Banach空间中有界线性算子的Moore-Penrose度量广义逆的扰动分析

对度量广义逆中Moore-Penrose度量广义逆的扰动进行了初步的研究.给出了度量稳定扰动的定义,应用度量稳定扰动的定义及广义正交分解定理给出在一定的范数下,有界线性算子的单值度量广义逆Moore-Penrose度量广义逆的误差界估计.     

乘性色噪声激励下广义分数阶van der Pol-Duffing振子的随机分岔分析

本文研究了在乘性色噪声激励下含分数阶导数项的广义Duffing振子的随机分岔.首先，利用一种回复力和阻尼力的线性组合等效替换系统中的分数阶导数项；其次，对系统中的三次项进行线性化处理，利用最小均方误差原理，将系统转变成整数阶系统，由随机平均法求得系统的稳态概率密度函数；最后，通过拟不可积Hamilton系统随机平均法得到系统不变测度的最大Lyapunov指数，并对系统进行随机D-分岔和P-分岔分析.研究发现，分数阶导数阶数、噪声的自相关时间等参数的改变可以诱发系统发生随机P-分岔.     

有限域上对角方程ax^{d}+by^{2d}=c的可解性

有限域研究中的一个重要问题是所谓的幂和问题，即在充分大的有限域F_q中任意元素能否表示成一个元素的d₁次幂和一个元素的d₂次幂之和，其中d₁和d₂均为正整数．设a,b∈F_q^*,c∈F_q,d为正整数．在本文中，我们利用有限域上的概率测度，Cauchy-Schwarz不等式及广义Fourier变换等工具研究了某些子集的测度，由此证明当■时方程ax^d+by^2d=c在F_q上恒有解．进一步，我们证明当q≠5时方程ax²+by⁴=c在F_q上恒有解．     

Insights into plastic deformation mechanisms of austenitic steels by coupling generalized stacking fault energy and semi-discrete variational Peierls-Nabarro model

The generalized stacking fault energy (GSFE) is a key parameter to determine the plastic deformation mechanisms of austenitic steels. However, the underlying physics why the GSFE can affect the plastic deformation behaviors remains unclear. In this paper, the plastic deformation mechanisms of austenitic steels with different carbon (C) additions were investigated by coupling the GSFE with the semi-discrete variational Peierls-Nabarro (P–N) model. The internal mechanisms behind the P–N stress and plastic deformation were explained at atomic scale. It is found that the positions and contents of C atoms affect the GSFE of austenite, and thus regulate plastic deformation behaviors of austenitic steels by influencing dislocation core structure. As exemplified that with 4 ​at.%C in austenite, the intrinsic stacking fault energy increases from −433 to −264 mJ/m², and the stacking fault width increases to 6.62b from 4.72b of FCC-Fe with b being the Burgers vector. This corresponds to the plastic deformation mechanism dominated by the ε martensitic transformation with the lattice changing from FCC to HCP. With increasing C contents to 8 ​at.%, the intrinsic stacking fault energy of austenite increases to −9.01 mJ/m², while the stacking fault width decreases to 6.03b. The plastic deformation tends to proceed via the mechanical twinning mode. The present investigation establishes a solid foundation for clarifying the plastic deformation mechanisms of austenitic steels from the perspective of the dislocation core structure.