TIME PERIODIC SOLUTIONS OF NON-ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC SYSTEM

In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in Rn. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n ≥ 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.     

PERIODIC SOLUTIONS TO A PREDATOR-PREY SYSTEM WITH HOLLING IV FUNCTIONAL RESPONSE ON TIME SCALES

In this paper, a non-autonomous predator-prey model with Holling IV functional response is investigated. By the Gaines and Mawhin’s continuation theorem of coincidence degree theory on time scales, sufficient conditions for the existence of periodic solutions are obtained.     

EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF DYNAMIC EQUATIONS WITH PARAMETERS ON TIME SCALES

In this paper, we consider a three-point boundary value problem for a system of dynamic equations with parameters on time scales. Applying fixed point theorems,we give the existence of positive solutions to the problem. Examples are also included to illustrate our results.     

THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

In this paper,we consider an inflow problem for the non-isentropic Navier-StokesPoisson system in a half line(0,∞).For the general gas including ideal polytropic gas,we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4×4 system of autonomous ordinary differential equations.We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.     

基于重新排序时间错位限制下的最小化总完工时间的平行分批排序（英文）

In the rescheduling on a single machine, a set of the original jobs has already been scheduled, in order to make a given objective function is optimal. The decision maker needs to insert the new jobs into the existing schedule without excessively disrupting it. A batching machine is a machine that can handle up to some jobs simultaneously. In this paper,we consider the total completion time under a limit on the sequence disruptions for parallel batching based on rescheduling. For the parallel batching problem based on rescheduling, we research the properties of feasible schedules and optimal schedules on the total completion time under a limit on the maximum time disruptions or total time disruptions, in which the jobs are sequenced in SPT order, and give out the pseudo-polynomial time algorithms on the number of jobs and the processing time of jobs by applying the dynamic programming method.     

Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.     

分数阶时滞微分系统的滑模控制(英文)

The problem of sliding mode control for fractional differential systems with statedelay is considered.A novel sliding surface is proposed and a controller is designed correspondingly,such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point.And the stability of the proposed control design is discussed.     

ASYMPTOTIC BEHAVIOR OF DYNAMIC EQUATIONS ON A PERIODIC TIME SCALES

We first prove some basic results on the periodic time scales, then on a special but practical periodic time scales T =∪[k(a + b),k(a + b) + a], the asymptotic behavior of x△ = px is explored with specific emphasis given to how the graininess of the time scales affects stability. At last, we analyze the asymptotic properties of the solutions of planar linear dynamic system, and obtain some sufficient conditions for the stability of the equalibium (0,0).     

Positivity and boundedness preserving schemes for the fractional reaction-difusion equation

In this paper,we design a semi-implicit scheme for the scalar time fractional reaction-difusion equation.We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes,and numerically show that the convergence orders are 1 in time and 2 in space.As a concrete model,the subdifusive predator-prey system is discussed in detail.First,we prove that the analytical solution to the system is positive and bounded.Then,we use the provided numerical scheme to solve the subdifusive predator-prey system,and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.     

一类具大初值的半线性抛物方程组的生存跨度

The paper deals with heat equations coupled via exponential nonlinearities. We are interested in the life span(or blow-up time) and obtain the maximal existence time of blow-up solutions. Our proof is based on the comparison principle and Kaplan’s method.     

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the discrete states have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, stationary point set of a Hankel matrix with fixed dimensions built from the Markov parameters is examined. Splitting of this set into disjoint intervals and complements reveals linear time-invariant dynamics prevailing on these intervals. Clustering over a feature space permits recovery of the discrete states up to similarity transformations which is complete if a unimodality assumption holds and the discrete states satisfy a residence requirement. In the third stage, the switching sequence is estimated by three schemes. The first scheme is non-iterative in time. The second scheme is based on matching the estimated and the true Markov parameters of the SLS system over segments. The third scheme works also on the same principle, but it is a discrete optimization/hypothesis testing algorithm. The three schemes operate on different dwell time and model structure requirements, but the dwell time requirements are weaker than that needed to recover the discrete states. In the fourth stage, the discrete state estimates are brought to a common basis by a novel basis transformation which is necessary for predicting outputs to prescribed inputs. Robustness of the four-stage algorithm to amplitude bounded noise is studied and it is shown that small perturbations may only produce small deviations in the estimates vanishing as noise amplitude diminishes. Time complexities of the stages are also studied. A numerical example illustrates the derived results.     

Picone type identities and definiteness of quadratic functionals on time scales

In this paper we derive a new sufficient condition for the nonnegativity of time scale quadratic functionals associated to time scale symplectic systems. To establish this result, a new global Picone formula is derived. Another proof of a special case of the result is shown to be obtained via a Sturmian comparison technique. Furthermore, we derive several new Picone type identities which, in particular, do not impose a certain delta-differentiability assumption, and we survey known ones from the literature. The results in this paper complete our earlier work on the definiteness of a time scale quadratic functional in terms of its corresponding time scale symplectic system.     

