法，自动差分算法，ANOVA，伴随矩阵法，举例

About Dirac eigenvalue problem with general two points' liner algebra, corresponding operator of which often is non-self-adjoint operator.

对于一般两点线性边界条件下的Dirac特征值问题，相应的算子一般说是非自伴的。

The vertical diffusivity coefficient of the South China Sea is studied by the adjoint data assimilation method in this thesis. The satellite data SST and the harmonic constant of M2, S2, Kb 0, extracted from TOPEX/POSEIDON satellite altimeter are used in data assimilation. So the average of the vertical diffusivity coefficients of the South China Sea in the thermocline in January, April, July, October, 1997 are2.2 10-4/m2s-1, 7.8 10-5m2s-1 , 1.0 10-4m2s-1 , 1.0 10-4m2s-1 respectively.

本文是用伴随同化的方法研究南中国海垂直混合系数，将卫星观测SST数据和从TOPEX/POSEIDON卫星高度计提取的M_2，S_2，K_1，O_1分潮调和常数作为同化资料，得出1997年1、4、7、10月份的南中国海在温跃层处的垂直混合系数，它们的平均值分别是2.2×10~(-4)m~2s~(-1)， 7.8×10~(-5)m~2s~(-1)，1.0×10~(-4)m~2s~(-1)，1.0×10~(-4)m~2s~(-1)。

Further, according to the positity of the Hessian matrix, which is got from the second order adjoint model, the uniqueness of the assimilation result is manifest. And the relationship between the rate of convergence and the frequency of the observation utilization in the assimilation is investigated.

进一步，借助二阶伴随模式所得到的Hessian矩阵，说明同化解是唯一的，并分析了优化算法的收敛速度与同化过程中观测资料使用频率的关系。

Special considerations are given to spatial discretization of hyperbolic equation with non self-adjoint operator nature.

同时构造了一个用于求解此耦合过程的统一混合弱形式，并且针对其中具有非自伴随算子特性的双曲线控制方程的空间离散进行了特殊考虑。

In this paper, by computing the Laplace of the square of the length of the second fundamental form and introducing a self-adjoint operator and using Stokes Theorem and Hopf Theorem, we obtained some pinching theorems and rigidity theorems for hypersurfaces and submanifolds in hyperbolic space.

本论文通过计算双曲空间中子流形的第二基本形式模长平方的拉普拉斯和引进一个新的自共轭二阶算子，利用Stokes定理和Hopf定理得到了子流形的一些拼挤定理和刚性定理。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。