查询词典 modified Newton method

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

In the dissertation, a new stabilization method, equal-density method was adopted to prepare modified asphalts with storage stability at high temperature. In this method, a compound was prepared by premixing polymer and filler, and the compound was mixed with asphalt to prepare Polymer-Modified Asphalt by changing the ratio of polymer and filler. The asphalts with good storage stability were formed with the addition of filler, by regulating the density difference between polymer and asphalt. With identifying the effect of composition factor and the technique conditions on mechanical properties of polymer/filler compound and the molecular distribution of the polymer, identifying the effect of composition factor and the technique conditions on the properties and structure of polymer/filler modified asphalt, Styrene-Butadiene-Styrene copolymer, Low Density PolyEthylene, Styrene-Ethylene-Butadiene-Styrene block copolymer modified asphalts with good storage stability and performance were prepared. Rheological method, gel content analysis and swelling measurement were adopted to elucidate the interaction between the polymer and filler. Filler reduced the difference between the polymer and asphalt with the premixing technique, which led to the improvement of the storage stability of the modified asphalts. The thermo-oxidative aging process of base asphalt and PMA were studied and the effect of antioxidant additives on the base asphalt and PMA were analyzed.

本论文采用等密度方法，即预先混合聚合物与填料制备复合物，复合物在沥青中会吸收油份而溶胀，改变填料的用量从而调节聚合物与沥青的密度差异的方法，制备出高温贮存稳定的改性沥青，并研究了工艺条件和配方因素对聚合物/填料复合物力学和聚合物分子量分布的影响，系统考察了工艺条件和配方因素对聚合物/填料改性沥青性能与形态结构的影响，研制出性能优良、高温贮存稳定的苯乙烯-丁二烯-苯乙烯三嵌段共聚物、氢化SBS、低密度聚乙烯改性沥青，并通过流变学分析方法及凝胶和溶胀测试探讨了聚合物与填料的相互作用，指出经过预混工艺填料改变了聚合物与沥青的密度差异，以此说明聚合物/填料改性沥青高温贮存稳定的原因；研究了基质沥青和聚合物改性沥青热氧老化过程，并分析了抗氧剂对基质沥青及聚合物改性沥青的影响，探讨了抗氧剂提高沥青耐老化性能的原因。

Three types of base asphalt and six SBS were used to produce SBS modified asphalt. The interaction of SBS modified asphalt was discussed in different states between the base asphalt and SBS based on their compositions. Through the traditional tests, such as penetration, soften point and ductility, and US SHRP tests, the results indicated that influences to affect the temperature susceptibility, high and low temperature performance, aging characteristics are base asphalt, SBS types and their dosages. The functions of penetration to viscosity and complex shear modulus G~* to complex dynamic shear viscosity η~* were set up, and then theviscosity-temperature susceptibility of wide temperature span and the calculation method of low temperature viscosity were obtained."Process" evaluation criterions, high grading critical temperature T_ and low grading criticaltemperature T_ , were suggested according to the high and low temperatureperformances of SBS modified asphalt. Using the experience of Repeated Creep and Recovery Test for Binders, a new high-temperature evaluation index,modification rutting factor G~*~(-9) was obtained. The results after RTFO and PAV aging indicated that traditional tests didnt differentiate base asphalt and SBS modified asphalt, but dynamic mechanics temperature spectrum and G*-5 black chart clearly reflected the influence of aging to the SBS modified asphalt. With the IR and GPC tests, the reason of aging to the SBS modified asphalt were due to asphalt phase oxygenated and SBS phase depredated.

论文选择3种油源的基质沥青和6种SBS改性剂制备改性沥青，通过分析基质沥青和SBS改性剂的组成结构特点，得出了不同状态下SBS改性沥青的SBS与基质沥青的相互作用机理；通过针入度、软化点、延度等常规试验以及美国SHRP试验，分析了基质沥青、SBS改性剂类型与剂量对SBS改性沥青的温度敏感性、高低温特性及老化特性的影响；建立了针入度-粘度、复数模量G~*-复数粘度η~*的换算关系，得出了宽温度域的粘温指数VTS和较低温度下粘度的计算方法；通过高低温性能分析提出了&过程&评价参数高温等级温度T_和低温等级温度T_；借鉴重复恢复与蠕变试验研究成果，得到了SBS改性沥青高温评价指标改进型抗车辙因子G~*~(-9)；RTFO和PAV老化后的性能试验结果表明，常规试验难以区分SBS改性沥青与基质沥青的差异，而动态力学温度谱、G~*-δ黑斑图可以反映老化作用对SBS改性沥青的影响，且通过IR试验和GPC试验得出SBS改性沥青老化是沥青相的氧化和SBS的降解共同引起的；通过不同温度下SBS改性沥青混合料的旋转压实SGC试验，根据粘度与剪变率的关系，提出用剪变率60(1／s)测试SBS改性沥青的粘温曲线，并按照0.17±0.02Pa.s和0.28±0.03Pa.s确定施工温度。

