• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Journal of KIISE:Software and Applications
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• v.37 no.10
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• pp.736-744
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• 2010

Log data collected from mobile devices contain diverse and meaningful personal information. However, it is not easy to implement a context-aware mobile agent using this personal information due to the inherent limitation in mobile platform such as memory capacity, computation power and its difficulty of analysis of the data. We propose a method of selective inference for modular Bayesian Network for context-aware mobile agent with effectiveness and reliability. Each BN module performs inference only when it can change the result by comparing to the history module which contains evidences and posterior probability, and gets results effectively using a method of influence score of the modules. We adopt memory decay theory and virtual linking method for the evaluation of the reliability and conservation of casual relationship between BN modules, respectively. Finally, we confirm the usefulness of the proposed method by several experiments on mobile phones.