The Peter principle revisited: A computational study

In the late sixties the Canadian psychologist Laurence J. Peter advanced an apparently paradoxical principle, named since then after him, which can be summarized as follows: ‘Every new member in a hierarchical organization climbs the hierarchy until he/she reaches his/her level of maximum incompetence’. Despite its apparent unreasonableness, such a principle would realistically act in any organization where the mechanism of promotion rewards the best members and where the competence at their new level in the hierarchical structure does not depend on the competence they had at the previous level, usually because the tasks of the levels are very different to each other. Here we show, by means of agent based simulations, that if the latter two features actually hold in a given model of an organization with a hierarchical structure, then not only is the Peter principle unavoidable, but also it yields in turn a significant reduction of the global efficiency of the organization. Within a game theory-like approach, we explore different promotion strategies and we find, counterintuitively, that in order to avoid such an effect the best ways for improving the efficiency of a given organization are either to promote each time an agent at random or to promote randomly the best and the worst members in terms of competence.     

Tracking control of high-performance robots via stabilizing controllers for uncertain systems

The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.     

Second order parabolic equations in nonvariational form: Boundary Harnack principle and comparison theorems for nonnegative solutions

Summary We study non-divergence parabolic equations with continuous coefficients in a cylinder with Lipschitzian cross-section. A Harnack type inequality at the boundary is established for nonnegative solutions vanishing in a surface neighborhood of a boundary point. As an application of this result we show that (in a C ² cylinder) all nonnegative solutions which vanish in a surface neighborhood of a point on the lateral side must go to zero at an equivalent rate. We present some consequences of these results which find application to the study of non-tangential behavior of nonnegative solutions.The author was partially supported by the Italian C.N.R., G.N.A.F.A.     

Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

We consider the class of minimal surfaces given by the graphical strips ${{\mathcal S}}We consider the class of minimal surfaces given by the graphical strips S{{\mathcal S}} in the Heisenberg group \mathbb H¹{{\mathbb {H}}^1} and we prove that for points p along the center of \mathbb H¹{{\mathbb {H}}^1} the quantity \fracs_H(S?B(p,r))r^Q-1{\frac{\sigma_H(\mathcal S\cap B(p,r))}{r^{Q-1}}} is monotone increasing. Here, Q is the homogeneous dimension of \mathbb H¹{{\mathbb {H}}^1} . We also prove that these minimal surfaces have maximum volume growth at infinity.     

Local Behavior of <Emphasis Type="Italic">p</Emphasis>-harmonic Green’s Functions in Metric Spaces

We describe the behavior of p-harmonic Green’s functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.     

Geometric second derivative estimates in Carnot groups and convexity

We prove some new a priori estimates for H ₂-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H ₂-convex function in vanishing on ∂Ω one has

Efficient and simple synthesis of 6-aryl-1,4-dimethyl-9H-carbazoles

A synthetic method for the preparation of 6-aryl-1,4-dimethyl-9H-carbazoles involving a palladium catalyzed coupling reaction of 1,4-dimethyl-9H-carbazole-6-boronic acids and (hetero)aryl halides is described.