明了地

Second, we think about the Conjecture(Conjecture8.7,Conjecture8.23;[2]Conjec-ture2.3) and prove that some particular ideals have the same graded Betti numbers via shifting operations,that s,.if is a simpcial complex and I is a monomial ideal generated in one degree,we have that...

后一部分的主要结论是：针对J.Herzog提出的猜想([1]猜想8.7，猜想8.23；[2]猜想2.3)，证明了当I_Δ为同一次数生成元生成的稳定理想时，对i，j，有β_=β_。当I_Δ为无平方分量线性理想，特别地当I_Δ是弱稳定理想时，对i，j，有β_=β_=β_。

The Black Prince vividly describes this kind of process.

小说《黑王子》的解读形象化地说明了这一过程。

Period. You can't even negotiate for a free set of floor mats.

简单明了。你甚至都不能通过讲价搞到一张免费的车厢地毡。

Some special features ofthe static mixer tube are demonstrated.4 An evaluation method of velocity-based disturbance effect of fluid field wasproposed. Qualitative results are obtained by using this method in fluid fielddesign and structure optimization of disturbing elements.5 Experimental models are made efficiently and accurately by RPM method.

主要内容包括： 1、总结了化工过程强化技术的现状和强化研究的途径，提出了紧凑式工业炉的概念，确定用静态混合式炉管进行局部强化。2、提出了静态混合式炉管应用的虚拟工程放大研究方法，指出研究中提高效率的关键是计算模型快速生成技术和实验模型的快速原型制造。3、对工业炉的关键部位——炉管，从材料成分、强度、制造等方面对静态混合式炉管的设计、制造进行了分析，与常规炉管对比，说明了静态混合式炉管的独特性和要求。4、应用快速原型方法，迅速、准确地得到了符合精度、强度要求的静态混合式炉管模型，产品的精度和强度完全符合要求，提高了模型制造效率。5、应用计算流体动力学方法，进行静态混合式炉管的工程放大研究。

The state-of-the-art of chemical process and equipment intensificationtechniques is reviewed. A novel concept of compact industrial furnace isproposed, in which tube with static mixer for partly intensification is determined. 2 A virtual engineering scale-up approach is put forward. The key points toimprove the scaling-up efficiency include two tools: one is rapid generationtechniques for computational models in which a re-use library is built, the otheris rapid prototyping manufacturing, employed for rapid generation forexperimental models.3 The tube is the key component for industrial furnace. Material microstructure,high temperature strength, and casting process of the tube with static mixer arediscussed as compared with those of traditional tube. Some special features ofthe static mixer tube are demonstrated.4 An evaluation method of velocity-based disturbance effect of fluid field wasproposed.

主要内容包括： 1、总结了化工过程强化技术的现状和强化研究的途径，提出了紧凑式工业炉的概念，确定用静态混合式炉管进行局部强化。2、提出了静态混合式炉管应用的虚拟工程放大研究方法，指出研究中提高效率的关键是计算模型快速生成技术和实验模型的快速原型制造。3、对工业炉的关键部位——炉管，从材料成分、强度、制造等方面对静态混合式炉管的设计、制造进行了分析，与常规炉管对比，说明了静态混合式炉管的独特性和要求。4、应用快速原型方法，迅速、准确地得到了符合精度、强度要求的静态混合式炉管模型，产品的精度和强度完全符合要求，提高了模型制造效率。5、应用计算流体动力学方法，进行静态混合式炉管的工程放大研究。

Isometries and equivalences of quantum codes also are researched.

深入研究了量子码的等价性问题，给出了若干基本结论，特别地，证明了MacWilliams的一个著名定理在量子情形不成立。

Infancy, and yet got no house built of cards to live in, grew thinner than

跳蚤和蚱蜢这两位毫不含糊地说明了它们是怎样的人物。

Ignoring the chair offered him, Chu Teh stood squarely before this youth more than ten years his junior and in a level voice told him who he was...

朱徳顾不得拉过来的椅子，端正地站在这个比他年轻十岁的青年面前，用平稳的语调说明了自己的身份。。。。。

The map went on public display for the first time this week in the Archaeological National Museum of Taranto.

这块陶片地图上一共标明了13座城镇，其中奥特朗托、乌真托、莱乌卡等地至今仍在。

Polynesian oral history talks of clan violence on Rapa Nui, in part shown by the toppling of Moai, likely considered a supreme desecration.

波利尼西亚人口头讲述的历史提到了拉帕努伊岛上部落之间的暴力冲突，推倒莫埃的举动（可能被视为对神灵的极大亵渎）部分地说明了这一点。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。