# American Institute of Mathematical Sciences

ISSN:
2155-3289

eISSN:
2155-3297

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## Numerical Algebra, Control & Optimization

2014 , Volume 4 , Issue 2

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2014, 4(2): 93-101 doi: 10.3934/naco.2014.4.93 +[Abstract](1503) +[PDF](295.7KB)
Abstract:
A sufficient condition of Euclidean rings is given by polynomial optimization. Then, through computation, we give all norm-Euclidean square number fields, four examples of norm-Euclidean cubic number fields and two examples of norm-Euclidean cyclotomic fields, with the absolute of a norm less than 1 over the corresponding box, respectively.
2014, 4(2): 103-113 doi: 10.3934/naco.2014.4.103 +[Abstract](1702) +[PDF](370.8KB)
Abstract:
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.
2014, 4(2): 115-132 doi: 10.3934/naco.2014.4.115 +[Abstract](1610) +[PDF](525.5KB)
Abstract:
In this paper, we consider a non-preemptive task scheduling problem for unrelated parallel processors (UPP) with the objective of minimizing the makespan. We address priority consideration as an added feature to the basic task characteristics of UPP scheduling. A mixed integer linear programming model is developed to obtain an optimal solution for the problem. Computational testing is implemented using AIMMS 3.10 package and CPLEX 12.1 as the solver. Computational results show that the proposed MILP model is effective and produces optimal results with up to 100 tasks run on 5 processors with an average solution time of less than an hour.
2014, 4(2): 133-140 doi: 10.3934/naco.2014.4.133 +[Abstract](1348) +[PDF](290.2KB)
Abstract:
In this paper, the author introduces generalized cone proximal $\varphi$-cyclic contraction pairs in cone metric spaces and considers the existence and convergence of best proximity point for a pair in cone metric spaces. His results generalize the corresponding results in [1, 4, 5, 7, 8, 12, 13, 15].
2014, 4(2): 141-150 doi: 10.3934/naco.2014.4.141 +[Abstract](1497) +[PDF](370.8KB)
Abstract:
In this paper a weighted-path-following interior-point algorithm for linear complementarity problem over symmetric cones is proposed that uses new search directions. The complexity results of the new algorithm derived and proved that the proposed algorithm has quadratically convergent with polynomial-time. We conclude that following the central path yields to the best iteration bound in this case as well.
2014, 4(2): 151-179 doi: 10.3934/naco.2014.4.151 +[Abstract](1525) +[PDF](506.6KB)
Abstract:
Fault detection and identification (FDI) are important tasks in most modern industrial and mechanical systems and processes. Many of these systems are most naturally modeled by differential-algebraic equations (DAE). This paper addresses active fault detection in DAE. A technique is presented to calculate an auxiliary test signal guaranteeing detection, assuming bounded additive noise. An efficient real time detection algorithm is also provided as are example simulations. The extension to model uncertainty is discussed.