Diffraction problems for quasilinear parabolic systems with boundary intersecting interfaces

Stability of Unilateral Posterior Crossbite Correction in the Mixed Dentition - an RCT-study with 3-year Follow-Up. Aim: To compare and evaluate long-term stability of crossbite correction with Quad Helix or expansion plate in the mixed dentition. Methods: In this RCT-study 35 patients with unilateral posterior crossbite were randomized to be treated with either Quad Helix or expansion plate. The inclusion criteria were: mixed dentition, unilateral posterior crossbite, no sucking habits or previous orthodontic treatment. Stability was evaluated after 3 years by study cast measurements. Twenty subjects with normal occlusion were included as controls. Success rate, maxillary and mandibular transverse dimensions, overjet, overbite and arch length were registered. Results: Stability was equal for the two treatment methods. Small, albeit significant, differences between the groups were assessed with reference to transverse dimensions. No significant difference was seen for overjet and overbite. The treated patients never reached the same transversal width as the normal control group. Conclusions: The long-term stability of posterior crossbite correction with Quad helix and expansion plate was equal. The maxillary width was greater in the control group than the treated groups

Optimal Control of Nonlocal Thermistor Equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterization of the optimal control. Uniqueness of solution to the optimality system, and therefore the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012; for publication in the International Journal of Contro