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In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform invariance preserving steplength thresholds is proved when the invariant sets are polyhedra,… (More)
A rapid micropropagation system for Scabiosa tschiliensis Grunning, an ethnic medicinal plant, has been developed. Calluses were induced from leaf and petiole explants on Murashige and Skoog (MS) medium supplemented with 2.0 mg l−1 thidiazuron and 0.5 mg l−1 2,4-dicholorophenoxyacetic acid. In this medium, callus induction rate was about 94.05 %.… (More)
Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is… (More)
Mogroside IIE is a bitter triterpenoid saponin which is the main component of unripe Luo Han Guo fruit and a precursor of the commercially available sweetener mogroside V. In this study, we developed an enzymatic glycosyl transfer method, by which bitter mogroside IIE could be converted into a sweet triterpenoid saponin mixture. The reactant concentration,… (More)
Recently, Horváth, Song, and Terlaky [A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation] proposed a novel unified approach to study, i.e., invariance conditions, sufficient and necessary conditions, under which some convex sets are invariant sets for linear dynamical systems. In this… (More)
The characteristic invariant manifolds (CIMs) is an important means for the calculation of credible region. The adjoint system method has been proposed for computing the controlling unstable equilibrium point. We derive the CIMs of the adjoint system and an example is given.