浅谈如何求双曲线的离心率

双曲线的离心率,是双曲线的重要性质之一,它决定着双曲线开口的大小,是双曲线的本质属性,一直是高考中常考的知识点.本文以2008年的高考题为例进行解析,请同学们总结双曲线离心率的常用解法.

从离心率看圆锥曲线间的关系

早在17世纪初,在当时关于一个数学对象能从一个形状连续地变到另一个形状的新思想的影响下,法国天文学家开普勒对圆锥曲线的性质作了新的阐述.他发现了圆锥曲线的焦点和离心率,并指明抛物线还有一个在无穷远处的焦点,直线是圆心在无穷远处的圆.

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets Part A： Mathematical Model and the Influence of Dimple Radius

With increasing heat fluxes caused by electronic components, dimples have attracted wide attention by researchers and have been applied to microchannel heat sink in modem advanced cooling technologies. In this work, the combination of dimples, impinging jets and microchannel heat sink was proposed to improve the heat transfer performance on a cooling surface with a constant heat flux 500 W/cm2. A mathematical model was ad- vanced for numerically analyzing the fluid flow and heat transfer characteristics of a microchannel heat sink with impinging jets and dimples （MHSIJD）, and the velocity distribution, pressure drop, and thermal performance of MI-ISIJD were analyzed by varying the radii of dimples. The results showed that the combination of dimples and MHSIJ can achieve excellent heat transfer performance; for the MHSIJD model in this work, the maximum and average temperatures can be as low as 320 K and 305 K, respectively when mass flow rate is 30 g/s; when dimple radius is larger than 0.195 mm, both the heat transfer coefficient and the overall performance h/AP of MHSIJD are higher than those of MHSIJ.

Alkalis-doping of mixed tin-lead perovskites for efficient near-infrared light-emitting diodes

Substitution of lead(Pb)with tin(Sn)is a very important way to reduce the bandgap of metal halide perovskite for applications in solar cells,and near infrared(NIR)light-emitting diodes(LEDs),etc.However,mixed Pb/Sn perovskite becomes very disordered with high trap density when the Sn molar ratio is less than 20%.This limits the applications of mixed Pb/Sn perovskites in optoelectronic devices such as wavelength tunable NIR perovskite LEDs(Pe LEDs).In this work,we demonstrate that alkali cations doping can release the microstrain and passivate the traps in mixed Pb/Sn perovskites with Sn molar ratios of less than 20%,leading to higher carrier lifetime and photoluminescence quantum yield(PLQY).The external quantum efficiency(EQE)of Sn_(0.2)Pb_(0.8)-based NIR Pe LEDs is dramatically enhanced from 0.1%to a record value of 9.6%(emission wavelength:868 nm).This work provides a way of making high quality mixed Pb/Sn optoelectronic devices with small Sn molar ratios.

Flow Structure and Heat Exchange Analysis in Internal Cooling Channel of Gas Turbine Blade

This paper presents the study of the flow structure and heat transfer,and also their correlations on the four walls of a radial cooling passage model of a gas turbine blade.The investigations focus on heat transfer and aerodynamic measurements in the channel,which is an accurate representation of the configuration used in aeroengines.Correlations for the heat transfer coefficient and the pressure drop used in the design of radial cooling passages are often developed from simplified models.It is important to note that real engine passages do not have perfect rectangular cross sections,but include coiner fillet,ribs with fillet radii and special orientation.Therefore,this work provides detailed fluid flow and heat transfer data for a model of radial cooling geometry which possesses very realistic features.

Optimization of the Mean Radius Flow Path of a Multi-Stage Steam Turbine with Evolution Algorithms

A prototype model of the mean radius flow path of a four-stage, high speed 1 MWe axial steam turbine was optimized by using evolution algorithms, DE （differential evolution） algorithm in this case. Also the cost-benefits of the optimization were inspected. The optimization was successfully performed but the accuracy of the optimization was slightly less than hoped when compared to the control modeling executed with the CFD （computational fluid dynamics）. The mentioned inaccuracy could have been hardly avoided because of problems with an initial presumption involving semi-empiric calculations and of the uncertainty concerning the absolute areas of qualification of the functions. This kind of algebraic modeling was essential for the success of the optimization because e.g. CFD-calculation could not have been done on each step of the optimization. During the optimization some problems occurred with the adequacy of the computer capacity and with finding a suitable solution that would keep the algorithms within mathematically allowable boundaries but would not restrict the progress of the opti- mization too much. The rest of the problems were due to the novelty of the application and problems with pre- ciseness when handling the areas of qualification of the functions. Although the accuracy of the optimization re- suits was not exactly in accordance with the objective, they did have a favorable effect on the designing of the turbine. The optimization executed with the help of the DE-algorithm got at least about 3.5 % more power out of the turbine which means about 150 000 ε cost-benefit per turbine in the form of additional electricity capacity.