Rare case of bilateral complex odontoma associated with mandibular bicuspids.

Among oral pathologic lesions, odontomas are the most common odontogenic tumor of the jaws and generally asymptomatic. They are mostly diagnosed as a result of routine radiographic investigation. In this report, we describe a very rare occurrence of bilateral complex odontoma in the region of the mandibular second premolar. Conservative surgical procedure was planned, and removal of the odontomas was carried out through the socket after extraction of the deciduous second molars, and the diagnosis was confirmed with a histopathological study.

Generalized variable projective synchronization of time delayed systems.

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of first order delay differential equations. Finally, a new neural oscillator is considered as a numerical example to show the effectiveness of the proposed scheme.

Comment on "Generalized projective synchronization in time-delayed systems: nonlinear observer approach" [Chaos 19, 013102 (2009); 20, 029902 (2010)].

In Chaos 19, 013102 (2009), the author proposed generalized projective synchronization for time delay systems using nonlinear observer and obtained sufficient condition to ensure projective synchronization for modulated time varying delay. There are concerns with the obtained conditions as the result was applicable only to trivial case of time varying delay τ[over dot](1)(t)=dτ(1)(t)/dt<1. In this paper, we note the drawbacks of the proposed sufficient condition. The new improved sufficient condition for ensuring the projective synchronization of time varying delayed systems is presented. The proposed new criteria have been verified by adopting the Ikeda system.

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay.

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.