Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary

This paper is concerned with the spreading and vanishing phenomena in a diffusive intraguild (IG) predation model with intraspecific competition and free boundary in one dimensional space. The main objective is to obtain the asymptotic behavior of spread of an invasive or new IG prey species via a free boundary. In two cases, we prove a spreading‐vanishing dichotomy for this model, specifically, the IG prey species either successfully spreads to infinity as t→∞ at the front and survives in the new environment or spreads within a bounded area and dies out in the long run. The long time behavior of (R,N,P) and criteria for spreading and vanishing are also obtained. And then, we estimate the asymptotic spreading speed of the free boundary when spreading happens. Besides, two numerical examples are given to illustrate the impacts of initial occupying area and expanding capability on the free boundary.     

Isomorphism in Wavelets

Journal of Fourier Analysis and Applications - Two scaling functions $$\varphi _A$$ and $$\varphi _B$$ for Parseval frame wavelets are algebraically isomorphic, $$\varphi _A \simeq \varphi _B$$, if...     

Dynamics of a Predator-prey Model with Delay and Fear Effect

Recent manipulations on vertebrates showed that the fear of preda- tors, caused by prey after they perceived predation risk, could reduce the prey''s reproduction greatly. And it''s known that predator-prey systems with fear ef- fect exhibit very rich dynamics. On the other hand, incorporating the time delay into predator-prey models could also induce instability and oscillations via Hopf bifurcation. In this paper, we are interested in studying the com- bined effects of the fear effect and time delay on the dynamics of the classic Lotka-Volterra predator-prey model. It''s shown that the time delay can cause the stable equilibrium to become unstable, while the fear effect has a stabi- lizing effect on the equilibrium. In particular, the model loses stability when the delay varies and then regains its stability when the fear effect is stronger. At last, by using the normal form theory and center manifold argument, we derive explicit formulas which determine the stability and direction of periodic solutions bifurcating from Hopf bifurcation. Numerical simulations are carried to explain the mathematical conclusions.     

Rapid transfer alignment of laser SINS using quaternion based angular measurement

A novel rapid transfer alignment algorithm for laser strapdown inertial navigation system (SINS) is studied. Transfer alignment have typically relied on velocity measurements from the master SINS as the source of alignment information, but lever arm error must be compensated accurately while velocity information is utilized, all most every quaternion based error model is nonlinear, so nonlinear filtering algorithms are need, suffering from computational complex and large error. Aim at these problems, a novel improved rapid transfer alignment algorithm formulation is presented, applying quaternion to built the process and measurement models, the improvement employs a special manipulation of the measurement equation results in a linear pseudo-measurement equation, thus the classical linear Kalman filter is employed to estimate the state, need not lever arm error compensation, results in the reduce of computational burden. Observability analysis of this new transfer alignment algorithm has been done based on the piece-wise constant system (PWCS) method, results show that the presented algorithm can accomplish the initial alignment task perfectly. A transfer alignment simulation system is also developed for the evaluation and analysis of the presented algorithm, simulation results are confirmed with the theoretical conclusion, which can achieve the transfer alignment accuracy about 1 mrad within 10 s.     

Wavelength dependent damage thresholds of a bandpass filter under femtosecond laser irradiation

Laser induced damage thresholds of a bandpass filter with TiO₂/SiO₂ coatings are measured, with the laser delivering wavelength tunable, high-repetition rate, and ultrashort pulses. The multiple wavelengths are selected within the transitional region between the filter passband and stopband. A method that scans the sample along the focused laser beam is employed to vary the spot size on the coating and, consequently, change the fluence. The damage is detected by both a CCD camera and by monitoring the transmitted power simultaneously. During the experiment, an increase in the filter transmission was observed prior to damage occurrence. We demonstrate that damage induced on the coating by the high repetition rate, femtosecond pulses is governed by macroscopic thermal behavior rather than by critical free electron density in the conduction band. In addition, the process of energy deposition is determined by intrinsic nature of the coating materials. Further analysis indicates that the thresholds as a function of wavelength are determined by the combination of the properties of TiO₂, interference field in the coating stack, and thermal effects. Moreover, we attribute the observed increase in the coating transmission to these thermal effects rather than ionization processes.     

