In this paper we have shall generalize Shearer’s entropy inequality and its recent extensions by Madiman and Tetali, and shall apply projection inequalities to deduce extensions of some of the inequalities concerning sums of sets of integers proved recently by Gyarmati, Matolcsi and Ruzsa. We shall also discuss projection and entropy inequalities and their connections.

We present a tight bound on the exact maximum complexity of Minkowski sums of polytopes in R. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2, . . . ,mk facets respectively is bounded from above by

The Future Tube T + n of n-dimensional Minkowski spacetime may be identified with the reduced phase space P , or " space of motions " of a particle moving in (n + 1)-dimensional Anti-de-Sitter Spacetime. Both are isomorphic to a homogeneous bounded domain in C n whose Shilov boundary may be identified with n-dimensional conformally compactified Minkowski spacetime.

We study the symplectic geometry of the moduli spaces of polygons in the Minkowski 3-space. These spaces naturally carry completely integrable systems with periodic flows. We extend the Gelfand-Tsetlin method to pseudo-unitary groups and show that the action variables are given by the Minkowski lengths of non-intersecting diagonals.

An exact parameterization for the boundary of the Minkowski product of N circular disks in the complex plane is derived. When N > 2, this boundary curve may be regarded as a generalization of the Cartesian oval that bounds the Minkowski product of two disks. The derivation is based on choosing a system of coordinated polar representations for the N operands, identifying sets of corresponding po...

Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant ...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of κ-Minkowski phase space algebra that yields the κ-extended finite Lorentz transformations derived in [16]. This is a particular form of a Deformed Special Relativity model that admits a modified energy-mom...

It is shown that for any sufficiently regular even Minkowski valuation Φ which homogeneous and intertwines rigid motions, convex body K in a smooth neighborhood of the unit ball, there exists sequence positive numbers (γm)m=1∞ such (γmΦmK)m=1∞ converges to ball with respect Hausdorff metric.