A necessary and sufficient condition is given that a semicontinuous, nonnegative, concave function on a finite dimensional closed convex set $X$ necessarily be ...

Physical geometry and optical properties of objects are correlated: cylinders focus light to a line, spheres to a point and arbitrarily shaped objects introduce optical aberrations. Multi-functional ...

Several new classes of discrete stochastic orderings are introduced for comparing discrete random variables that are valued in an arbitrary ordered finite grid of nonnegative points. These order ...

Barycentric coordinates provide a robust framework for expressing any point within a simplex—typically a triangle or convex polygon—as an affine combination of its vertices. This representation has ...

Convex and concave lenses can both be used to correct defects of vision. The most commonly occurring defects of vision are ‘short sightedness’ and ‘long sightedness’. People who are ‘short sighted’ ...