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This research announcement continues the study of the symplectic homology of Weinstein manifolds undertaken by the authors [Bourgeois F, Ekholm T, Eliashberg Y (2009) arXiv:0911.0026] where the symplectic homology, as a vector space, was expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles. Here, we express the product and Batalin-Vilkovisky operator of symplectic homology in that context.

When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.

The authors studied the development of movement control in speed-accuracy tradeoff conditions in children aged 5-11 years and in adults performing cyclical pointings. Twelve difficulty levels (IDs), ranging from 2 to 6.58 bits, were defined (P. M. Fitts, 1954). Peak and time to peak velocity, acceleration, and deceleration, and acceleration profiles as a function of hand position (Hooke's portraits) were analyzed. Movement time decreased with age and was less affected by ID. Peak velocity and acceleration increased, acceleration and deceleration were decreasingly time consuming, and movement profiles turned to increased harmonicity with age and task easiness. Nevertheless, the developmental trends differed between parameters. Gain in velocity seemed chiefly dependent on improved muscular cooperation patterns before 7 years of age and on improved information processing from age 7 onward; achievement of an optimized strategy in the speed-accuracy tradeoff occurred at age 11 years.