一次成功的类比

琚老师编拟此题的目的是提醒学生在解二元二次方程组时,应注意判别式△可能会失效,并总结出了求含有参数的两个二次曲线的交点时,转化为二次方程后只考虑判别式△是不够的,还应该要注意方程根的范围。同时也给出了该问题的解答,现将原方法摘抄如下．     

一个环境保护问题的数学建模活动体验

问题 某化工企业每月收入为80万元．从今年起,若不改善生产环境,则在生产过程中产生的污水交由污水厂处理,每月上交定额5万元的治污费．如果该企业从今年1月份起投资300万元增加回收净化设备以改善生产环境,降低企业生产成本．已知该设备每月的运转费用是0．2万元．问：经过多少个月,投资开始见效,即投资改造后的月累计纯收入多于不改造时的月累计纯收入？     

对一道高考题的再思考

一．题目 （2007年高考数学全国卷Ⅱ压轴题）已知f（x）=x^3-x．（1）求曲线y=f（x）在点M（t,f（t））处的切线方程。（2）设a〉0,如果过（a,b）可作曲线y=f（x）的三条切线,证明：-a〈b〈f（a）。     

对一道高考数列题解法的探讨

本题主要考查数列、函数、不等式证明等知识,其综合性能大,解题技能要求较高,是一道既考知识,又考能力的好试题．     

在化学课中如何贯彻综合技术教育

綜合技術教育应該使学生了解一切生產过程的一般科学原則。同時,傳授学生使用一切生產基本工具的熟練技巧。因此,綜合技術教育应作到使理論結合实际,智力劳動結合体力劳動,使科学原理的掌握結合工業和農業的基礎。其目的是,为了保証中学畢業生有自由选擇職業和很快掌握職業的可能。     

Expansion of Lie Algebra and Its Application

Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.     

Ocean dynamic noise energy flux directivity in the 400 Hz to 700 Hz frequency band

Results of field studies of underwater dynamic noise energy flux directivity at two wind speeds, 6 m/s and 12 m/s, in the 400 Hz to 700 Hz frequency band in the deep open ocean are presented. The measurements were made by a freely drifting telemetric combined system at 500 m depth. Statistical characteristics of the horizontal and vertical dynamic noise energy flux directivity are considered as functions of wind speed and direction. Correlation between the horizontal dynamic noise energy flux direction and that of the wind was determined; a mechanism of the horizontal dynamic noise energy flux generation is related to the initial noise field scattering on ocean surface waves.     

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier-Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.