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The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

The critical point means such a state that all the differences between gas and liquid disappear completely,being a most important parameter of dividing the types of fluid and being widely verified in both theory and practice.Currently,four methods of determining critical point are summarized as follows:①laboratory measurement through examining critical opalescence or recording the bubble point and dew point curves;②empiric relation;③calculation of the bubble point and dew point curves by PVT software;and ④ direct calculation according to thermodynamic theories.

随后对临界点进行确定，临界点是气液一切性质差异均消失的状态，是区分流体类型最重要的参数，并得到了理论和工程应用的广泛验证，目前确定临界点大致有四种方法：①实验测定，通过观察临界乳光现象或记录流体的泡点和露点线；②经验关系式；③通过PVT软件计算流体的泡点和露点线；④利用热力学理论直接计算。

In this paper, using the methods of Fourier transformation and moment-space renormalization group et al, we studied the phase transition of several complex Gauss systems, figured out the critical point and critical exponents of the system, simply discussed the critical problem of the system with long rang interactions and the universality of phase transition.

本文利用傅立叶变换和动量空间重整化群变换等方法，研究了一些复杂Gauss系统的相变和临界性质，求解了系统的临界温度和临界指数，简单地探讨了相变的普适性和系统中存在长程相互作用的问题。

The paper studied that HACCP projects was established,critical control point was controlled,hazard analyzed was evaluated in oxidation starch procedure in production,filtration,bath and dehydration,sirocco desicalion,metal detect were confirmed as critical control points, critical limits ,monitor procedures,corrective actions were established,as was that the safety and quality were improved.

对氧化淀粉生产过程进行危害分析评估、关键控制点控制及相对应的HACCP计划的制定进行探讨，确立了湿法生产氧化淀粉过程中的过滤、水洗脱水、热风干燥和金属探测4个关键控制点，制定了相关的关键限值、监控程序和纠编措施，从而为提高氧化淀粉生产过程中的质量和安全性提供保障。

The primary studying works and characteristics:1 To summarize reinforcing theory of cement mixing pile composite foundation2 To analyze the primary mechanics characters and changing rules of cement mixing pile, based on analysis of test data both indoor and outdoor.3 To discuss siding frictional resistance, ending resistance, ultimate bearing capacity of simple mixing pile and effectiveness factor of grouped piles, loading ratio of soil between piles under cushion cap of grouped piles and stress ratio of pile and soil and so on, and use many computation method and experimentation method to ensure bearing capacity of mixing piles composite foundation.4 To point out and analyze eight sides flaws and problems of the bearing capacity calculation method of mixing pile compositefoundation which ensured by national and normative method/ formula.5 To apply test results of loading tests and a few settlement observation data, use gray theory to predicate ultimate bearing capacity of deep mixing piles, actual example demonstrate engaging between theoretical predicted value and actual value.6 To apply groovy layerwise summation method to discuss entity piles method, double foundation method, equivalent layerwise summation method and consolidation theoretical method and so on, especially by combination of engineering example, use FEM to calculate or discuss the settlement and changing rules of composite foundation.7 To discuss problems of critical length of composite foundation by combination of engineering example and numerical analysis method, and analyze the contrast of critical length between simple pile load and most area load of composite foundation, not only critical length of composite foundation is relative to modulus ratio between piles and soil, but also upside load distribution area of composite foundation.

主要的研究工作与特色为：(1)总结了水泥搅拌桩复合地基的加固原理；(2)在对室内外试验资料进行统计分析的基础上，系统分析了搅拌桩水泥土的主要力学特性及其变化规律；(3)探讨了搅拌单桩的侧摩阻力、端阻力、极限承载力及群桩效率系数、群桩承台下桩间土荷载分担比及桩土应力比等，提出用多种计算方法并结合试验方法来综合确定搅拌桩复合地基的承载力；(4)明确指出和分析了按国家有关规范的方法确定搅拌桩复合地基承载力所存在的八个方面的缺陷与问题；(5)利用过去没有加载至破坏阶段的载荷试验成果和较少的沉降观测数据，尝试了用灰色理论预测深层搅拌桩的极限承载力，实例表明理论预测值与实测值吻合较好；(6)在常规分层总和法的基础上，探讨了复合地基沉降计算的实体墩基法、双层地基法、等效作用分层总和法、固结理论法等，特别是结合工程实例，用有限元数值计算等方法计算和讨论了搅拌桩复合地基的沉降及其变化规律；(7)结合工程实例，用数值分析方法探讨了复合地基临界桩长的问题，指出和分析了单桩荷载下的临界桩长与复合地基大面积荷载下的临界桩长存在很大的差别，复合地基的临界桩长不仅与桩土模量比有关，而且与复合地基上部荷载分布面积有关。

A critical temperature of water is 100 degrees C--its boiling point at standard atmospheric pressure; critical mass; go critical .

水的临界温度是摄氏100度——标准大气压下的沸点；临界物质；达到临界。

Therefore, different critical area extraction algorithms are developed according to different defect types With the concept of critical area, the unitarity of Monte Carlo method and critical area method is discussed in fault-sensitivity analysis.

并利用关键面积的概念，论述了Monte Carlo方法和关键面积方法在芯片故障敏感度分析中的统一性。

The pressure drop along the horizontal wellhole was combined with the critical pressure drop of the bottom water-driven reservoirs, thus the relation between the critical pressure and the critical flow rate when the horizontal well originally put into production was researched,which provide a reference for the design.of the deliverability of the horizontal well used in the bottom water reservoir existing the bottom water coning.

把水平段压降和底水油藏临界压力结合起来，研究了考虑水平段压降时的水平井初期生产的临界压力和临界产量的关系，为存在底水锥进油藏水平井产能设计提供了参考依据。

Critical C/Fe ratio as a new concept has been put forward in this paper, when the amount of carbon adding into pellet large than critical C/Fe ratio, it will results that the S% of DRI goes beyond the criterion so that EAF refuse to use it, when less than critical C/Fe ratio, it will accelerate reduction and desulphur.

文章根据热态DRI的再氧化机理，提出了一种利用半熔融密封料覆盖反应罐口的防再氧化理论，在还原温度时半熔融密封料熔化成液相，将罐口密封，反应罐冷却时，这层半熔融密封料凝固并和罐壁紧密结合，阻止氧化性气体的侵入，达到防氧化的目的。

Graf, without question, is the greatest women's player in history.

格拉芙，现在，毫无疑问是女子网坛历史上最伟大的选手。

If not, you will have to look around at all your important data.

如果没有，您将需要检查所有的重要数据。