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Some methods mentioned in the elementary number theory and analytic number theory are used to consider the problems which are related with the Smarandache functions, then a conjecture and an asymptotic formula are given, a special equation is solved and Smarandache-Riemann sequences are generated.

本论文基于对Smarandache问题的学习与研究，运用了初等数论与解析数论中的一些研究方法，对与Smarandache函数相关的问题进行了简单的思考，给出了一个猜想，一个渐近公式，解决了一个特殊的方程，推广了Smarandache-Riemann序列。

Based on the excitation mechanics of evanescent-wave pumped WGM fiber laser and the analytic asymptotic formula to determine the resonant positions of a WGM,the observed experimental results are well explained.

根据消逝波激励的WGM光纤激光的激励机制，结合圆柱型微腔中确定WGM共振位置的解析渐近公式，合理地解释了观察到的实验结果。

A large uumber of numerical calculations using the analytic formula and the dispersion equation have been candied out on the relations of the attenuation and phase constant with wave frequency, thickness and conductivity of the lossy layer.

此式适用于截止频率附近，通过解析表达式和波导模式色散方程，对衰减常数和相位常数进行了大量数值计算，得到了它们随损耗层厚度、频率以及损耗层电导率的变化规律，两种方法所获得的结果有较好的一致性，研究表明，损耗强度和损耗层厚度的变化会改变波导中电磁模式的色散和简并特性，对于改善高功率回旋行波放大器中注波互作用带宽和模式竞争非常有益。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauder's fixed point theorem.

此外，本章还使用Schauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauders fixed point theorem.

此外，、本章还使用Sehauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

We developed an analytic resolution of 2-D azimuthal prediction and a least square method for 3-D azimuthal prediction.

提出了基于二维多方位预测的精确解法和基于三维多方位预测的最小二乘法。

Founds three-dimensional analytic model and analyses heat transfer with phase change with the help of numerical simulation software using Euler backward difference.

通过实验分析了冰水两相流在垂直和水平管道流动时的压降特性；建立了冰融解的三维分析模型，采用欧拉向后差分法，利用ANSYS数值模拟软件对冰水相变传热进行了数值模拟分析，得出冰粒大小与融解时间两者的关系曲线。

Methods According to the selection of the sample of bacteriuria througth NIT and LEU esterase testing,add to the positive sample directly to the antimicrobial susceptibility analytic board,to culture the bacˉteria at35℃for18～24hours,then take and analysis of antimicrobial susceptibility.

方法通过亚硝酸盐和白细胞酯酶试验进行菌尿标本筛选，阳性尿样直接加入到药敏分析试剂板经35℃18～24h培养后进行药敏分析。

Objective To provide the basis of the rapid choice of the medicine for the patients,and to avoid the misuse of the antibiotic.Methods According to the selection of the sample of bacteriuria througth NIT and LEU esterase testing,add to the positive sample directly to the antimicrobial susceptibility analytic board,to culture the bacˉteria at35℃for18～24hours,then take and analysis of antimicrobial susceptibility.

目的 急性泌尿道感染患者提供快速选药依据，避免抗生素滥用方法通过亚硝酸盐和白细胞酯酶试验进行菌尿标本筛选，阳性尿样直接加入到药敏分析试剂板经35℃18～24h培养后进行药敏分析。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失