点集Bézier曲线

提出了点集Bézier曲线的概念,给出了点集Bézier曲线的性质及细分算法.按照点集算术的定义,当点集是长方形闭域或圆盘时,点集Bézier曲线就是区间Bézier曲线或圆盘Bézier曲线,因此,点集Bézier曲线是对区间Bézier曲线和圆盘Bézier曲线的推广.     

具有多个奇点的广义的Liénard系统不存在任何闭轨的条件

本文不同于一般的方法，利用辅助函数建立了具有多个奇点的广义的Ｌｉéｎａｒｄ系统（Ｅ）不存在任何闭轨的若干判别条件，关于（Ｅ）的经典的Ｂｅｎｄｉｘｓｏｎ判别法则和Ｐｏｉｎｃａｒé地形系法则是其特例．此外，给出了包括三次振动系统在内的例子．     

Liénard型系统全局稳定性的充要条件

本文研究Lienard型系统x=φ（h（y）-F（x））,y=－g（x）的全局稳定性问题．利用Filippov变换和一些新的方法建立了系统为全局稳定的系列充要条件．     

对于局部有界函数的积分型Szász-Bézier算子的逼近估计

引入一种积分型的 Szász- Bézier算子 ,并研究其逼近性质 ,得到了此类算子对局部有界函数的逼近阶估计公式     

The Viro method for construction of Bernstein-Bézier algebraic hypersurface piece

This paper proposes a new method for the construction of Bernstein-Bézier algebraic hypersurface on a simplex with prescribed topology.The method is based on the combinatorial patchworking of Viro method.The topology of the Viro Bernstein-Bézier algebraic hypersurface piece is also described.     

非线性边界条件下拟线性瞬态方程组的Phragmén-Lindelöf型二择一结果

考虑了一类定义在三维半无穷柱体上的拟线性方程组,其中假设方程的解在柱体的有限端和侧面满足非齐次条件。定义了“能量”表达式,通过限制非线性项,利用微分不等式技术, 推导了一阶微分不等式,解此不等式得到二择一结果,即证明了“能量”随与有限端距离的增大要么呈指数式（多项式）增加,要么呈指数式（多项式）衰减。同时,在衰减情形下得到了全能量的上界。     

Quantum Entanglement of Parallel-Coupled Double Quantum Dots: a Theoretical Study Using the Hierarchical Equations of Motion Approach?

Quantum dots comprise a type of quantum impurity system. The entanglement and coherence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-motion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.     

带税率的Cramér-Lundberg风险模型的总征税次数的分布函数(英文)

本文研究了带税率的Cramér-Lundberg风险模型.利用迭代算法及该过程具有的的强马氏性,得出了保险公司从开始营运到破产期间总赋税次数的概率函数.作为例子,本文给出了指数分布索赔假定下该概率函数的具体表达式.     

Real-time accurate Free-Form Deformation in terms of triangular Bézier surfaces

We implemented accurate FFD in terms of triangular Bézier surfaces as matrix multiplications in CUDA and rendered them via Open GL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessellation shader algorithms.     

Influence of Ion Nonlinear Polarization Drift and Warm Ions on Solitary Kinetic Alfven Wave

Considering the effects of ion nonlinear polarization drift and warm ions, we adopt two-fluid model to investigate the character of low-frequency Solitary Kinetic Alfvén Wave (SKAW hereafter) in a magnetic plasma. The results derived in this paper indicate that dip SKAW and hump SKAW both exist in a wide range in magnetosphere (for the pressure parameter β～10^-5～0.01, where β is the ratio of thermal pressure to magnetic pressure, i.e. β=2μ₀nT/B₀²). These two kinds of SKAWs propagate at either Super-Alfvénic velocity or Sub-Alfvénic velocity. In the inertial region β＜＜m_e/m_i, the Sub-Alfvénic velocity dip SKAWs and hump SKAWs both exist; in the transmittal region β～ 2m_e/m_i, dip SKAWs and hump SKAWs propagate at Super-Alfvénic velocity or Sub-Alfvénic velocity; Super-Alfvénic velocity hump SKAWs and Super-Alfvénic and Sub-Alfvénic velocity dip SKAWs are in the kinetic region 1＞＞β＞＞ m_e/m_i. These results are different from previous ones. That indicates that the effects of ion nonlinear polarization drift and warm ions are important and they cannot be neglected. The SKAW has an electric field parallel to the ambient magnetic field, which makes the SKAW take an important role in the acceleration and energization of field-aligned charged particles in magnetic plasmas. And the SKAW is also important for the heating of a local plasma. So it makes a novel physical mechanism of energy transmission possible.