Existence and stability of periodic solution of a stage‐structured model with state‐dependent impulsive effects

A single population growth model with stage‐structured and state‐dependent impulsive control is proposed. By using the Poincar'e map and the analogue of Poincaré's criterion, we prove the existence and the stability of positive order‐1 or order‐2 periodic solution. Moreover, we show that there is no periodic solution with order greater than or equal to three. Numerical results are carried out to illustrate the feasibility of our main results and the superiority of state feedback control strategy is also discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Transition from statistical Coulomb interactions to averaged space-charge effect

The statistical Coulomb interaction effect and the averaged space-charge effect, which broaden electron-beam size, have been studied to clarify their applicable regions and their transition region as a function of beam current. The beam size of a single beam segment can be analytically estimated by two theories based on different approaches: the expression of the trajectory displacement effect based on stochastic electron-electron interactions, and the beam radius equation based on the Coulomb repulsion force by averaged space charge. Both theories were compared with Monte Carlo simulation results for a beam-current ranging from 0.1 nA to 10 mA. It was confirmed that the beam size at the end of the focusing segment could be predicted by the expression of the trajectory displacement effect in a low beam current and by the beam radius equation in a high beam current. In addition, the beam sizes predicted by these theories were found to result in almost the same for a medium beam current. The theories transited as the beam-current increased.     

二级氢气炮靶室内杂质辐射特性的研究

利用光纤传输光信号，对二级轻气炮发射后靶室内的杂质光谱进行了探测。这种杂质谱大致包含了高温废气的热辐射谱、一些杂质原子激发后产生的特征谱和分子振动带谱。杂质辐射持续的时间大约为９０ｍｓ。利用这种测试手段，还获得了塑料样品的冲击发射光谱。杂质辐射和弹丸碰靶后样品的冲击辐射在时间上是相互重叠的。由于材料在冲击作用下的不透明性，废气的热辐射基本上不会干扰对冲击材料发射光谱的探测。     

Trajectory tracking control of variable length pendulum by partial energy shaping

This paper concerns a trajectory tracking control problem for a pendulum with variable length, which is an underactuated mechanical system of two degrees-of-freedom with a single input of adjusting the length of the pendulum. We aim to study whether it is possible to design a time-invariant control law to pump appropriate energy into the variable length pendulum for achieving a desired swing motion (trajectory) with given desired energy and length of the pendulum. First, we show that it is difficult to avoid singular points in the controller designed by using the conventional energy-based control approach in which the total mechanical energy of the pendulum is controlled. Second, we present a tracking controller free of singular points by using only the kinetic energy of rotation and the potential energy of the pendulum and not using the kinetic energy of the motion along the rod. Third, we analyze globally the motion of the pendulum and clarify the stability issue of two closed-loop equilibrium points; and we also provide some conditions on control parameters for achieving the tracking objective. Finally, we show numerical simulation results to validate the presented theoretical results.     

Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate

In this paper, a stage‐structured SI epidemic model with time delay and nonlinear incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease‐free equilibrium, and the existence of Hopf bifurcations are established. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease‐free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Copyright © 2013 John Wiley & Sons, Ltd.     

含阶段结构的单种群模型正周期解的存在性与全局吸引性

研究了具有阶段结构的非自治单种群模型.运用叠合度定理和Lyapunov函数的方法,得到了模型的正周期解的存在性和全局吸引性的充分条件.     

捕食者非密度制约的捕食食饵模型的持久性

主要讨论具有无穷时滞捕食者非密度制约的阶段结构的捕食食饵模型,通过应用分析的手段及比较原理,得到了系统的有界性,持久性和捕食者灭绝性的积分形式的判别条件,并且给出了一些生态方面的解释．把捕食者密度制约的一些重要结论推广到捕食者非密度制约的情形．最后通过实例的数值模拟和仿真验证结果的有效性．     

Enhanced linearized reduced-order models for subsurface flow simulation

Trajectory piecewise linearization (TPWL) represents a promising approach for constructing reduced-order models. Using TPWL, new solutions are represented in terms of expansions around previously simulated (and saved) solutions. High degrees of efficiency are achieved when the representation is projected into a low-dimensional space using a basis constructed by proper orthogonal decomposition of snapshots generated in a training run. In recent work, a TPWL procedure applicable for two-phase subsurface flow problems was presented. The method was shown to perform well for many cases, such as those with no density differences between phases, though accuracy and robustness were found to degrade in other cases. In this work, these limitations are shown to be related to model accuracy at key locations and model stability. Enhancements addressing both of these issues are introduced. A new TPWL procedure, referred to as local resolution TPWL, enables key grid blocks (such as those containing injection or production wells) to be represented at full resolution; i.e., these blocks are not projected into the low-dimensional space. This leads to high accuracy at selected locations, and will be shown to improve the accuracy of important simulation quantities such as injection and production rates. Next, two techniques for enhancing the stability of the TPWL model are presented. The first approach involves a basis optimization procedure in which the number of columns in the basis matrix is determined to minimize the spectral radius of an appropriately defined amplification matrix. The second procedure incorporates a basis matrix constructed using snapshots from a simulation with equal phase densities. Both approaches are compatible with the local resolution procedure. Results for a series of test cases demonstrate the accuracy and stability provided by the new treatments. Finally, the TPWL model is used as a surrogate in a direct search optimization algorithm, and comparison with results using the full-order model demonstrates the efficacy of the enhanced TPWL procedures for this application.     

多层螺旋CT多平面重建在胃肠道淋巴瘤诊断中的应用及与临床分期的相关性研究

为研究多层螺旋CT多平面重建在胃肠道淋巴瘤诊断中的应用价值及检测结果与临床分期的相关性,本次研究筛选我院2016年1月~2019年6月收治的50例经病理学检查证实的胃肠道淋巴瘤患者为观察组,另选同期50例非胃肠道淋巴瘤患者为对照组,均实施多层螺旋CT多平面重建,对比两组及观察组内不同组织类型、不同临床分期患者CT重建参数(图像客观噪声、信噪比)的差异,利用Pearson相关性分析法对CT重建参数与胃肠道淋巴瘤临床分期的相关性进行检验。病理学检查证实,50例胃肠道淋巴瘤患者中有弥漫性大B细胞淋巴瘤25例、黏膜相关淋巴瘤19例、小B细胞淋巴瘤4例、套细胞淋巴瘤2例,与多层螺旋CT多平面重建符合率差异无统计学意义(P>0.05)。观察组图像客观噪声低于对照组,信噪比高于对照组,差异有统计学意义(P<0.05)。观察组内不同组织类型患者、不同临床分期患者CT重建参数差异有统计学意义(P<0.05)。Pearson相关性分析结果提示,多层螺旋CT多平面重建参数中图像客观噪声与胃肠道淋巴瘤临床分期呈负向相关性(r=-0.74,P<0.05),信噪比与胃肠道淋巴瘤临床分期呈正相关性(r=0.71,P<0.05)。据此可得,在胃肠道淋巴瘤诊断中多层螺旋CT多平面重建取得的效果更佳且CT重建参数与临床分期密切相关,对于辨别组织类型和判断临床分期具有重要参照价值,值得推广。     

Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier–Stokes equations

We first prove the existence and regularity of the trajectory attractor for a three-dimensional system of globally modified Navier–Stokes equations. Then we use the natural translation semigroup and trajectory attractor to construct the trajectory statistical solutions in the trajectory space. In our construction the trajectory statistical solution is an invariant Borel probability measure, which is supported by the trajectory attractor and is invariant under the action of the translation semigroup. As a byproduct of the regularity of the trajectory attractor, we obtain the asymptotic regularity of the trajectory statistical solution in the sense that it is supported by a set in the trajectory space in which all weak solutions are in fact strong solutions.