A new 3-dimensional cephalometry model. A new 3-dimensional parameter analysis: the axis of inertia. A new idea: maxillofacial equilibrium

The authors propose a biomensurativ 3 D method based on the plotting of 8 anatomical landmarks situated on the trigeminal axis and the selection of teeth. In the analysis of this construction, we have employed mathematical tools unusual in developmental biology, the axis of inertia. The 3 D analysis allows to evidence the architectural, structural and functional balance of the dentomaxillofacial complex. This balance must be substituted to the normality concept to directly linked to cultural criterias and to the selection of mean parameters among culturally and ethnically homogeneous populations. Therapy does not have to lead to the normality of mean parameters but to the return or to the discovery of a real balance.     

A counterexample on continuous coprime factors

In Georgiou and Smith (1992), the following question was raised: Consider a linear, shift-invariant system on L₂[0, ∞). Let the graph of the system have Fourier transform (MN)H² (i.e., the system has a transfer function P=N/M) where M, N are elements of C_A={f∈H^∞: f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure |M|²+|N|²=1) in C_A? The author shows by example that this is not always possible     

Output feedback observation and control for visual servoing of VTOL UAVs

This paper considers the question of stabilizing vertical take‐off and landing (VTOL) unmanned aerial vehicles (UAVs) using a minimal and an inexpensive sensor suite. The sensor suite considered consists of rate gyros and a single embedded video camera system. The approach taken is based on the principles of dynamic image‐based visual servo control and extends the authors' earlier work by removing dependence on additional sensors, such as accelerometers and magnetometers. The technique presented has potential for mini‐UAVs evolving in urban areas where global positioning system signals may not be available. The control algorithms and coupled state observers are presented in details. The main result of the paper is synthesized in a theorem along with a rigorous stability analysis of the closed‐loop system. An estimate of the basin of attraction for the closed‐loop system is provided. Simulation results are performed to illustrate the performance of the proposed control. Copyright © 2010 John Wiley & Sons, Ltd.