Optimal control and stability analysis of an online game addiction model with two stages

In this paper, we establish a mathematical model of online game addiction with two stages to research the dynamic properties of it. The existence of all equilibria is obtained, and the basic reproduction number is calculated by the method of next-generation matrix. The global asymptotic stability of disease-free equilibrium (DFE) is proved by comparison principle, and the global asymptotic stability of endemic equilibrium (EE) is proved by constructing an appropriate Lyapunov function. Then we use the Pontryagin's maximum principle to find the optimal solution of the model, so that the number of infected people can be minimized. In numerical simulation, firstly, we validate the global stability of DFE and EE. Secondly, we consider three kind of control measures (treatment, isolation, and education) and divide them into four cases. The models with control and without control are solved numerically by using forward and backward sweep Runge-Kutta method. In order to achieve the best control effect, we suggest that three kind of measures should be used simultaneously according to the optimal control strategy.     

Numerical optimisation of chemotherapy dosage under antiangiogenic treatment in the presence of drug resistance

We consider a two-compartment model of chemotherapy resistant tumour growth under angiogenic signalling. Our model is based on the one proposed by Hahnfeldt et al. (1999), but we divide tumour cells into sensitive and resistant subpopulations. We study the influence of antiangiogenic treatment in combination with chemotherapy. The main goal is to investigate how sensitive are the theoretically optimal protocols to changes in parameters quantifying the interactions between tumour cells in the sensitive and resistant compartments, that is, the competition coefficients and mutation rates, and whether inclusion of an antiangiogenic treatment affects these results. Global existence and positivity of solutions and bifurcations (including bistability and hysteresis) with respect to the chemotherapy dose are studied. We assume that the antiangiogenic agents are supplied indefinitely and at a constant rate. Two optimisation problems are then considered. In the first problem a constant, indefinite chemotherapy dose is optimised to maximise the time needed for the tumour to reach a critical (fatal) volume. It is shown that maximum survival time is generally obtained for intermediate drug dose. Moreover, the competition coefficients have a more visible influence on survival time than the mutation rates. In the second problem, an optimal dosage over a short, 30-day time period, is found. A novel, explicit running penalty for drug resistance is included in the objective functional. It is concluded that, after an initial full-dose interval, an administration of intermediate dose is optimal over a broad range of parameters. Moreover, mutation rates play an important role in deciding which short-term protocol is optimal. These results are independent of whether antiangiogenic treatment is applied or not.     

An Uzawa-type algorithm for the coupled Stokes equations

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

Active control of time-delay in cutting vibration

The system dynamics of turning processes can be described by a delay differential equation. How to improve the stability and suppress the vibration of cutting is of an interesting topic. In this paper, a multiple time-delay controller is developed based on discrete optimal control method for the turning vibrations control. Numerical simulations are carried out to verify the efficiency of the controller. Results indicate the designed controller can suppress the cutting vibration efficiently and improve the stability of the cutting processes. The influence of designed time-delay and sampling time on the control performance is also discussed.     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

Modified characteristic finite difference fractional step method for moving boundary value problem of percolation coupled system

For the coupled system with moving boundary values of multilayer dynamicsof fluids in porous media,a characteristic finite difference fractional step scheme appli-cable to the parallel arithmetic is put forward.Some techniques,such as the change ofregions,the calculus of variations,the piecewise threefold quadratic interpolation,themultiplicative commutation rule of difference operators,the decomposition of high orderdifference operators,and the prior estimates,are adopted.The optimal order estimatesin the l2norm are derived to determine the error in the approximate solution.This nu-merical method has been successfully used to simulate the flow of migration-accumulationof the multilayer percolation coupled system.Some numerical results are well illustratedin this paper.     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.