Lachance. M.A. and A.J. Schwartz. Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149. We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points. We provide methods for distinguishing the cases and constructing the parabolas.

In this paper we study measure preserving flows associated with nonholonomic systems with internal degrees of freedom. Our approach reveals geometric reasons for existence of measures in the form of an integral invariant with smooth density that depends on the internal configuration of the system.

Tensegrity structures are composed of tension compression components, where the compression components (bars) are discontinuously enclosed within continuous tensile components (cables). From an engineering point of view, a tensegrity structure is characterized by geometric non-linearity and large displacements under loading. Therefore, its prestressed shape and deformation under loading are the...

Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equili...

Extended, fading emissions in multi-wavelength are observed following Gamma-ray bursts (GRBs). Recent broadband observational campaigns led by the Swift Observatory reveal rich features of these GRB afterglows. Here we review the latest observational progress and discuss the theoretical implications for understanding the central engine, composition, and geometric configuration of GRB jets, as w...

A standard technique for numerically solving elliptic partial differential equations on structured grids is to discretize them, and, then, to apply an efficient geometric multi-grid solver. Unfortunately, finding the optimal choice of multi-grid components and parameter settings is challenging and existing auto-tuning techniques fail to explain performanceoptimal settings. To improve the state ...

In a delayed matching task, the influence of spatial congruence between study and test on visual short-term memory for geometric figures and words was investigated. Subjects processed series of pictures which showed three words or three geometric figures arranged as rows or as triangular configurations. At test, the elements were presented in the identical or in the alternative configuration as...

A standard technique to numerically solve elliptic partial differential equations on structured grids is to discretize them via finite differences and then to apply an efficient geometric multi-grid solver. Unfortunately, finding the optimal choice of multi-grid components and parameters is challenging and platform dependent, especially, in cases where domain knowledge is incomplete. Auto-tunin...

We propose a representation and a planning algorithm able to deal with problems integrating task planning as well as motion and manipulation planning knowledge involving several robots and objects. Robot plans often include actions where the robot has to place itself in some position in order to perform some other action or to “modify” the configuration of its environment by displacing objects....

A new cylindrical capacitive sensor (CCS) design for the displacement measurement of precision active magnetic bearing (AMB) spindle is presented in this paper. This research is motivated by the problem that the existing 4-segment CCS is still sensitive to the third harmonic component of the geometric errors of a rotor. The procedure of designing a new CCS starts from the modeling and error ana...