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

It is well known that, in 1829, the French mathematician Jacques Charles François Sturm (1803-1855) solved the problem of finding the number of real roots of a polynomial equation f(x) = 0, with rational coefficients and without multiple roots, over a given interval, say ]a, b[. As a byproduct, he also solved the related problem of isolating the real roots of f(x). In 1835 Sturm published anoth...

We derive tight bounds for the maximum number of k-faces, 0 ≤ k ≤ d − 1, of the Minkowski sum, P1 ⊕ P2, of two ddimensional convex polytopes P1 and P2, as a function of the number of vertices of the polytopes. For even dimensions d ≥ 2, the maximum values are attained when P1 and P2 are cyclic d-polytopes with disjoint vertex sets. For odd dimensions d ≥ 3, the maximum values are attained when ...

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P ⊕ Q which consist of convexly independent points. We show that, if |P | = m and |Q| = n then |S| = O(m2/3n2/3 + m + n).

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, ...

The present work involves numerical simulation of a steady, incompressible forcedconvection fluid flow through a matrix of porous media between two parallel plates at constanttemperature. A Darcy model for the momentum equation was employed. The mathematical model forenergy transport was based on single phase equation model which assumes local thermal equilibriumbetween fluid and solid phases. ...

determination of critical points on hot stress-strain curve of metals is crucial in thermo-mechanical processes design. in this investigation a mathematical modeling is given to illustrate the behavior of metal during hot deformation processes such as hot rolling. the critical strain for the onset of dynamic recrystallization has been obtained as a function of strain at the maximum stress. in a...

three new rimantadine schiff bases (rsbs) were prepared, and then the interaction of rsbs with bovine serum albumin (bsa) was investigated using fluorescence, synchronous fluorescence, uv-vis absorption spectroscopy under physiological conditions. the results showed that the three rsbs effectively quenched the intrinsic fluorescence of bsa via static quenching. binding constant (ka), number of ...