多元二次式因式分解的一个简便方法

本刊84年第七期《二元二次式因式分解的一个简便方法》一文(下面称为“上文”)中,讨论了“取零凑尾法”在二元二次式因式分解中的应用。本文接着讨论“取零凑尾法”在多元(多于二元)二次式因式分解中的应用。为叙述方便,将上述有关结论写在这里,作为     

Numerical simulation of a gradient-index fibre probe and its properties of light propagation

In order to verify the properties of the light propagating through a gradient-index (GRIN) fibre probe for optical coherence tomography (OCT), numerical simulation using the optical software GLAD is carried out. Firstly, the model of the GRIN fibre probe is presented, which is consisted of a single mode fibre (SMF), a no-core fibre (NCF), a GRIN fibre lens and an air path. Then, the software GLAD is adopted to numerically investigate how the lengths of the NCF and the GRIN fibre lens influence the performance of the Gaussian beam focusing through the GRIN fibre probe. The simulation results are well consistent with the experimental ones, showing that the GLAD based numerical simulation technique is an intuitive and effective tool for the verification of the properties of the light propagation. In this paper, we find that on the conditions of a constant GRIN fibre lens length of 0.1 mm and an NCF length of 0.36 mm, the working distance of the probe will be 0.75 mm and the focus spot size is 32 μm.     

二元二次式因式分解的一个简便方法

形如Ax~2+Bxy+Cy~2+Dx+Ey+F的二元二次式的因式分解,一般可用求根公式法,待定系数法等方法进行分解,但计算都比较复杂。下面我们介绍一种简便的分解方法——取零凑尾法。这个方法的理论根据是定理二元二次多项式f(x,y)=Ax~2+Bxy+Cy~2+Dx+Ey+F能分解为一次式之积(a_1x+b_1y+c_1)(a_2x+b_2y+c_2)的充要条件是对 B=a_1b_2+a_2b_1, (1)使得 f(x,o)=(a_1x+c_1)(a_2x+c_2) (2) f(o,y)=(b_1y+c_1)(b_2y+c2) (3)证明:条件的充分性。设上三式同时成立,     

侧面进料在循环流化床密相区混合特性的试验研究

建立三维循环流化床冷态试验研究装置,采用热颗粒示踪技术,在不同风速和静止床高下,考察了两种粒径的示踪颗粒注入密相区后沿水平进料方向、横向和垂直方向的混合特性.结果显示,在不同工况下,注入口下方的温升始终最明显,表明边壁处的乳化相有明显的向下运动.垂直方向测点的温升大于水平方向,但水平进料方向和水平横向的温升没有明显差别.提高风速有利于侧面进料与床料的混合.与注入口完全淹没在密相区相比,注入口位于飞溅区有助于侧面进料在密相区横截面的混合.