It also makes analysis on the connection of Newton's prism experiments, and describes how Newton proved these propositions by taking advantage of these experiments in the article. As well the author makes analysis and generalization on the make of Newton's reflecting telescope and Newton's

首先，在对《光学》认真研读的基础上，首次对其光的颜色理论部分的大量棱镜实验之间的关系进行了分析，从而说明牛顿是如何利用这些实验证明这些命题的；其次，笔者在前人研究的基础上，对反射望远镜的制造和牛顿环理论进行分析和总结，力求描述得清楚全面；最后，鉴于国内外对牛顿光本性认识的研究存在分歧的情况，笔者对惠更斯和牛顿的相关著作进行了详细考察，对他们的光本性观点进行了系统的研究和比较，从而指出那种只因牛顿

But it is a hard task to solve this equation, one reason is that the TV-norm is nondifferentiable when |▽_u|= 0, so we cant apply a linearizationtechnique such as the Newton method. The other reason is that the Euler-Lagrange equation has a highly nonlinear term. The Newton method for such equation is known to have a very small domain of convergence, and it is very difficult to make sure that the initial value such as the observed image belongs to this domain. So the Newton method is not an ideal method for solving this equation.

但是求解它比较困难，主要是因为TV-范数在|▽u|=0处不可微，不能用诸如牛顿法之类的方法将其线性化；且Euler-Lagrange方程含有一个高度非线性的项，牛顿法只有局部收敛性，对于高度非线性问题它的收敛域很小，因此难以保证所取的初始点在它的收敛域内，故一般不用牛顿法直接求解。

Effects of dry temperature and dry time on properties of heat cured sand and the relationship with binder composition are as follows:sands bonded by binders that are not modified have high strength when dry temperature is high and dry time is long,but their anti-wettability power is poor . Sands bonded by binders that are modified by B but not modified by M can be dried quickly and sand strength is high but anti-wettability power is also poor. Sands bonded by binders that are modified by M but not modified by B can also be dried quickly to obtain maximum strength,then the strength becomes lower when they are dried continually for more time. and sand strength is high but anti-wettability power is also poor. Sands bonded by binders that are modified by M as well as by B at the same time can be dried quickly to obtain maximum strength at low temperature and short time. But the anti-wettability of sand mold is best when they are dried at high temperature and long time.

烘干温度和烘干时间对热硬砂性能的影响及其与粘结剂改性的关系是：未经改性剂B和改性剂M改性的粘结剂砂，脱水速度较慢，烘干温度越高，时间越长，则硬化强度也越高，但未经改性的粘结剂热硬砂的抗吸湿性较差；经改性剂B而不经改性剂M改性的粘结剂热硬砂，烘干硬化速度较快，强度也高，但在高湿度下的抗吸湿性不好；经改性剂M改性而不经改性剂B改性的粘结剂热硬砂，烘干时强度先随烘干时间升高至最大值后，继续烘干时强度又出现下降；经改性剂B和经改性剂M共同改性的粘结剂热硬砂能在短时间和较低的烘干温度下就可烘干到最高强度，即烘干脱水的速度较快，但试样的抗吸湿性差，若在更高温度和更长时间下烘干，试样的抗吸湿性得到改善，综合考虑烘干强度和抗吸湿性要求，对于φ30×30mm试样，理想的烘干温度是200℃，烘干时间20分钟。

Main -cassava starch Hanmei special starch powder candy fillings wrapped with modified starch powder used cationic modified starch paper surface sizing starch paper coating starch dedicated Wet add starch layers dedicated spray starch dedicated plasterboard dedicated starch re-wet adhesive tape with exclusive -starch tapioca starch Hanmei dedicated powder candy fillings wrapped with modified starch powder used cationic modified starch paper surface sizing starch paper coating starch dedicated dedicated add in Wet starch layer dedicated inter-spray starch starch gypsum board dedicated re-wet adhesive tape with exclusive -starch tapioca starch Hanmei dedicated powder candy fillings wrapped with Modified Starch Modified Starch powder with cationic surface sizing starch paper coating special paper made of starch wet end of paper to add a dedicated starch

公司朝着管理严谨，经营有序的现代化企业的方向前进。

By using accelerating Aitken method in iterative method of nonlinear equations, a new modified method is given. The method is applied to modified Newton method, thereby a new method is developed, which is faster and stable. Also, its algorithm is given. Numerical results show that the new method is very efficient.

通过对非线性方程组的迭代法引入Aitken加速技术，设计了一种非线性方程组的迭代解法的加速方法；将该方法与M步Newton法相结合，得到一种收敛速度快而且计算稳定的方法，并给出了具体算法；数值结果表明了新算法是有效的。

At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.

本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。

Bob Eckert has been chairman and chief executive of Mattel for eight years.

美泰董事长兼首席执行官鲍勃·埃克尔特在任已8年。

The outlook for honors and disgraces carries on and surpasses the traditional outlook for honors and disgraces theoretically, and carries on and develops the theory of construction of socialist mora...

社会主义荣辱观的提出在理论上是对传统荣辱观的一次继承和超越，是对社会主义道德建设理论的继承和发展，在实践上有利于形成良好的社会风尚。