常微分方程学习指导(一)

本对《常微分方程》^[1]的第一、二章进行了归纳总结，剖析了重、难点，并通过典型例题介绍解题思路、方法和技巧，以帮助学生进一步理解基本概念，掌握基本方法，提高学生的解题能力。     

板坯结晶器钢水凝固的数值模拟

以实测结晶器铜板温度计算的热流量作边界条件,采用有限元方法,建立了结晶器内凝固传热方程.对凝固传热方程进行了离散化,利用ANSYS商业软件进行求解,得到凝固坯壳的应力、应变情况,从而确定连铸结晶器壁的合理锥度.     

PDE-Based Medial Axis Extraction and Shape Manipulation of Arbitrary Meshes

Shape skeletonization （i.e., medial axis extraction） is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D differential properties. It offers an alternative solids represented by polygonal meshes based on their but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects.     

动态汽车衡运行期间注意事项

本文探讨了动态汽车衡运行期间需要注意事项的各个方面并给出解决方案,在实践中获得良好的社会效益和企业效益。指出,结构动态汽车衡运行期间的日常维护工作,可以大大改进期其测量精度及设备使用寿命。     

市场的稳定性取决于人心

传统的市场经济的金科玉律——供求关系影响价格,价格围绕价值上下波动,使许多人误认为市场的稳定性也是由供求关系或价格决定。但是利用蛛网模型可得出结论:市场的稳定性取决于人心,即人们对商品的敏感程度。     

广义IMBq方程的各向异性有限元方法

研究了广义IMBq方程的各向异性有限元方法,在不需要传统的Ritz投影的情况下,得到了半离散格式下的误差估计.     

一个有界弹性项Duffing方程周期解的存在性

证明了有界弹性项Duffing方程x″ arccotx=p(t)的周期解的存在性,其中周期为2π的连续函数p(t)满足0     

炮采对拉工作面机头大棚支护和回采步距分析

在采煤作业中,为了防治水或探明、揭露断层或回采运输方便等需要,在设计布置工作面时,会形成两个工作面对拉出煤回采的情况.这样,机头大棚需支护的面积明显增大,采用原来"四对八根"控制顶板(图1)显然满足不了现场工作需要,这就给机头大棚的支护提出了新的要求.在现定工作中我们摸索出了如下图2的支护方式,支护效果比较明显,确保了安全生产.     

PEAK COVARIANCE STABILITY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.