查询词典 adjoint hilbert problem

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。

I am sure after a few weeks of adaptation and familiarization I will have no difficulty in functioning on a daily basis in an English speaking society or in participating fully in graduate studies.

在大学的三年的学习生活不仅给予我自身的充实，更重要的是磨练和培养了我较强的自觉能力和严谨，踏实的作风以及不怕困难的精神，对未来充满了信心！

As the first volcanoes erupted, one of the gases that bellowed out was steam.

在第一批火山喷发时，喷出的气体之一就是水蒸汽。