Minkowski sums cover a wide range of applications in many different fields like algebra, morphing, robotics, mechanical CAD/CAM systems ... This paper deals with sums of polytopes in a n dimensional space provided that both H-representation and V-representation are available i.e. the polytopes are described by both their half-spaces and vertices. The first method uses the polytope normal fans a...

‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

We have used an adaptive-optics scanning laser ophthalmoscope to image the cone photoreceptor mosaic throughout the central 10 degrees -12 degrees of the retina for four normal subjects. We then constructed montages of the images and processed the montages to determine cone locations. Cone densities range from approximately 10,000 cones/mm2 at 7 degrees to 40,000 cones/mm2 at 1 degrees . The sm...

Retinas of adult teleost fish can regenerate after injury. Two important issues regarding this phenomenon are the assembly of the regenerated retina and the neuronal images of the visual scene that the regenerated retina produces. Here we report experiments in which the visual pigment content of photoreceptors derived from native and regenerated sunfish retinas was determined by microspectropho...

Elimination of the floor plate, a row of distinctive cells at the ventral midline of the spinal cord, dramatically increased the frequency of errors made by specific growth cones in the zebrafish embryo. This demonstrated that the floor plate participated in guiding specific growth cones at the ventral midline of the spinal cord. However, since a significant proportion of these growth cones fol...

Most terrestrial mammals have colour vision based on two spectrally different visual pigments located in two types of retinal cone photoreceptors, i.e. they are cone dichromats with long-to-middle-wave-sensitive (commonly green) L-cones and short-wave-sensitive (commonly blue) S-cones. With visual pigment-specific antibodies, we here demonstrate an absence of S-cones in the retinae of all whale...

Calcium ions (Ca(2+)) modulate the phototransduction cascade of vertebrate cone photoreceptors to tune gain, inactivation, and light adaptation. In darkness, the continuous current entering the cone outer segment through cGMP-gated (CNG) channels is carried in part by Ca(2+), which is then extruded back to the extracellular space. The mechanism of Ca(2+) extrusion from mammalian cones is not un...

Let X be a subscheme of a reduced scheme Y. Then Y has a flat degeneration to the normal cone CXY of X, and this degeneration plays a key step in Fulton and MacPherson’s “basic construction” in intersection theory. The intersection product has a canonical refinement as a sum over the components of CXY, for X and Y depending on the given intersection problem. The cone CXY is usually not reduced,...