Optimal harvesting policy of a stochastic predator–prey model with time delay

This paper concerns the optimal harvesting of a stochastic delay predator–prey model. Sufficient and necessary conditions for the existence of an optimal control are established. The optimal harvesting effort and the maximum value of the cost function are obtained as well. Some numerical tests are given to illustrate the main results.     

Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach

The linear operator plays an important role in the computational process of Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can be chosen to develop a solution. Hence, it is easy to introduce the modified/physical parameter dependent linear operators. The effective use of these operators has been judged through solving fluid flow problems. Modification in linear operators affects the solution and improves the computational efficiency of HAM for larger values of parameters. The convergence rate of the solution is rapid and several times higher resulting in less computational time.     

Study on autonomous navigation based on pulsar timing model

The basic principle of pulsar timing model was introduced, and the general relativistic corrections were analyzed when pulse time of arrival (TOA) was transferred to coordinate TOA at the Solar System Barycentre. Based on the shifting, an iterative method of autonomous position determination for spacecraft was developed. Accordingly, the linear form of the position offset equation was evolved. Using the initial estimated value of spacecraft’s position as the input of pulsar timing equation, through calculation of the offset between measured or transferred and predicted TOA, the position offset can be solved by Least Squares. At last, the main error sources including modeling error and parameters error were discussed. Supported by the National Defence Laboratory Foundation of China (Grant No. 9140C3601010901) and Science Foundation of Shaanxi Province (Grant No. 2007F12) and the Technology Specialism Foundation of Shaanxi Education Department of Shaanxi Province (Grant No. 07JK332), and the Innovative Research Plan of Xi’an University of Technology (Grant No. 105-210714)     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

Insights into stretching ratio and velocity slip on MHD rotating flow of Maxwell nanofluid over a stretching sheet: Semi-analytical technique OHAM

Main core part of the research is to develop a novel mathematical model of MHD-Maxwell nanofluid over a stretching and shrinking surface. The stretching ratio, velocity slip and convective boundary conditions are also incorporated. The PDE's with associative boundary conditions are deduced into coupled highly non-linear ODE's by utilizing suitable transformations. The deduced dimensionless sets of Ordinary differential equations are solved by Optimal-Homotopy Analysis Method (OHAM). Behavior of pertinent parameters on the velocity, temperature and concentration fields as well as important aspects skin friction, Nusselt number and Sherwood number are recorded in Table 2. Outcomes declared that role of stretching ratio plays a prominent role in stretching surfaces its clearly recorded in Table 1(a & b).     

Quantum model of selective multiphoton processes: The role of external (field) and internal (anharmonic coupling) detunings

Quantum equations of motion describing the energy transfer dynamics via intramolecular anharmonic coupling are presented and solved numerically. Dynamical features of the average excitations of a homogeneous system (SF₆) and a heterogeneous system (H/W) are quantitatively discussed in terms of the intramolecular vibrational relaxation (IVR) rates. Possible mechanisms of surface-enhanced desorption via low-power laser radiation are proposed.This work was supported in part by the Office of Naval Research, the Air Force Office of Scientific Research (AFSC), United States Air Force, under Grant AFOSR-82-0046 and the National Science Foundation under Grant No. CHE-8022874Camille and Henry Dreyfus Teacher-Scholar (1975–82)     

Decentralized optimum load frequency control of interconnected power systems

A new approach for designing a linear regulator for the problem of load frequency control (LFC) of interconnected power systems is developed. The control is specified to be of proportional-plus-integral (P-I) form and is only a function of the measurable states. The LFC problem is formulated as a parameter optimization problem.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

Optimal design of non-equilibrium experiments for genetic network interrogation

Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.     

Optimal risk transfer for agents with germs

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.     

On the optimal control problem for Schrödinger equation with complex potential

The existence and uniqueness for the solution of the problem of determining the v(x,t) potential in the Schrödinger equation from the measured final data ψ(x,T)=y(x) is investigated. For the objective functional , it is proven that the problem has at least one solution for α?0, and has a unique solution for α>0. The necessary condition for solvability the problem is stated as the variational principle.