Unitary quasi-affine transforms of contractions

The unitary quasi-affine transforms of contractions are the cornerstone of the exact theory of irreversibility introduced by Misra, Prigogine and Courbage. This work shows that the class of contractions with unitary quasi-affine transforms is just C⋅1 and that every unitary quasi-affine transform of a contraction is unitarily equivalent to the residual part of its Sz.-Nagy-Foia? dilation. Some connections with the Grossmann theory of nested Hilbert spaces and generalized eigenvalues are established. These results are applied to the study of the baker map.     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

土剪胀性的应力路径相关规律及其模拟

建立能够反映土的变形和强度特性应力路径依存性的本构模型, 首先需要解决土剪胀规律的应力路径依存性问题. 对黏土和砂土剪胀性的应力路径依存性做了系统的分析和比较,模型预测与试验结果的比较表明: 剑桥模型和统一硬化模型在描述土的这一特性方面都有一定缺陷; 采用部分塑性体应变与塑性剪应变耦合的思路建立的渐近状态模型能够较好地反映土剪胀性的应力路径依存性.      

应用随机数渐近线分布法评估飞机飞行安全

严重纵向人机耦合事件是公认的危及飞行安全问题 ,出现概率一般为 10 -6.若采用传统的频率统计法进行趋势预测 ,需要的样本数大于 10 7个 ,工程实际中是无法实现的 .为此 ,文中提出了有效的随机数渐近线分布法对其进行评估 .     

Approximate formula for the vertical asymptote of projectile motion in midair

The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytical approach is used for the investigation. An approximate formula is obtained for one of the characteristics of the motion – the vertical asymptote. The value of an asymptote is determined directly by the initial conditions of throwing. Analytically derived values of asymptotes in comparison with numerical values obtained by integrating the equations of motion are given. The motion of a baseball is presented as an example.     

Taylor级数展开法中初始位置的选择方法

在时差定位中Taylor级数展开法是否有效收敛受到初始位置选择的约束,比较三种初始位置选择方法：真实位置法,Chan算法以及渐近线交点法,通过试验说明三种方法在Taylor级数展开法定位中不同的性能。     

关于凹函数性质的探讨

从凹函数的一个问题出发,给出了该问题的反例以及问题结论成立的充要条件和充分条件.     

多元Bernstein—Sikkema算子的逼近性质

本文对定义在单形上的Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子讨论其导数的收敛性质，同时出给出了高阶渐近展开式及Ｂｅｓｏｖ空间中的几个等价关系。