We also obtain similar results on nearly reducible boolean matrices . we determine the maximum values of the first type of indices of convergence of n x n boolean matrices , reducible matrices , critically reducible matrices respectively , characterize the corresponding extreme matrices 对第一种类型的广义幂敛指数，我们得到了n n布尔矩阵类， n n可约布尔矩阵类， n n临界可约布尔矩阵类的这种指数的最大值，刻画了极矩阵。
" oh , i am aware of that , " said madame de villefort ; " but i have a passion for the occult sciences , which speak to the imagination like poetry , and are reducible to figures , like an algebraic equation ; but go on , i beg of you ; what you say interests me to the greatest degree . “噢，我是知道的， ”维尔福夫人说道， “我对于神秘科学非常感兴趣，它们象诗歌一样的需要想象力，又象一个代数方程式似的可以还原。请您说下去吧，您所说的我觉得有趣极了。 ”
That music should thus be subjected to forms of automation is inevitable ; and that it should remove itself more and more from singing and dancing and embrace a world of sound devoid of human content is surely the end result of believing that music like everything else today is reducible to formulas , to equations , to statistical probabilities , to predictable and controllable functions and behavior - in short to technology 音乐以后会成为自动型式,是无可改变的.它会越离唱与舞越远.相信: [音乐,正如每件事,都可以简化成公式,简化成方程式,成统计概率,成可预期与可控制的功能与行为-简之,就是简化成科技] ,的最后的结果,就是:拥抱,没有人性,的声音,的世界
In this paper we mainly study the kth multi - g base index for non - powerful primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices . we obtain sharp ' upper bounds , together with complete characterization of the equality cases of the kth multi - g base index for primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices 在本文中我们研究了广义non - powerful不可约符号矩阵和几乎可约符号矩阵的广义k重基指数，得到了广义不可约符号矩阵的广义k重基指数的最好上界，以及广义几乎可约符号矩阵广义k重基指数的上界和某些达到上界的矩阵。
The necessary and sufficient condition for degree reducible nurbs curves in an explicit form is given . and a new way of doing degree reduction of nurbs curves is also presented in detail , including the multi - degree reduction of a nurbs curve on each knot span and the multi - degree reduction of a whole nurbs curve . the corresponding formula of error estimation and error bound are given also 推导出了nurbs曲线可退化的显式充要条件，并进一步详细地给出nurbs曲线降多阶的一种新方法，包括一段nurbs曲线的降多阶和一整条nurbs曲线的降多阶，并给出了相应的误差估一计公式及误差界
