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

W artykule przeprowadzono analizę autentyczności jednego z układów pomiędzy wielkim księciem litewskim Jagiełłą i trockim Skirgiełłą a zakonem krzyżackim 31 października 1382 r., na mocy którego książęta litewscy odstąpili Żmudź krzyżakom. Autentyczność dokumentu została zakwestionowana w ostatnich latach literaturze białoruskiej, która upatruje nim fałszerstwo krzyżackie. wykazano, że zachowan...

OBJECTIVE To describe the pattern of occurrence of malocclusion and orthodontic treatment need. DESIGN A descriptive cross-sectional survey. SETTING Six public primary schools in Nairobi, Kenya. SUBJECTS A randomly selected sample of 1382 children aged 12 to 15 years. Clinical examination for malocclusion was conducted using the Dental Aesthetic Index (DAI). Orthodontic treatment need was...

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 purpose of this study is to determine the general trend research in field educational robotics through bibliometric analysis. 1382 papers indexed WOS database between 1975-2021 were subjected analyses. data analyzed using VOSviwer and SciMAT. At end study, it has been concluded that most productive country was USA, influential journal Computers Education, author Bers, M.U., institution Tuft...

14. Van Heertum RL. Clinical diagnosis: major depressive disorder. In: Van Heertum RL. Tikofsky RS, eds. Cerebral SPECT imaging, 2nd ed. New York: Raven Press; 1995:194. 15. Pohl P, Vogel G, Fill H, Rössler H. Zangerle R. Gerstenbrand F. Single-photon emission computed tomography in AIDS dementia complex. J NucÃ-Med I988;29: 1382-1386. 16. Costa DC, Ell P, Burns A, Philpot M, Levy R. CBF tomog...