A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let δ(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine δ(d, k) for small instances. We show that δ(3, 4) = 7 and δ(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby δ(d, ...

In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume, volume and surface area related to the Brunn-Minkowski theory. All measures considered are invariant under translations; furthermore, they may also be invariant under subgroups of the aane transformation group. For the case of rotation and scale ...

Driven by both technology and market, telecom industry is becoming a part of several converged industries in information society gradually from an independent industry which provides telecom products like voice or data. Under such background, this paper introduces a new value chain model of telecom value-added services in the new environment, providing theoretic support for transformation of te...

Additive Number Theory can be best described as the study of sums of sets of integers. A simple example is given two subsets A and B of a set of integers, what facts can we determine about A + B where A + B := {a + b | a ∈ A and b ∈ B}? We will state a result regarding this example shortly. We note that a very familiar problem in Number Theory, namely Lagrange’s theorem that every nonnegative i...

This study investigates the effect of sub-phonemic variation in bilabial stop and sibilant fricative consonants on word identification. Recent research suggests that sub-phonemic variation in stop voicing contrasts influences lexical processing. The present study seeks further support for this view by examining listeners’ responses to synthetic speech varying along VOT and fricative place conti...

Within this paper we study the Minkowski sum of prisms (" Cephoids ") in a finite dimensional vector space. For a vector a ∈ R n with positive components we write ¯ a = (1 ¯ a 1 1 ¯ an) and denote by = ¯ a = {x ∈ R n || ¯ a, x 1 , x 0} the associated prism. We provide a representation of a finite sum of prisms in terms of inequalities.

Let SH denote the homothety class generated by a convex set S ⊂ R: SH = {a + λS | a ∈ R, λ > 0}. We determine conditions for the Minkowski sum BH + CH or the Minkowski difference BH ∼ CH of homothety classes BH and CH generated by closed convex sets B,C ⊂ R to lie in a homothety class generated by a closed convex set (more generally, in the union of countably many homothety classes generated by...

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .