OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z of positive integers and for differential equations when the time scale is the set R of real numbers.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

基于虚拟源时间反转的经颅超声精确聚焦*

针对经颅超声难以精确聚焦的问题,本文研究了基于虚拟源的时间反转方法,建立颅骨二维数字模型,在聚焦目标处设置虚拟声源,利用时域有限差分法模拟超声时间反转过程,并考察基于虚拟源时间反转方法的聚焦效果。数值仿真结果表明,基于虚拟源的时间反转方法可以实现经颅超声的精确聚焦,聚焦强度和精度好于传统的相控聚焦;换能器中心频率和数量对聚焦效果的影响规律与相控聚焦时类似;该方法可以同时向多个焦点聚焦,并自适应调节各焦点处声压幅度。     

Existence of extremal solutions by approximation to a first-order initial dynamic equation with Carathéodory's conditions and discontinuous non-linearities*

This paper is devoted to the study of the existence of extremal solutions to a first-order initial value problem on an interval of an arbitrary time scale. We prove the existence of extremal solutions for problems satisfying Carathéodory's conditions. Moreover, they are approximated uniformly by a sequence of lower and upper solutions to this problem, respectively.

We also can warrant the existence and approximation of extremal solutions for the problem by relaxing their continuity properties.     

金银三层纳米管局域表面等离激元共振特性研究

相对于单一金属纳米材料,二金属复合纳米材料具有更大的潜在应用价值.基于时域有限差分方法,研究了SiO₂-Ag-Au和SiO₂-Au-Ag二金属三层纳米管的消光光谱,并对其局域表面等离激元共振(Localized Surface Plasmon Resonance,LSPR)特性进行了分析.研究发现,内核尺寸变大将导致上述两种金属纳米管LSPR峰红移;内层金属及外层金属壳层厚度增大均会导致其LSPR峰蓝移.银壳厚度变化对纳米管LSPR的调制作用大于金壳厚度变化造成的影响.上述现象可以利用等离激元杂化理论及自由电子和振荡电子变化的竞争机制进行分析.     

Evacuation assistants: An extended model for determining effective locations and optimal numbers

The present research presents an extended evacuation field model for simulating crowd emergency evacuation processes under the control of evacuation assistants. Furthermore, a communication field for describing the escape information transmission process and its effect on evacuees is introduced. The effective locations and optimal numbers of evacuation assistants as generated through the model are proposed in an effort to verify as well as enhance existing models. Results show the following. (1) Locating evacuation assistants near exits reduces the time delay for pre-evacuation. (2) There is an optimal number of evacuation assistants for achieving evacuation efficiency; having excessive numbers of evacuation assistants does not improve the evacuation efficiency, and they may result in evacuation time delay and hinder the evacuation efficiency. (3) As the number of evacuees increases, the number of evacuation assistants needed decreases.     

Neuron phase shift adaptive to time delay in locomotor control

Based on neurophysiological evidence, theoretical studies have shown that walking can be generated by mutual entrainment of oscillations of a central pattern generator (CPG) and a body. However, it has also been shown that the time delay in the sensorimotor loop destabilizes mutual entrainment, and results in the failure to walk. Recently, it has been reported that if (a) the neuron model used to construct the CPG is replaced by physiologically faithful neuron model (Bonhoeffer–Van der Pol type) and (b) the mechanical impedance of the body (muscle viscoelasticity) is controlled depending on the angle between two legs, the phase relationship between CPG activity and body motion could be flexibly locked according to the loop delay and, therefore, mutual entrainment can be stabilized. That is, locomotor control adaptive to the loop delay can emerge from the coupling between CPG and body. Here, we call this mechanism flexible-phase locking. In this paper, we construct a system of coupled oscillators as a simplified model of a walking system to theoretically investigate the mechanism of flexible-phase locking, and to analyze the simplified model. The analysis suggests that the following are required as the essential mechanism: (i) an asymptotically stable limit cycle of the coupling system of CPG and body and (ii) a sign difference between afferent and efferent coupling coefficients.     

Confirmatory analysis of Trenbolone using accurate mass measurement with LC/TOF-MS

The use of accurate mass measurement as a confirmation tool is examined on a TOF-MS and compared with confirmation using a triple quadrupole mass spectrometer (QqQ-MS). Confirmation of the identity of a substance using mass-spectrometric detection has been described. However, the use of accurate mass measurement for confirmatory analysis has not been taken into account. In this study, criteria for confirmation with accurate mass are proposed and feasibility is demonstrated. Mass accuracy better than 3 ppm of the quasi-molecular ion and a fragment and their relative ratios determined with LC/TOF-MS are compared to the criteria of two transition ions and their ratio of LC/QqQ-MS. The results show that these criteria can be met for Trenbolone in samples of bovine urine and that single MS accurate mass measurement is comparable to nominal mass MS/MS for confirmation. The increase in popularity and availability of LC/TOF-MS instruments and the ease, of which exact masses can be measured, make it important to formulate criteria for this type of instrumentation. It is shown in this study that accurate mass measurement can be used for confirmatory analysis. However, more experiments need to be conducted to demonstrate the applicability of accurate mass measurement in general for residue analysis.     

钒氧阴离子团簇与小分子碳氢化合物反应的实验和理论研究

为了在分子层次上揭示相关催化反应的机理, 人们对过渡金属氧化物团簇与碳氢化合物分子反应进行了大量研究. 相比于过渡金属氧化物团簇阳离子, 阴离子对一些碳氢化合物的活性弱得多, 因此研究还很少. 在本工作中, 我们通过激光溅射产生钒氧团簇阴离子VxOy, 产生的团簇在接近热碰撞条件下与烷烃(C2H6和C4H10)以及烯烃(C2H4和C3H6) 在一个快速流动反应管中进行反应, 飞行时间质谱用来检测反应前后的团簇分布. 在VxOy与烷烃的反应中, 生成了产物V2O6H-和V4O11H-; 在与烯烃的反应中, 产生了相应的吸附产物V4O11X-(X=C2H4或C3H6). 密度泛函理论计算表明: V2O-6和V4O-11可以活化烷烃(C2H6和C4H10)的C—H键, 也可以与烯烃(C2H4和C3H6)发生3+2环化加成反应形成一个五元环结构(-V-O-C-C-O-), C—H键活化与环加成反应都需经历可以克服的反应能垒. 理论计算与实验观测结果相符合. V2O-6和V4O-11团簇都具有氧原子自由基(O·或O-)的成键特征, 活性O-物种也经常出现在钒氧催化剂表面, 因而本研究在分子水平上, 揭示了表面活性氧物种与碳氢化合物反应的机理.