乘数在91～109之间的乘法心算及其推导

接近百的两组大数和中间是“О”的两组三位数乘法，在用珠算计算上是比较麻烦的，若用心算，难度就更大了。但是，我们要能把握住这类数做乘法运算规律，并运用其规律进行深入推导，是能够得出更简捷的更适用的速算方法的，用它来指导心算，那就可以变难为易，变繁为简，变慢为快。     

美英早期几何教材中的棱台体积公式

笔者选取1829年-1948年期间出版的75种美英几何教材,考察其中关于棱台体积公式的内容,研究发现相关教材中推导棱台体积公式的四种方法,即分割法、构造法、定义法和公式法.相关观点和素材为HPM视角下棱台体积公式的教学提供有益的参考.     

Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.     

副反应和副反应系数在酸碱滴定误差公式推导中的应用

通过引入副反应和副反应系数的概念,借助林邦公式的表达形式,讨论了强碱滴定一元弱酸、混合弱酸和多元弱酸滴定误差公式的推导方法,并以实际例题证实所推公式的正确性。     

直观推导式演进特征投影法在拖尾重叠色谱峰解析中的应用

直观推导式演进特征投影法(HELP)已成功应用于复杂体系的重叠色谱峰解析.当色谱峰拖尾时,演进特征投影图(ELPG)显示的直线段对应的区域中可能含有前面拖尾组分的信息,据此进行HELP解析可能得不到满意结果.选择ELPG上直线段的一部分,即拖尾组分末端,前面组分的信息已基本消失的区域作为选择性区域进行HELP解析.同时,提出一种新的定量方法:用主成分分析法(PCA)分解待测组分标准样品的二维数据,将得到的“标准”色谱引入HELP的定量过程,在色谱峰拖尾或解得谱峰不平滑时,得到更准确的结果.用HELP方法解析了依诺沙星、诺氟沙星和环丙沙星三组分实验体系,结果表明,加入上述措施的HELP可有效改善拖尾重叠色谱峰的解析结果.     

High frequency forcing on nonlinear systems

High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions.Based on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency.Numerical simulations on several nonlinear oscillator systems show a very good agreement with the theoretic results.These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.     

多釜串联模型停留时间分布方差的推导

简要分析了理想反应器的特点,并指出现实反应器与理想反应器的区别,介绍了多釜串联模型描述实际反应器的思想.针对多釜串联模型的停留时间分布的计算函数进行逐步的推导,以阶跃法对模型进行分析,采用数学归纳法和分部积分法等方法推导出了多釜串联模型无因次停留时间分布函数表达式;根据停留时间分布密度函数定义,推导出了无因次停留时间分布密度函数的表达式;根据概率中方差的定义,推导出了无因次方差的表达式.     

Sound absorption characteristics of a thin plate with PZT and shunt circuit I. Theoretical analysis

The feasibility of sound absorbing by a vibrating plate with piezoelectric material and shunt circuits is theoretically investigated. Based on an equivalent compliance of a piezoelectric wafer shunted with RL circuits, the governing equations for the fiexural vibration of the plate with the piezoelectric wafer are derived using Lagrange＇s approach. The equations take into account not only the mass, stiffness and structural damping of the plate and the wafer, but also the electrical resistance and electrical inductance of the RL circuits. By using the governing equations derived, the surface impedance and sound absorption coefficient of the plate backed with a cavity are given. Numerical results show that the sound absorption coefficient of the plate near its first mode can be significantly improved by adjusting the RL parameters.     

中学化学教学中的证据推理*

1没有证据的推理通过推理可以得出重要的结论,但是没有证据的推理往往是一种猜测,可能是臆造事实上不成立的问题;即使猜测的是事实,没有证据也不具有说服力。所以,中学化学中没有证据的推理学生难以理解,难以接受,甚至苍白无力。2没有推理的证据没有推理的证据是不借助理论思维、没有逻辑推理的事实或材料,是一些孤立的事实或材料,把握不了证据和结论之间的关系。在中学化学教学中缺少原理推导,使得化学知识之间难以组织,感觉是化学知识点较为零散,学习化学需要死记硬背。     

关于PW－1480 X44软件中的数学通式问题

本文讨论ＰＷ－１４８０Ｘ４４软件中的数学通式问题。作者指出，软件中所提供的数学通式不妥，应该改正，软件应作适当修改。