Prediction of hot deformation behavior in Ni-based alloy considering the effect of initial microstructure

High temperature heat treatments were conducted for as-cast N08028 alloy to obtain various microstructures with different amounts of σ-phase,and then hot compression tests were carried out using Gleeble-3500 thermo-mechanical simulator in deformation temperature range from 1100 to1200 ℃ and strain rate range from 0.01 to 1 s-1. For the same initial microstructure, the flow stress was observed to increase with increasing the strain rate and decreasing the deformation temperature, while for the same deformation condition, the flow stress was found to increase with increasing the amount of σ-phase in the initial microstructure. Moreover, dynamic recrystallization was found to be the main dynamic soften mechanism. On this basis, Arrhenius-type constitutive equations and artificial neural network(ANN) model with back-propagation learning algorithm were established to predict hot deformation behavior of the alloy. Furthermore, the parameters of constitutive equations were found to be dependent on the initial microstructure, which was also as one of the inputs for the ANN model. Suitability of the two models was evaluated by comparing the accuracy, correlation coefficient and average absolute relative error, of the prediction. It is concluded that the ANN model is more accurately than the constitutive equations.     

伯努利方程在判定巷道贯通后风流方向中的应用

首次提出伯努利方程在判定巷道贯通后风流方向时的作用，分析了伯努利方程数学方法的建立，详细论述了巷道贯通前风流机械能在两种情况下的测定，说明了机械能具体参数的测定及要求。     

一类奇异偏微分方程的化简方法

针对一类在原点有奇异性的偏微分方程,本文用一复数域内奇异常微分方程全纯解的存在唯一性的结论,给出了一种具体的双全纯变换,将之化为更简形式.     

随机理论在经济建模中的应用

在金融市场上，局部无风险的债券与高风险的股票价格瞬息万变，本文给出了债券和股票价格的随机模型，该模型反映了价格与债券的利率ｒ（ｔ），股票的升值率ｂ（ｔ）及扩散矩阵σ（ｔ）等的联系。当投资者同时参与消费时，考虑到效用函数Ｕ及无穷分段的折扣函数β（ｔ），在ｒ、ｂ、σ为常值的条件下，得出了反馈形式的最优消费投资公式     

生态学中具有稀疏效应的Lotka—Volterra系统的分支问题

本文研究具有稀疏效应的一类捕食与食饣系统的分支问题.在部分参数条件下,讨论了系统的全局结构,并利用Hopf分支理论,分界线环分支理论得到了在不同的参数条件下,至少存在两个或三个极限环的结论.     

关于广义Fibonacci矩阵的Fermat方程

设ｍ是大于１的正整数，Ａｍ是ｍ阶广义Ｆｉｂｏｎａｃｃｉ矩阵，＝｛Ａｋｍ｜ｋ∈Ｚ，ｋ≥０｝，本文证明了：Ｆｅｒｍａｔ方程Ｘｎ＋Ｙｎ＝Ｚｎ，Ｘ、Ｙ、Ｚ∈Ｚ，ｎ∈ＩＮ，ｎ＞２，无解（Ｘ，Ｙ，Ｚ，ｎ）。     

基于梯度理论计算纯水表面张力

应用梯度理论和Ｐａｔｅｌ－Ｔｅｊａ方程相结合的半理论方法，计算了２０～１００℃时纯水的表面张力，提出了计算作用参数Ｃ的新型方程。结果表明，采用本文模型计算的表面张力值与文献实验值相比，平均相对误差仅为０．３％。     

再论Hill方程的解析解

应用一变换使Hill方程线性化,然后提出了一种确定函数φ的有效方法。     

BWRS状态方程密度根两种求解方法的考核及其应用

分别应用正割法和多点函数迭代法求解BWRS状态方程的密度根.并对多组分精馏塔进行模拟计算.实例计算表明,多点函数迭代法具有收敛速度快和稳定的优点,在精馏塔的计算中,多点函数法比正割法节约机时约26％.     

值得商榷的两种可降阶微分方程解法归类讨论

针对目前《高等数学》中采用对两种可降阶二阶微分方程的解法归类与实际做题时的依据不符,提出增加非线性强化条件和新的一种二阶非线性可降阶微分方程的解法,能很好地避免根据类型解题时无法求解的矛盾。