界面不稳定性引起湍流混合的二阶封闭模型

在Ｂｅｓｎａｒｄ［１～３］等人的模型基础上发展了一个二阶封闭模型。它比原模型少二个方程，降低了计算量，使模型更具有经济性。并采用各向异性的扩散系数，能够更好地描述各向异性的湍流流场。编写了一维可压缩流体力学湍流混合程序，数值模拟Ｂｒｏｕｉｌｅｔｔｅ［４］等的实验结果。数值模拟结果与实验完全一致。     

Historical evolution and mathematical models: A sociocultural algorithm

Though there are a lot of approaches to the problem of sociocultural evolution most of them are only one-sided, i.e., they deal only with either social or cultural processes. With few exceptions they are also only informal theories with no formal rigour. In this article we propose a theoretical model which considers both sides of the problem, that is the mutual interdependence of the evolution of social structures and of the culture of a society. A mathematical model, the sociocultural algorithm (SCA), based on these theoretical considerations maps several of the dynamic characteristics of sociocultural evolution, suggesting that universal principles underlie the dynamics of historical evolution.     

The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4

Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R⁴. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et al.     

Isotype knice subgroups of global Warfield groups

If H is an isotype knice subgroup of a global Warfield group G, we introduce the notion of a k-subgroup to obtain various necessary and sufficient conditions on the quotient group G/H in order for H itself to be a global Warfield group. Our main theorem is that H is a global Warfield group if and only if G/H possesses an H(ℵ₀)-family of almost strongly separable k-subgroups. By an H(ℵ₀)-family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize those global k-groups of sequentially pure projective dimension ⩽ 1.     

原子核间距对平行电磁场中He2+的回归谱与闭合轨道影响的研究

利用半经典闭合轨道理论和分区自洽迭代方法计算了Rydberg态下在平行电磁场中的回归谱与闭合轨道.通过计算分子中两原子之间的距离在平衡位置、最小以及最大时的闭合轨道和回归谱讨论了分子实散射效应对平行电磁场中的回归谱与闭合轨道的影响.     

关于序半群的N—类

本文给出了关于序半群 N—类的若干等价性质     

Scattering matrix theory for Cs Rydberg atoms in magnetic field

Based on the closed orbit theory framework together with the quantum defect theory and time-independent scattering matrices theory, we calculate the recurrence spectra of diamagnetic Cs atoms at several different scaled energies near the second ionization threshold. It is revealed that the new extra peaks in spectra are attributed to the combination recurrences of semiclassical closed orbits arising from core-scattered events. This method considers the dynamic states of the Rydberg electron in the core region and long-range region and can be analytically resumed to include all orders of core-scattering automatically. With this approach a convergent recurrence spectrum can be reasonably achieved. It is found that the spectral complexity depends highly sensitively on the scaled energy. With the increase of the scaled energy, the spectral structure changes from simple to complicate and the dynamic feature from regular to chaotic. The comparison of the recurrence spectra with Dando’s result under the same conditions demonstrates that there exist some similarities and differences between them, and furthermore, the feasibility of the scattering matrix method is explained. Supported by the National Natural Science Foundation of China (Grant Nos. 10774093 and 10374061)     

It模型金融市场的完备性

本文研究了标的资产价格服从连续时间It过程模型的金融市场的完备性问题。在允许有摩擦的金融市场中,当可允许投资策略取值于一个非空凸闭集时,给出了金融市场在内蕴完备条件下广义不完备的充分必要条件.     

Gosper算法与一类组合和是否有闭形式的问题

本文由Gosper算法研究了一类形如f_(p,r,x)(n)=∑_(k=0)~(rn)((?))x~k的组合和是否有闭形式的问题。