We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer aided design. In order to study these motions new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Further it is shown that any such general moving frame motion is the product of a Frenet-S...

We study the thermal and mechanical behaviors of DNA denaturation in the frame of the mesoscopic Peyrard-Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of t...

OBJECTIVE The natural distribution and predictive accuracy of Bishop scores was evaluated to predict cesarean delivery (CD) in nulliparas between 37 and 42 weeks gestation. STUDY DESIGN Subjects underwent serial digital cervical examinations. The Bishop score was evaluated as a binary and continuous factor to predict CD at each gestational week beginning at 37 weeks. Bishop scores were catego...