Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness
Lei Wang Jinlong Yuan Yingfang Li Enmin Feng Zhilong Xiu
In this paper, the nonlinear enzyme-catalytic kinetic system of batch and continuous fermentation in the process of glycerol bio-dissimilation is investigated. On the basis of both glycerol and 1,3-PD pass the cell membrane by active and passive diffusion under substrate-sufficient conditions, we consider the delay of concentration changes on both extracellular substances and intracellular substances. We establish a nonlinear delay dynamical system according to the batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propanediol(1,3-PD) and we propose an identification problem, in which the biological robustness is taken as a performance index, constrained with nonlinear delay dynamical system. An algorithm is constructed to solve the identification problem and the numerical result shows the values of time delays of glycerol, 3-HPA, 1,3-PD intracellular and extracellular substances. This work will be helpful for deeply understanding the metabolic mechanism of glycerol in batch and continuous fermentation.
keywords: biological robustness parameter identification Nonlinear time-delay system continuous and batch fermentation.
Parameter identification and numerical simulation for the exchange coefficient of dissolved oxygen concentration under ice in a boreal lake
Qinxi Bai Zhijun Li Lei Wang Bing Tan Enmin Feng

Dissolved oxygen (DO) is one of the main parameters to assess the quality of lake water. This study is intended to construct a parabolic distributed parameter system to describe the variation of DO under the ice, and identify the vertical exchange coefficient K of DO with the field data. Based on the existence and uniqueness of the weak solution of this system, the fixed solution problem of the parabolic equation is transformed into a parameter identification model, which takes K as the identification parameter, and the deviation of the simulated and measured DO as the performance index. We prove the existence of the optimal parameter of the identification model, and derive the first order optimality conditions. Finally, we construct the optimization algorithm, and have carried out numerical simulation. According to the measured DO data in Lake Valkea-Kotinen (Finland), it can be found that the orders of magnitude of the coefficient K varying from 10-6 to 10-1 m2 s-1, the calculated and measured DO values are in good agreement. Within this range of K values, the overall trends are very similar. In order to get better fitting, the formula needs to be adjusted based on microbial and chemical consumption rates of DO.

keywords: Dissolved oxygen parameter identification numerical simulation partial differential equation frozen lakes
Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer
Yan Wang Yanxiang Zhao Lei Wang Aimin Song Yanping Ma

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

keywords: Optimal investment dividend insurance claim process maximum principle regular-singular stochastic control partial information
Renormalized entropy solutions for degenerate parabolic-hyperbolic equations with time-space dependent coefficients
Zhigang Wang Lei Wang Yachun Li
We study the well-posedness of renormalized entropy solutions to the Cauchy problem for general degenerate parabolic-hyperbolic equations of the form \begin{eqnarray*} \partial_{t}u+ \sum_{i=1}^{d}\partial_{x_{i}f_{i}(u,t,x)}= \sum_{i,j=1}^{d}\partial_{x_j}(a_{ij}(u,t,x)\partial_{x_i}u)+\gamma(t,x) \end{eqnarray*} with initial data $u(0,x)=u_{0}(x)$, where the convection flux function $f$, the diffusion function $a$, and the source term $\gamma$ depend explicitly on the independent variables $t$ and $x$. We prove the uniqueness by using Kružkov's device of doubling variables and the existence by using vanishing viscosity method.
keywords: device of doubling variables Degenerate parabolic-hyperbolic equation vanishing viscosity method. renormalized entropy solutions entropy solutions
Heuristics for parallel machine scheduling with batch delivery consideration
Leiyang Wang Zhaohui Liu
We consider the parallel machine scheduling problem in which the finished jobs need to be delivered to a customer in batches by a single vehicle. The goal is to minimize the makespan, i.e., the time by which the vehicle has delivered all jobs and returned to its initial location. We distinguish two types of batching strategies. The strategy of Type 1 permits the jobs processed on different machines to compose a delivery batch, and the strategy of Type 2 assumes that only the jobs processed on the same machine can compose a batch. For both types of the $m$-machine case, we propose $(2-\frac{1}{m})$-approximation algorithms respectively. For both types of the two-machine case, we obtain two improved $\frac{4}{3}$-approximation algorithms.
keywords: approximation algorithm. batch delivery Scheduling
Yan Gao Zhiqiang Xu Lei Wang Honglei Xu
This Special Issue of Numerical Algebra, Control and Optimization (NACO) is dedicated to Professor Enmin Feng for his important contributions in Applied Optimization, Optimal Control, System Identification and Large Scale Computing and their Engineering Applications and on the occasion of his 75th Birthday.

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Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems
Lei Wang Quan Yuan Jia Li
We consider a class of nearly integrable Hamiltonian systems with Hamiltonian being $H(\theta,I,u,v)=h(I)+\frac{1}{2}\sum_{j=1}^{m}\Omega_j(u_j^2-v_j^2)+f(\theta,I,u,v)$. By introducing external parameter and KAM methods, we prove that, if the frequency mapping has nonzero Brouwer topological degree at some Diophantine frequency, the hyperbolic invariant torus with this frequency persists under small perturbations.
keywords: Invariant tori non-degeneracy conditions KAM theory Hamiltonian systems.
Exponential-stability and super-stability of a thermoelastic system of type II with boundary damping
Lei Wang Zhong-Jie Han Gen-Qi Xu
In this paper, the stability of a one-dimensional thermoelastic system with boundary damping is considered. The theory of thermoelasticity under consideration is developed by Green and Naghdi, which is named as ``thermoelasticity of type II''. This system consists of two strongly coupled wave equations. By the frequency domain method, we prove that the energy of this system generally decays to zero exponentially. Furthermore, by showing the spectrum of the system is empty under certain condition and estimating the norm of the resolvent operator, we give a sufficient condition on the super-stability of this thermoelastic system. Under this condition, the solution to the system is identical to zero after finite time. Moreover, we also estimate the maximum existence time of the nonzero part of the solution. Finally, we give some numerical simulations.
keywords: Thermoelasticity spectrum semigroup exponential-stability super-stability.
A stochastic model for microbial fermentation process under Gaussian white noise environment
Yan Wang Lei Wang Yanxiang Zhao Aimin Song Yanping Ma
In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.
keywords: stochastic model stochastic differential equation Gaussian white noise microbial fermentation process.

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