楔形盒染料掺杂胆甾相液晶激光器研究

设计制作了楔形盒掺杂激光染料PM580的胆甾相液晶器件, 研究了激光辐射行为. 在楔形液晶盒中出现了一系列与楔棱平行的向错线和不同规则形状的晶畴, 胆甾相液晶形成了平面态排列. 采用固体Nd:YAG倍频532 nm 波长激光作为抽运光, 获得调谐精度约1 nm, 调谐范围约17 nm的一维波长可调谐激光器. 楔形盒中, 液晶扭曲力与取向膜表面锚定力相互平衡的过程中胆甾相液晶螺距伸张, 光子禁带位置移动, 从而调谐光子禁带边沿出射激光波长. 关键词： 胆甾相液晶 楔形盒 激光辐射     

Semi-Synthesis and In Vitro Anti-Cancer Evaluation of Magnolol Derivatives

Magnolol (MAG), a biphenolic neolignan, has various biological activities including antitumor effects. In this study, 15 MAG derivatives were semi-synthesized and evaluated for their in vitro anticancer activities. From these derivatives, compound 6a exhibited the best cytotoxic activity against four human cancer cell lines, with IC₅₀ values ranging from 20.43 to 28.27 μM. Wound-healing and transwell assays showed that compound 6a significantly inhibited the migration and invasion of MDA-MB-231 cells. In addition, Western blotting experiments, performed using various concentrations of 6a, demonstrated that it downregulates the expression of HIF-1α, MMP-2, and MMP-9 in a concentration-dependent manner. Overall, these results suggest that substituting a benzyl group having F atoms substituted at the C2 position on MAG is a viable strategy for the structural optimization of MAG derivatives as anticancer agents.     

Symmetric and Anti-Symmetric Solitons of the Fractional Second-and Third-Order Nonlinear Schrodinger Equation

The fractional second-and third-order nonlinear Schr?dinger equation is studied,symmetric and antisymmetric soliton solutions are derived,and the influence of t...     

成分和厚度的依赖

通过调整Mn的成分，系统地研究了Ni81Fe19/Ni100-xMnx双层膜的磁学性质，特别是交换偏置场(Hex)的变化.当Ni100-xMnx中Mn的原子百分比在534%到600%之间时，对于150nm的Ni81Fe19，得到了最大的交换偏置场175kA/m，同时由于Mn对Ni81Fe19层的扩散所造成的磁矩的降低小于20%；高角x射线衍射证明Ni100-xMnx的晶格常数随着Mn成分的改变而变化，Mn含量越多，其晶格常数越大；制备态Ni100-xMnx膜晶格常数与θ相NiMn膜晶格常数的接近程度与NiMn膜θ相形成的容易程度相对应.也研究了交换偏置场随着Ni１００-xMnx厚度的变化，第一次得到了当Ni100-xMnx中Mn的原子百分比为706%时，Ni81Fe19(150nm)/Ni100-xMnx(90nm)双层膜在经过240℃，5h退火后，可以有80kA/m的交换偏置场，此时铁磁层磁矩的大小几乎不变. 关键词： Ni81Fe19/Ni100-xMnx 交换偏置场     

光学渡越辐射电子束发散角二维拟合数值分析

光学渡越辐射具有良好的方向性,通过对光学渡越辐射空间分布曲线进行拟合可以对束流发散角进行计算。采用理论计算的方法,分析了电子入射到金属-介质界面时,入射角变化对光学渡越辐射二维空间分布的影响。计算分析表明,光学渡越辐射在特定偏振方向上的分布并不仅仅由电子束在该方向的发散角分量决定,同时还受到其他方向发散角分量的影响。计算对比了电子束散角一维分布和二维分布模型下光学渡越辐射空间分布的差异。结果表明,采用一维分布模型拟合计算的电子束均方根发散角存在偏差,较二维分布拟合结果偏小。