Modelling the Sorption of 63Ni to Granitic Materials： Application of the Component Additive Model

The component additive modelling approach is based on summing the results from models already calibrated with pure mineral phases. The summation can occur as the sum of results for thermodynamic surface speciation models or as the sum of pseudo-thermodynamic models for adsorption on individual mineral phases. Static batch sorption experiments of 63Ni are with different granitic rocks and component minerals. XRD analyses have been used to calculate the percentage mineralogical composition of the granitic rocks. Sorption data has been modelled using non electrostatic correction models to obtain Rdfor the granitic rocks and mineral. Ra values for the granitic rocks predicted from the component additive model have been compared to experimental values. Results showed that predicted Rd values for granite adamellite, biotite granite and rapakivi granite were identical to the experimentally determined values, whereas, for graphic granite and grey Granite, the predicted and experimentally determined Ra values were much different. The results also showed a greater contribution to the bulk Raby feldspar while quartz showed the least contribution to the Rd.

A Stability Criterion for Singular Systems with Two Additive Time-varying Delay Components

The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities （LMIs）. Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.

Functional singular component analysis based functional additive models

We propose a method which uses functional singular component to establish functional additive models. The proposed methodology reduces the curve regression problem to ordinary(i.e., scalar) additive regression problems of the singular components of the predictor process and response process. Consistency of estimators for the nonparametric function and prediction are proved, respectively. A simulation study is conducted to investigate the finite sample performances of the proposed estimators.