Libration Points Inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball

The problem of the existence and stability of relative equilibria (libration points) of a uniformly rotating gravitating body, which is a homogeneous ball with a spherical cavity, is considered. It is assumed that the rotation is carried out around an axis perpendicular to the axis of symmetry of the body and passing through its center of mass. The libration points located inside the cavity are investigated. Families of both isolated and nonisolated relative equilibria are found. Their stability and bifurcations are investigated. Realms of possible motion are constructed.

Effectiveness Comparison of Supporting Surfaces in The Ball System for Vibration Isolation of High-Rise Buildings

The mechanical system «a hard homogeneous ball» between the movable upper and lower supports is considered. Its dynamic equations by plane motions are obtained under the action of an external harmonic perturbation. Various cases of support surfaces are considered.

Finding the most effective cerumenolytic

Aim:To conduct anin-vitrostudy to determine the most effective topical cerumenolytic.Method:Cerumen was collected from patients who attended the ENT out-patient clinic. The collected cerumen was formed into a homogeneous ball. Discs of wax were punched out and weighed to create samples of uniform shape and size. Each cerumen sample was placed in a tube which contained one of six test solutions. The tubes were observed at specific time points. Digital photographs were taken to record the degree of cerumen disintegration. The cerumen discs were then removed from the solutions, dried and re-weighed.Results:Distilled water caused the greatest reduction in the mass of the cerumen disc. Cerumen placed in distilled water and in sodium bicarbonate solution showed substantial disintegration at 12 hours. Cerumen placed in solutions containing oil-based agents showed no visible sign of disintegration and no reduction in dried weight.Conclusion:Distilled water resulted in the greatest degree of cerumenolysis. Oil-based cerumenolytics were ineffective.

Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

LetBXbe the unit ball in a complex Banach spaceX. AssumeBXis homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ballBntoBXassociated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.