In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off me...In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes offwithout jumping. In this study, we used 3-Dimensional （3D） high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be con- sidered as a main source of lift for heavy beetle.展开更多
【目的】为使Heston(赫斯顿)模型能更细致地刻画标的资产价格演变规律以应对复杂多变的金融市场,提出了带跳的非仿射粗糙Heston模型。【方法】首先用傅里叶余弦级数(Fourier Cosine Series Expansion,Fourier-Cosine)方法分离期权密度...【目的】为使Heston(赫斯顿)模型能更细致地刻画标的资产价格演变规律以应对复杂多变的金融市场,提出了带跳的非仿射粗糙Heston模型。【方法】首先用傅里叶余弦级数(Fourier Cosine Series Expansion,Fourier-Cosine)方法分离期权密度函数和特征函数,用扰动法转化非线性偏积分微分方程,并用Adams-Bashforth-Moulton(亚当斯-巴什福斯-默尔顿)预测-校正法求解分数黎卡提方程,从而得到欧式看涨期权定价公式;然后用蒙特卡洛模拟结果验证解的有效性;最后分析了模型非仿射参数、粗糙参数和跳幅度参数对期权价格的影响,并对比了不同模型的定价结果。【结果】数值解与蒙特卡洛模拟结果相对误差为0.01%~0.2%,非仿射参数、粗糙参数和跳幅度参数对模型有不同程度的影响同时又相互制约。【结论】本模型刻画标的资产价格变化规律更具灵活性和多样性,从而为期权定价提供了理论支撑。展开更多
Let r≥2 be an integer.The real numberα∈[0,1)is a jump for r if there exists a constant c>0 such that for any?>0 and any integer m≥r,there exists an integer n_0(ε,m)satisfying any r-uniform graph with n≥n_0...Let r≥2 be an integer.The real numberα∈[0,1)is a jump for r if there exists a constant c>0 such that for any?>0 and any integer m≥r,there exists an integer n_0(ε,m)satisfying any r-uniform graph with n≥n_0(ε,m)vertices and density at leastα+?contains a subgraph with m vertices and density at leastα+c.A result of Erd?s and Simonovits(1966)and Erdos and Stone(1946)implies that everyα∈[0,1)is a jump for r=2.Erdos(1964)asked whether the same is true for r≥3.Frankl and Rodl(1984)gave a negative answer by showing that1-1/(ε^(r-1))is not a jump for r if r 3 and l>2r.After that,more non-jumps are found by using a method of Frankl and R?dl(1984).Motivated by an idea of Liu and Pikhurko(2023),in this paper,we show a method to construct maps f:[0,1)→[0,1)that preserve non-jumps,i.e.,ifαis a non-jump for r given by the method of Frankl and Rodl(1984),then f(α)is also a non-jump for r.We use these maps to study hypergraph Turán densities and answer a question posed by Grosu(2016).展开更多
文摘In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes offwithout jumping. In this study, we used 3-Dimensional （3D） high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be con- sidered as a main source of lift for heavy beetle.
文摘【目的】为使Heston(赫斯顿)模型能更细致地刻画标的资产价格演变规律以应对复杂多变的金融市场,提出了带跳的非仿射粗糙Heston模型。【方法】首先用傅里叶余弦级数(Fourier Cosine Series Expansion,Fourier-Cosine)方法分离期权密度函数和特征函数,用扰动法转化非线性偏积分微分方程,并用Adams-Bashforth-Moulton(亚当斯-巴什福斯-默尔顿)预测-校正法求解分数黎卡提方程,从而得到欧式看涨期权定价公式;然后用蒙特卡洛模拟结果验证解的有效性;最后分析了模型非仿射参数、粗糙参数和跳幅度参数对期权价格的影响,并对比了不同模型的定价结果。【结果】数值解与蒙特卡洛模拟结果相对误差为0.01%~0.2%,非仿射参数、粗糙参数和跳幅度参数对模型有不同程度的影响同时又相互制约。【结论】本模型刻画标的资产价格变化规律更具灵活性和多样性,从而为期权定价提供了理论支撑。
基金supported by National Natural Science Foundation of China(Grant No.12071077)。
文摘Let r≥2 be an integer.The real numberα∈[0,1)is a jump for r if there exists a constant c>0 such that for any?>0 and any integer m≥r,there exists an integer n_0(ε,m)satisfying any r-uniform graph with n≥n_0(ε,m)vertices and density at leastα+?contains a subgraph with m vertices and density at leastα+c.A result of Erd?s and Simonovits(1966)and Erdos and Stone(1946)implies that everyα∈[0,1)is a jump for r=2.Erdos(1964)asked whether the same is true for r≥3.Frankl and Rodl(1984)gave a negative answer by showing that1-1/(ε^(r-1))is not a jump for r if r 3 and l>2r.After that,more non-jumps are found by using a method of Frankl and R?dl(1984).Motivated by an idea of Liu and Pikhurko(2023),in this paper,we show a method to construct maps f:[0,1)→[0,1)that preserve non-jumps,i.e.,ifαis a non-jump for r given by the method of Frankl and Rodl(1984),then f(α)is also a non-jump for r.We use these maps to study hypergraph Turán densities and answer a question posed by Grosu(2016).
文摘考虑金融时间序列发生的跳跃、随机波动率和"杠杆效应",建立由不同Lévy过程驱动的非高斯OU随机波动模型.通过结构保持等价鞅测度变换和FFT技术,对不同Lévy过程驱动下的非高斯OU(non-Gaussian Ornstein-Uhlenbeck process)期权定价问题进行研究.同时,在结构保持等价鞅测度下,推导出不同Lévy过程驱动下BNS模型离散化表达形式,并构建了基于SMC(sequential Monte Carlo)的极大似然估计、联合样本估计、梯度-SMC估计的非高斯OU期权定价模型参数估计方法.实证研究中,采用近470万个S&P500期权价格数据,从样本内拟合效果、样本外预测、模型稳定性、综合矫正风险几个方面,对不同Lévy过程驱动的非高斯OU期权定价模型、参数估计方法以及期权定价效果进行全面系统研究.实证研究表明,所有模型对实值期权的定价效果要优于虚值期权.本文基于联合样本估计和梯度-SMC估计的非高斯OU期权定价模型具有明显的优势.
