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Applying theories of numerical analysis and higher geometry, the corresponding mathematical model of stem line is established according to different stems. Whereby, the centers, radii of the arc and its tangent points with the water-line can be found and the curve of arc radius is thus determined. A general formula for expressing stem curved surface is introduced.

应用数值分析和计算几何理论,根据船体首部线型特点,建立首柱轮廓线数学模型;计算水线首圆弧圆心、半径和切点,确定首圆弧半径线;给出首部曲面的通用方程式。

Bohr radius was the radius of the circle in which the electron moved in the ground state of the hydrogen atom, according to the Bohr theory.

根据玻尔理论,玻尔半径是在基态氢原子中电子运动的圆周半径。

But Ganymede and Callisto are bigger, with diameters that are half again as large as the moon's diameter.

但是木卫三和木卫四要更大些,半径有一个半月亮的半径那么大。

The line segment connecting the center and any point of a circle is called the radius.

连接圆心和圆上任意一点的线段叫做半径,半径一般用字母 r 表示。

Consider the circle that is tangent to the curve at and has the same curvature there. Its center will lie on the concave side of the curve. This circle is called the circle of curvature. Its radius is the radius of curvature, and

在点处的曲线的法线上,在凹的一侧取一点,使得,以为圆心,半径为的圆叫做曲线在点处的曲率圆,曲率圆的圆心叫做曲线在点处的曲率中心,曲率圆的半径叫做曲线在点处的曲率半径。

Finally it analyzes the feasibility that using hydromechanics to analyze traffic flow by contrasting various characters between traffic flow and fluid flow. It analyzes influence of road alignment to basic expressway segment capacity by hydromechanics, and obtains viscous resistance and viscous movement differential equation when the vehicle drives on circular curve segment of expressway. And it infers that viscous resistance is correlated with sideway force coefficient, slope of crown and radius of circular curve. Radius of circular curve, sideway force coefficient and slope of crown are bigger, viscous resistance is smaller, the influence to capacity is smaller when the vehicle is running on nearside lane of circular curve; but radius of circular curve and sideway force coefficient are bigger, slope of crown is smaller, viscous resistance is smaller, the influence to capacity is smaller when the vehicle is running on fast lane of circular curve.

最后通过对比交通流与流体流的相似性,运用流体力学分析了道路线形对快速路基本路段通行能力的影响,求出了车辆在曲线路段的粘性阻力,建立了车辆在曲线路段的粘性运动微分方程,并由此推知,粘性阻力与横向力系数、路拱横坡度和圆曲线半径都有关系,当车辆在圆曲线外侧车道上行驶时,圆曲线半径、横向力系数和路拱横坡度越大,粘性阻力就越小,对道路的通行能力影响就越小;而当车辆在圆曲线内侧车道上行驶时,圆曲线半径和横向力系数越大,路拱横坡度越小,粘性阻力就越小,对道路的通行能力影响就越小。

It is found that the former provide more uneven circular stress state than the latter after comparing the circular stresses both of intrados and extrados,which extrados stress is large and intrados stress is small.That is confirmed by the results of experiment that the practical burst pressure...

结论认为,内压作用下的弯管结构属于有力矩旋转壳,整体环壳第二弯曲半径由外拱区的正半径变化为内拱区的负半径,引起应力性质的变化,只考虑薄膜应力的弯管内压爆破理论存在不安全的因素。

Lanthanides belong to the sixth cycle of the periodic table Ⅲ B family, are all solid metal, they are La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, holmium, erbium, thulium, ytterbium, and lutetium were 15 kinds of metals and their periphery are two layers of electronic 5d16s2, while the peripheral third layer f orbital but never zero to 14, so the external electronic structure of 4f0-145d16s2, and therefore these elements in oxidation number are to 3, very close chemical properties, extraction, when it is difficult to separate them they are mostly multi-element mineral mix, more difficult to increase refining, and their atomic number of 57-71, one by one to increase the number of protons the nucleus, and thus extranuclear electron of gravity is also growing, so that atomic radius decreases with increasing atomic number Z, which makes lanthanides contraction, ionic radius is also reduced, which also makes Zr, Hf, Nb and Ta, Mo and W, the atom and ionic radius very close to each other they also determine a similar nature, resulting in difficult separation, also the tribe Ⅷ of the fifth cycle, ruthenium, rhodium, palladium, and the sixth cycle, osmium, iridium, platinum is very similar in nature, thus The six elements, said platinum group elements.

镧系元素属于周期表第六周期中ⅢB族,全部是固体金属,它们是镧、铈、镨、钕、钷、钐、铕、钆、铽、镝、钬、铒、铥、镱和镥共十五种金属元素,它们的外围两层的电子均是5d16s2,而外围第三层的f轨道电子却从零增加到14个,所以外围电子结构为4f0-145d16s2,而使这些元素氧化数均为+3,化学性质极为接近,提炼时很难分开,它们的矿石又大多是多种元素混在一起的,更增加提纯难度,它们的原子序数为57-71,核内质子数逐个增加,因而对核外电子引力也不断增强,使原子半径随原子序数Z增加而减小,这就使镧系元素收缩、离子半径也缩小,这也使得Zr和Hf,Nb和Ta、Mo和W等原子和离子半径都很接近、也决定了它们彼此性质类似,以致难以分离、也使第Ⅷ族中第五周期的钌、铑、钯和第六周期的锇、铱、铂在性质上极为相似,因而称这六个元素为铂系元素。

Because the workpiece is in dynamic balance, the resultant moment acting on it should be zero. Introducing the moment from lapping tool and press head a moving differential equation is built. In this equation only workpiece rotating speed is unknown. It means that workpiece rotating speed can be got by this equation. Since there is a transcendental function in integral function of the equation an analytic result can not be got, only digital result can be got by a computer. Thus a change rule of workpiece rotating speed with lapping parameters is known, e.g. the radius of press disc ball socket, radius of press head ball, the distance between the workpiece rotating axis and lapping tool rotating axis, workpiece radius, modulus of elasticity of the press head and press disc, friction coefficients between the lapping tool and workpiece, and between the head and disc, pressure between the lapping tool and workpiece and pressure between the press head and press disc.

因工件处于动态平衡状态,其上所受到的来自于磨具和压头的力矩应相等,将二力矩表达式联立,建立工件运动微分方程,该方程中只有工件的旋转角速度是未知量,因此可以求出工件旋转角速度,但该方程积分式中含有超越函数,得不出解析解,只能通过计算机求出数值解,得出工件旋转角速度随各研磨参数的变化规律,如压盖球座半径、压头的球头半径、工件回转中心相对磨具回转中心的偏心距、工件半径、压头和压盖材料的弹性模量、磨具与工件间的摩擦系数、压头压盖间的摩擦系数、磨具与工件间的压强、压头压盖间的压力等。

The analysis shows that vertical growth is achieved thanks to discrete contact points and regions with continuous contact, that the contact pressure creates tension in the stem as observed experimentally, and that there is a maximal radius of the pole around which a twiner can climb.

这个模型可以解释为什么藤蔓不能在半径大于一定值的树干上生长,他们计算出当树干半径大于3.3倍的藤蔓自然曲率半径时,藤的尖端便不能继续缠绕树干向上生长,而是自身卷曲起来。文章的后一页半研究了摩擦力的影响,很明显,摩擦力是使藤蔓植物能够支撑自身重量的主要原因。

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