The geometry of the secant caustic of a planar curve

The secant caustic of a planar curve M is the image of the singular set of the secant map of M. We analyze the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature.     

Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$\lim_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|<\frac14$$ and intermittent behaviors occur for $|c-\frac12|>\frac14$, where $0\le c\le 1$ is the coupling.     

FABEMD和改进局部能量窗口的红外中波和长波图像融合

针对探测波段为3.7～4.8 μm的中波红外图像和探测波段为8～14 μm长波红外图像融合过程中存在场景对比度低,显著性目标不够凸出,伪影引入严重的问题,采用快速自适应二维经验模态分解（FABEMD)对红外中波和长波图像进行多尺度分解以得到二维内蕴模函数(BIMFs)和残余分量(Residual)。对于每一层内蕴模函数选用改进的局部能量窗口融合规则,首先配置好加权算子以增加区域窗口中心像素的能量占比;选用不同的加权算子,经实验验证能有效突出红外中波和长波图像的能量特征信息;其次充分利用内蕴模函数的相位信息,当相位相反时,采用能量加权平均的方式,以解决融合系数的正负符号极性难以确定的问题;当相位相同时,判断二者的能量差距并依据差距大小选择设定的融合规则,融合规则基于红外中波和长波图像的灰度差异特性设定。对于残余分量则利用红外中波图像和改进区域能量窗口的最大对称环绕显著性权重图指导基础层系数的融合,自适应的局部环绕窗口充分利用了低频显著性信息,对无用背景的抑制效果也相当出色,能够在复杂背景图像中突出显著性对象,最终得到细节信息丰富,对比度明显的指导图像。最后通过FABEMD的逆变化重构过程得到融合图像,对4组不同背景、不同大小的红外中长波图像进行主观和客观性能评价,4组图像均来自多波段红外采集系统且都经过严格配准并和7种相关算法进行对比实验,在主观性能上显著性对象突出、清晰度度高;客观性能上在平均梯度和空间频率这两个评价指标上性能优异,验证了该算法的有效性。     

广义凸空间上重合点定理和极大极小不等式

利用已知的KKM型定理,在广义空间上得到若干个新的重合点定理和推广的Fan-Browder型不动点定理,并且讨论了Von Newmann-Sion型极大极小不等式.主要结果改进和推广了文献中的相应结论.     

逼近非扩张非自映像不动点（英文）

设E是一致凸Banach空间,K是E中非空闭凸集且是一个非扩张收缩核,T：K→E是具非空不动点集F（T）：={x∈K：Tx=x}的非扩张映像.设{α_n},{β_n},{γ_n},{α′_n},{β′_n},{γ′_n}是[0,1]中实数列满足α_n＋β_n＋γ_n=α′_n＋γ′_n＋γ′_n=1,对任意初值x_1∈K,定义{x_n}如下（ⅰ）如果对偶空间E＊具有Kadec-Klee性质,那么{x_n}弱收敛于T的某不动点x＊∈F（T）;（ⅱ）若T满足（A）条件,那么{x_n}强收敛于T的某不动点x＊∈F（T）.     

Schrödinger soliton from Lorentzian manifolds

In this paper, we introduce a new notion named as Schrödinger soliton. The so-called Schrödinger solitons are a class of solitary wave solutions to the Schrödinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a Kähler manifold N. If the target manifold N admits a Killing potential, then the Schrödinger soliton reduces to a harmonic map with potential from M into N. Especially, when the domain manifold M is a Lorentzian manifold, the Schrödinger soliton is a wave map with potential into N. Then we apply the geometric energy method to this wave map system, and obtain the local well-posedness of the corresponding Cauchy problem as well as global existence in 1+1 dimension. As an application, we obtain the existence of Schrödinger soliton solution to the hyperbolic Ishimori system.     

自伴矩阵代数上约当半三可乘映射

In this paper,we show that every injective Jordan semi-triple multiplicative map on the Hermitian matrices must be surjective,and hence is a Jordan ring isomorphism.     

Image encryption algorithm based on the multi-order discrete fractional Mellin transform

A multi-order discrete fractional Mellin transform (MODFrMT) is constructed and directly used to encrypt the private images. The MODFrMT is a generalization of the fractional Mellin transform (FrMT) and is derived by transforming the image with multi-order discrete fractional Fourier transform (MODFrFT) in log-polar coordinates, where the MODFrFT is generalized from the closed-form expression of the discrete fractional Fourier transform (DFrFT) and can be calculated by fast Fourier transform (FFT) to reduce the computation burden. The fractional order vectors of the MODFrMT are sensitive enough to be the keys, and consequently key space of the encryption system is enlarged. The proposed image encryption algorithm has significant ability to resist some common attacks like known-plaintext attack, chosen-plaintext attack, etc. due to the nonlinear property of the MODFrMT. Additionally, Kaplan-Yorke map is employed in coordinate transformation process of the MODFrMT to further enhance the security of the encryption system. The computer simulation results show that the proposed encryption algorithm is feasible, secure and robust to noise attack and occlusion.     

Double-image encryption based on discrete fractional random transform and chaotic maps

A novel double-image encryption algorithm is proposed, based on discrete fractional random transform and chaotic maps. The random matrices used in the discrete fractional random transform are generated by using a chaotic map. One of the two original images is scrambled by using another chaotic map, and then encoded into the phase of a complex matrix with the other original image as its amplitude. Then this complex matrix is encrypted by the discrete fractional random transform. By applying the correct keys which consist of initial values, control parameters, and truncated positions of the chaotic maps, and fractional orders, the two original images can be recovered without cross-talk. Numerical simulation has been performed to test the validity and the security of the proposed encryption algorithm. Encrypting two images together by this algorithm creates only one encrypted image, whereas other single-image encryption methods create two encrypted images. Furthermore, this algorithm requires neither the use of phase keys nor the use of matrix keys. In this sense, this algorithm can raise the efficiency when encrypting, storing or transmitting.     

F-(H2O)+CH3I Ligand Exchange Reaction Dynamics

Single hydration of the gas phase F\begin{document}$^-$\end{document}+CH\begin{document}$_3$\end{document}I\begin{document}$\rightarrow$\end{document} I\begin{document}$^-$\end{document}+CH\begin{document}$_3$\end{document}F reaction allows to probe solvent effects on a fundamental nucleophilic substitution reaction. At the same time, the addition of a solvent molecule opens alternative product channels. Here, we present crossed beam imaging results on the dynamics of the F\begin{document}$^-$\end{document}(H\begin{document}$_2$\end{document}O)+CH\begin{document}$_3$\end{document}I\begin{document}$\rightarrow$\end{document}[FCH\begin{document}$_3$\end{document}I]\begin{document}$^-$\end{document}+H\begin{document}$_2$\end{document}O ligand exchange pathway at collision energies between 0.3 and 2.6 eV. Product kinetic energies are constrained by the stability requirement of the weakly bound product complexes. This implies substantial internal excitation of the water molecule and disfavors efficient energy redistribution in an intermediate complex, which is reflected by the suppression of low kinetic energies as collision energy increases. At 0.3 eV, internal nucleophilic displacement is important and is discussed in light of the competing nucleophilic substitution pathways that form I\begin{document}$^-$\end{document} and I\begin{document}$^-$\end{document}(H\begin{document}$_2$\end{document}O).