活跃在解析几何中的“动点群”

什么叫“动点群”?就是题中的动点不止一个，而是有多个，某一动点运动时带动或制约其他一些点的运动，这些动点组成的群体称之为动点群，由于动点的增多，牵涉面加大，如果不掌握一些方法，往往在纷繁复杂的情况下理不出头绪来，解析几何“动点群”在高考中也时有出现，现就“动点群”

活跃在解析几何中的“动点群”

什么叫“动点群”?就是题中的动点不止一个，而是有多个．某一动点运动时带动或制约其它一些点的运动，这些动点组成的群体称之为动点群．由于动点的增多，牵涉面加大，如果不掌握一些方法，往往在纷繁复杂的情况下理不出头绪来．解析几何“动点群”在高考中也时有出现．现就“动点群”下求某一动点轨迹问题，以及求最值等问题谈一些方法．

活跃在解析几何中的动点群

什么叫“动点群”？就是题中的动点不止一个，而是有多个，某一动点运动时带动或制约其他一些点的运动，这些动点组成的群体称之为动点群。由于动点的增多，牵涉面加大，如果不掌握一些方法，往往在纷繁复杂的情况下理不出头绪来。现就“动点群”下求某一动点轨迹问题，以及求最值等问题谈一些方法。

A simulation study of sampling time point designing for therapeutic drug monitoring based on a population pharmacokinetic model

Aim To develop a method to estimate population pharmacokinetic parameters with the limited sampling time points provided clinically during therapeutic drug monitoring. Methods Various simulations were attempted using a one-compartment open model with the first order absorption to determine PK parameter estimates with different sampling strategies as a validation of the method. The estimated parameters were further verified by comparing to the observed values. Results The samples collected at the single time point close to the non-informative sampling time point designed by this method led to bias and inaccurate parameter estimations. Furthermore, the relationship between the estimated non-informative sampling time points and the values of the parameter was examined. The non-informative sampling time points have been developed under some typical occasions and the results were plotted to show the tendency. As a result, one non-informative time point was demonstrated to be appropriate for clearance and two for both volume of distribution and constant of absorption in the present study. It was found that the estimates of the non-informative sampling time points developed in the method increase with increases of volume of distribution and the decrease of clearance and constant of absorption. Conclusion A rational sampling strategy during therapeutic drug monitoring can be established using the method present in the study.

New Approach to Cluster Synchronization in Complex Dynamical Networks

In this paper, a distributed control strategy is proposed to make a complex dynamical network achieve cluster synchronization, which means that nodes in the same group achieve the same synchronization state, while nodes in different groups achieve different synchronization states. The local and global stability of the cluster synchronization state are analyzed. Moreover, simulation results verify the effectiveness of the new approach.

Packet Cache-Forward Method Based on Improved Bayesian Outlier Detection for Mobile Handover in Satellite Networks

In this paper, we propose a Packet Cache-Forward(PCF) method based on improved Bayesian outlier detection to eliminate out-of-order packets caused by transmission path drastically degradation during handover events in the moving satellite networks, for improving the performance of TCP. The proposed method uses an access node satellite to cache all received packets in a short time when handover occurs and forward them out in order. To calculate the cache time accurately, this paper establishes the Bayesian based mixture model for detecting delay outliers of the entire handover scheme. In view of the outliers' misjudgment, an updated classification threshold and the sliding window has been suggested to correct category collections and model parameters for the purpose of quickly identifying exact compensation delay in the varied network load statuses. Simulation shows that, comparing to average processing delay detection method, the average accuracy rate was scaled up by about 4.0%, and there is about 5.5% cut in error rate in the meantime. It also behaves well even though testing with big dataset. Benefiting from the advantage of the proposed scheme in terms of performance, comparing to conventional independent handover and network controlled synchronizedhandover in simulated LEO satellite networks, the proposed independent handover with PCF eliminates packet out-of-order issue to get better improvement on congestion window. Eventually the average delay decreases more than 70% and TCP performance has improved more than 300%.

Cluster Based Secure Dynamic Keying Technique for Heterogeneous Mobile Wireless Sensor Networks

In Heterogeneous Wireless Sensor Networks, the mobility of the sensor nodes becomes essential in various applications. During node mobility, there are possibilities for the malicious node to become the cluster head or cluster member. This causes the cluster or the whole network to be controlled by the malicious nodes. To offer high level of security, the mobile sensor nodes need to be authenticated. Further, clustering of nodes improves scalability, energy efficient routing and data delivery. In this paper, we propose a cluster based secure dynamic keying technique to authenticate the nodes during mobility. The nodes with high configuration are chosen as cluster heads based on the weight value which is estimated using parameters such as the node degree, average distance, node's average speed, and virtual battery power. The keys are dynamically generated and used for providing security. Even the keys are compromised by the attackers, they are not able to use the previous keys to cheat or disuse the authenticated nodes. In addition, a bidirectional malicious node detection technique is employed which eliminates the malicious node from the network. By simulation, it is proved that the proposed technique provides efficient security with reduced energy consumption during node mobility.

Lie Point Symmetry Algebras and Finite Transformation Groups of Baroclinic Mode for Rotating Stratified Flows

The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.

A Characteristic of Dedekind Groups

In this paper, we show that if a finite group G has a fixed-point-free weak power automorphism, then G is a Dedekind group.

Trajectory design for the Moon departure libration point mission in full ephemeris model

The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.

TRAVELING WAVE SOLUTIONS IN A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND DELAYS

This paper deals with the existence of traveling wave solutions in a three-species food-chain model with spatial diffusion and time delays due to gestation and negative feedback. By using a cross iteration scheme and Schauder＇s fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the trivial steady state and the positive steady state. Numerical simulations are carried out to illustrate the main results. In particular, our results extend and improve some known results.

Movement of Intransitive Permutation Groups Having Maximum Degree

Let G be a permutation group positive integer. Then the movement of G on a set Ω with no fixed points in Ω, and m be a is defined as move（G）：=supГ{[Г^9 ／Г｜｜g ∈ G}. It F was shown by Praeger that if move（G） = m, then ｜Ω｜ ≤ 3m ＋ t - 1, where t is the number of G-orbits on ≤. In this paper, all intransitive permutation groups with degree 3m ＋ t - 1 which have maximum bound are classified. Indeed, a positive answer to her question that whether the upper bound ｜Ω｜ = 3m ＋ t - 1 for ｜Ω｜ is sharp for every t 〉 1 is given.

The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case

For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.