Optimal control for parallel queues with a single batch server

We consider a queueing system with multiple Poisson arrival queues and a single batch server that has infinite capacity and a fixed service time. The problem is to allocate the server at each moment to minimize the long-run average waiting cost. We propose a Cost-Arrival Weighted (CAW) policy for this problem based on the structure of the optimal policy of a corresponding fluid model. We show that this simple policy enjoys a superior performance by numerical experiments.     

Leader-following consensus for networks with single- and double-integrator dynamics

In the paper, consensus protocols for networks of dynamic agents with single- and double-integrator dynamics are proposed. We provide necessary and sufficient conditions for leader-following consensus problem of the presented models. In order to examine the studied cases in a general way the time scale calculus is employed to get the results. The method used in the proofs is based on spectral characterization of stability for time invariant linear systems on time scales. All the results are enriched in illustrative examples and numerical simulations.     

实时双机系统的可靠性分析

对于强实时双机系统，应该建立考虑影响系统可靠性因素较多的模型。本文，在给出可用度改进因子（ＡＩＦ）的定义基础上，建立了强实时双机系统的可靠性模型，用于综合考虑故障判别成功率（Ｃ）和故障判别时间（１／β）对系统可用度的影响，研究结果表明：应分别建立强实时和弱实时双机系统的可靠性模型，不能将二者混淆。     

Multi-period efficiency and Malmquist productivity index in two-stage production systems

Conventional two-stage data envelopment analysis (DEA) models measure the overall performance of a production system composed of two stages (processes) in a specified period of time, where variations in different periods are ignored. This paper takes the operations of individual periods into account to develop a multi-period two-stage DEA model, which is able to measure the overall and period efficiencies at the same time, with the former expressed as a weighted average of the latter. Since the efficiency of a two-stage system in a period is the product of the two process efficiencies, the overall efficiency of a decision making unit (DMU) in the specified period of time can be decomposed into the process efficiency of each period. Based on this decomposition, the sources of inefficiency in a DMU can be identified. The efficiencies measured from the model can also be used to calculate a common-weight global Malmquist productivity index (MPI) between two periods, in that the overall MPI is the product of the two process MPIs. The non-life insurance industry in Taiwan is used to verify the proposed model, and to explain why some companies performed unsatisfactorily in the specified period of time.     

Continuous output integral sliding mode control for switched linear systems

A continuous output integral sliding mode robustification methodology for switched uncertain linear time invariant systems with state-dependent location transitions and dwell time is presented. The robustifying methodology is based on the adjustment of the super-twisting algorithm gains to assure the convergence time and the attenuation of the chattering. The use of the adjusted STA allows to reconstruct the states theoretically exactly before half of the dwell time without the usage of filters, via a continuous cascade observer. Moreover, it allows to generate a continuous control signal that is turn on after the observer has converged, guaranteeing theoretically exact compensation of the matched uncertainties/perturbations before the dwell time.     

A disruption recovery model for a single stage production-inventory system

This paper presents a newly developed disruption recovery model for a single stage production and inventory system, where the production is disrupted for a given period of time during the production up time. The model is categorized as a constrained non-linear optimization program which we have solved using an efficient heuristic developed in this paper. The model was also solved using an evolutionary algorithm and a comparison of the results from both methods was performed. The heuristic was able to accurately solve the model with significantly less time compared to the evolutionary algorithm. It can be shown that the optimal recovery schedule is dependent on the shortage cost parameters, as well as the extent of the disruption. The proposed model offers a potentially useful tool to help manufacturers decide on the optimal recovery plan in real time whenever the production system experiences a sudden disruption.     

Finite‐time stability of fractional‐order stochastic singular systems with time delay and white noise

In this article, the finite‐time stochastic stability of fractional‐order singular systems with time delay and white noise is investigated. First the existence and uniqueness of solution for the considered system is derived using the basic fractional calculus theory. Then based on the Gronwall's approach and stochastic analysis technique, the sufficient condition for the finite‐time stability criterion is developed. Finally, a numerical example is presented to verify the obtained theory. © 2016 Wiley Periodicals, Inc. Complexity 21: 370–379, 2016     

四阶杆振动方程的一族高稳定的十字架格式

用辛几何的观点得到了四阶杆振动方程的一族十字架辛格式，对于四阶杆振动方程的稳定条件不一定随时间方向的精度的提高而放宽，而随空间方向精度的提高稳定范围缩小．数值例子表明单辛算法具有良好的数值稳定性．