the aim of this study was to determine the most suitable shaking frequency and amplitude for shake harvesting lime fruit (c. aurantifolia). a tractor mounted limb shaker with adjustable shaking frequency and amplitude, powered by the tractor power-take-off shaft was designed and developed for this study. the rotating input power was transmitted to the shaker flywheel through a multiple sheave v...

The aim of this study was to determine the most suitable shaking frequency and amplitude for shake harvesting lime fruit (C. aurantifolia). A tractor mounted limb shaker with adjustable shaking frequency and amplitude, powered by the tractor power-take-off shaft was designed and developed for this study. The rotating input power was transmitted to the shaker flywheel through a multiple sheave v...

The least-area hypersurface enclosing and separating two given volumes in R is the standard double bubble.

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.

We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic three-torus T 3. For comparable small volumes, we prove that an area minimizing double bubble in T 3 is the standard double bubble from R 3 .

The classical isoperimetric inequality in R states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120◦.

The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2π/3.

In this paper, we show that the so-called “double bubbles” are not downward dense in the d.c.e. degrees. Here, a pair of d.c.e. degrees d1 > d2 > 0 forms a double bubble if all d.c.e. degrees below d1 are comparable with d2.