在不定积分计算中不能忽视"区间I"

有这么一道求不定积分的题目 :例 ∫ 1 -sin2θdθ在以往的教学乃至某些考研资料中发现有这样做的 :解 ∫ 1 -sin2θdθ=∫ (sinθ-cosθ) 2 dθ=∫ |sinθ-cosθ|dθ=± (cosθ+sinθ) +C初看似乎没错 ,但仔细推敲就会发现有问题。实际上只有当θ∈ [2kπ -3π4,2kπ + π4]时 (k是整数 ) ,cosθ-sinθ 0 ,才有(cosθ+sinθ)′=cosθ -sinθ=｜sinθ-cosθ｜从而cosθ+sinθ在这些区间上才是 |sinθ-cosθ|的一个的原函数。而当θ∈ [2kπ + π4,2kπ + 5π4]时 ,sinθ-cosθ 0 ,(-cosθ-sinθ)′=sinθ -cosθ=｜sinθ-cosθ｜从而与上面…     

实现信息高速公路的途径

本文提出了在人类进入信息时代的过程中，最先实现信息化的国家就可以获得飞速发展的机会的观点，并着重指出，实现信息高速公路的唯一途径是实行鼓励竞争和电信业全面开放的政策。     

Annihilation density distribution calculations for medically important positron emitters

The effect of positron range on the image-plane resolution of tomographic images is evaluated through calculations based on a model which employs beta-decay energy spectra and an empirical range formula. Predicted range distribution functions are compared with published measurements for three medically important positron emitters: (11 )C, (68)Ga, and (82)Rb. The effect of tomographic slice thickness on point-source annihilation distribution functions is also demonstrated. Line-spread functions are calculated using the model, for the above isotopes as well as for (18)F, (15)O, and (13)N. Image-plane resolution predictions are made for high-resolution positron cameras for various positron emitting isotopes with end-point energies up to 4 MeV.