查询词典 solution curve

The first class of curve contains the quartic Wang-Ball and Said-Ball curve and many curves locating between them. The second class of curve contains the quartic Said-Ball and Bézier curve and many curves locating between them. By analyzing the relation between the new curves and the quartic B6zier curve, the geometric meaning of the shape parameters is obtained, and the geometrical drawing method of the new curves is given.

第一种曲线包含了四次Wang-Ball和Said-Ball曲线以及介于它们之间的无数曲线；第二种曲线包含了四次Said-Ball和Bézier曲线以及介于它们之闻的无数曲线；通过分析新曲线与四次Bézier曲线之问的关系，得出了形状参数的几何意义，并给出了它们的几何作图法。

Rational planar curve; rational space curve; rational ruled surface; moving curve/surface;μ-bases; singularity; self-intersection curve; moving curve/moving surface ideal; ideal-theoretic/set-theoretic generators

基础科学，数学，几何、拓扑平面有理曲线；空间有理曲线；有理直纹面；动曲线/曲面；μ基；奇点；自交线；动曲线/动曲面理想；集论/理想论生成元

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

The polarization curve is not sufficient for a reliable and unique validation of a PEMFC model since different parameters can lead to an identical polarization curve. A three-step validation approach is proposed for a complete and unique validation. These three steps are:(1) validated by the global polarization curve,(2) validated by the local current density distribution curve, and (3) validated by the cathode over-potential and anode over-potential versus current density curve. The results from the comparison of four flow-fields show that the PEMFC performance of the flow-fields decreases in order by interdigitated, metal foam, pin-type and parallel.

通过PEMFC参数敏感性研究发现，PEMFC性能受多种参数的影响，这些参数可分为非敏感性参数、敏感性参数和高敏感性参数；与阳极侧参数相比，PEMFC性能对阴极侧的参数更敏感；不同参数值的组合可以得到几乎完全相同的极化曲线，因此电池的极化曲线不足以用于验证数学模型的唯一性与可靠性；为验证PEMFC数学模型的唯一性与可靠性，提出了模型验证的三步法：极化曲线验证、局部电流密度验证和阳极总过电位与阴极总过电位验证。

The rheological character of a polymer often appears as shear-thinning. Most polymers behaviour in a solution can be explained by the polymer chain or hard sphere theory. Other than that, shear-thickening polymer solution also exists. Its behavior can be explained by dilatant theory, which suggests that the shear-thickening of the solution is due to the swelling of the polymer particles. This phenomenon often occurs in suspension or emulsion. Solution exhibits a mixed behavior can also be found whose behavior is such that shear-thinning occurs under low shear force and shear-thickening occurs under high shear force. Under this circumstance, the viscosity versus shear force graph exhibits a spoon shaped curve. The rheological study can be applied to the dispersion of paint which can predict the dispersion effect of various polymer materials in solution.

中文摘要一般高分子聚合物溶液的流变行为多半呈现剪稀(shear-thinning)的现象，而大部分的高分子在溶液中的行为是以分子链或是硬球观点来解释，另外也有剪稠(shear-thickening)现象的高分子溶液，其流变行为则是以膨胀体观点来解释，即在高剪切力下，由於高分子团体积变大而使溶液黏度升高，这在悬伏液、乳液等常见；但也有在低剪切力下，溶液具有剪稀的行为，而在高剪切力下却成现剪稠的行为，在黏度对剪切力作图时，会呈现出一个勾形曲线的图形；流变行为的探讨可应用在涂布材料的分散技术上，以推测不同的高分子溶液对分散效果的影响。

The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.

对矩阵A是非对称情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，并给出了其解的表达式，描述了求解问题的算法；讨论了带对称和双对称约束的总体最小二乘问题，利用Ricaati矩阵方程的理论得到了解存在的一个充分条件，分别对对称矩阵和双对称矩阵两种情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，给出了其解的表达式，提出了求解这些问题的算法，并给出了数值例子。

Material and MethodsRA Rabbit Model group: 15 early RA rabbits of the same weight and variety Control group:10 normal rabbits of the same weight and varietyMethods of making RA rabbit model:elect 15 normal rabbits of the same weight and variety, dissolve Ovalbumin in 0.9% sodium chloride solution, to make the solution of 20mg/ml concengtration, blend the same quantity of complete Freund′s Adjuvant equably ,inject the mixed solution into endermic tissue of the rabbit′s scapular section, making the rabbits allergic, inject 1 ml of the mixed solution to one rabbit every time, inject 1 ml of the mixed solution in 5 different places of the rabbit′s scapular section, inject the rabbit one time every week,inject 3 weeks continuously,it turned out to be that the rabbits will be allergic, inject Ovalbumin blent with the 0.9% sodium chloride solution into the knee joint cavity of the rabbits in the fourth week, 5 mg Ovalbumin every knee joint cavity,two knees of every rabbit of the 15 rabbits are both injected,the arthrosis diameter and the exterior temperature of the knees will be added obviously in 24 hours,and they will drop gradually,at the time of the 14th or 21th day, the arthrosis diameter and the exterior temperature of the knees will get to the balance time,the incidence rate of RA is 100%.after the RA model succeeds,it is the early time of RA from the first week to the fourth week,after the fourth week,it is the late time of RA, the cartilage of the femoral condyle and the subchondral bone cortices will be changed unrecoverily.

资料与方法RA模型组：早期RA家兔模型15只，品种及体重接近。对照组：正常家兔10只，品种及体重接近。RA家兔模型制作方法：选取15只成年家兔，体重、品种接近，将卵蛋白溶解于生理盐水，配成浓度为20mg/ml的溶液，与等量完全弗氏佐剂混匀，注入家兔肩胛区皮下致敏，每只家兔每次注射1ml，于肩胛区5个不同区域注射，每周一次，连续注射3周而致敏，第4周向膝关节腔注射卵蛋白生理盐水溶液，每只关节腔注射5mg卵蛋白，15只家兔膝关节全部注射，24h内此关节直径和表面温度大幅度上升，以后缓慢下降，至14～21d达到平台期，发病率达100%。造模成功后第1～4周为早期改变，第4周以后出现不可逆的关节软骨及骨破坏。采用高频超声对RA模型组与对照组的膝关节髌上囊液体厚度、滑膜及股骨髁软骨厚度及软骨下骨皮质的回声情况进行对比观察。结果RA组模型组膝关节髌上囊积液及滑膜的厚度明显厚于对照组，其股骨髁软骨的厚度与对照组相比无明显差异，其软骨下骨皮质与对照组相比无明显改变。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

The polymeric sol is obtained by process of preparing a calcium salt solution, containing calcium ethoxide dissolved in organic acid, and a phosphate solution, containing triethyl phosphite or triethyl phosphate dissolved in the organic acid, mixing the calcium salt solution with the phosphate solution to produce a mixed solution, and aging the mixed solution.

本发明的磷酸钙化合物的聚合物溶胶是通过如下步骤制备的：制备含有溶解在有机酸中的乙醇钙的钙盐溶液和含有溶解在该有机酸中的亚磷酸三乙酯或磷酸三乙酯的磷酸盐溶液；及将该钙盐溶液和该磷酸盐溶液混和制得混合溶液，并老化该混合溶液。

The quality of both red and white wine depends very much on the wine maker talent and on the quality of the grapes.

他的红酒和白酒的品质，根据酿造者的能力和葡萄的质量，各有差异。

No, I don't want to get drunk before my next match.

" "不，我不想让我的下一场比赛前喝醉了。