带调和势的超临界非线性Schrdinger方程的最佳门槛

考虑带调和势的超临界非线性Schroedinger方程，解决了该方程整体解和爆破解存在所依赖的初始条件的最佳分界门槛．通过构造两类强制变分问题和建立局部不变半流，运用势井方法和凹方法，获得了该方程在两个不同的空间中的整体解和爆破解的最佳门槛条件．     

高阶非线性波动方程的有限差分方法

本文研究一类广泛的高阶非线性波动方程组初边值问题的有限差分格式，用离散泛函分析方法和先验估计的技巧得到了有限差分格式的收敛性。     

Electronic Structure and Magnetic Properties of SmCo7-xZrx

The electronic structure and magnetism of SmCo_7-xZr_x alloy are investigated using the spin-polarized MS-X. method. The results show that a few of electrons are transferred to the Sm(5d⁰) orbital due to orbital hybridization between Sm and Co atoms. The exchange interactions between 3d and 5d electrons are more important than the polarization effects of the conductive electrons, thus it is the main reason resulting in the long-range ferromagnetic order in SmCo_7-xZr_x. The Curie temperature of SmCo_7-xZr_x is generally lower than that of corresponding pure Co, which may be explained by the weaker average coupling strength between Co lattices due to some negative couplings mainly occurring of 2e site. The calculated results for the Sm₅Co₃₂Zr₂ cluster may lead to a better understanding of why SmCo_7-xZr_x is stable phase. Since the spin-up DOS peak of d electrons at E_F arises and the bonding of electrons at E_F strengthens with increasing Zr concentration, which results in the internal energy of the system decrease, the stable ferromagnetic order forms in SmCo_7-xZr_x.     

关于正形置换多项式的注记

n为正整数，m为大于1的正整数，本文证明了当n≡0，1（mod m）时，F2^n上不存在2^m-1次正形置换多项式，并给出了该结果的几个推论：F2^n上不存在次数为3的正形置换多项式；n〉2时，F2^n上的4次正形置换多项式都是仿射多项式．     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.     

第二讲合成孔径声纳成像及其研究进展

文章在介绍了图像声纳的特点、合成孔径声纳（synthetic aperture sonar,SAS）产生背景和发展过程的基础上,对合成孔径声纳的原理、技术难点、成像算法等问题进行了讨论.着重分析了合成孔径声纳成像过程中高分辨率的获取方法、水声信道对成像的影响、多子阵技术及其成像算法、稳定的声纳运动平台和运动监测问题、运动补偿与自聚焦方法等.文章还给出了国内外合成孔径声纳研究的最新进展情况,进而展望了合成孔径声纳的应用前景.     

Energy-Momentum Pseudo-Tensor of Relic Gravitational Wave of Both the Polarized States

Unlike usual celestial gravitational waves, the relic gravitational waves （RGWs） form random signals in curved spacetime background. We calculate the energy-momentum pseudo-tensor of a certain component of the RGWs propagating along arbitrary directions in Cartesian coordinates. It is found that the energy density of RGWs is positive definitely, and the momentum density components have reasonable behaviour. Such results may provide a theoretical basis for the detection of RGWs.     

Evolution of Weighted Networks by Duplication-Divergence Mechanism

The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight. The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability δ, weighted, structured exponential networks are realized.     

Synchronizing Complex Networks by an Adaptive Adjustment Mechanism

We propose an adaptive adjustment mechanism for synchronizing complex networks, in particular for sociological or/and biological systems. We do not take it for granted that a dynamical system is put on isolated nodes and they are coupled with each other by one （or more） variable（s）, as employed in most previous models. As a replacement, we suppose that each node may have any finite number of possible states, and their evolutions with time are determined by their nearest-neighbouring （or even second-nearest-neighbouring, etc） nodes in an adaptive adjustment mechanism. It is found that synchronization can be achieved for almost all connected networks and that the scale-free property can evidently improve the synchronizing speed.