Solution des exercices sur le tétraèdre proposés par M. Genty
Solution to a problem of S. Rolewicz
Solving a ± b = 2c in elements of finite sets
We show that if A and B are finite sets of real numbers, then the number of triples (a,b,c) ∈ A × B × (A ∪ B) with a + b = 2c is at most (0.15+o(1))(|A|+|B|)² as |A| + |B| → ∞. As a corollary, if A is antisymmetric (that is, A ∩ (-A) = ∅), then there are at most (0.3+o(1))|A|² triples (a,b,c) with a,b,c ∈ A and a - b = 2c. In the general case where A is not necessarily antisymmetric, we show that the number of triples (a,b,c) with a,b,c ∈ A and a - b = 2c is at most (0.5+o(1))|A|². These estimates...
Solving the sensor cover energy problem via integer linear programming
This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...
Some analogs of Zariski's Theorem on nodal line arrangements.
Some Basic Properties of Packing and Covering Constants.
Some characterization of infinite antimatroids.
Some characterization of locally nonconical convex sets
A closed convex set in a local convex topological Hausdorff spaces is called locally nonconical (LNC) if for every there exists an open neighbourhood of such that . A set is local cylindric (LC) if for , , there exists an open neighbourhood of such that (equivalently: ) is a union of open segments parallel to . In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication was proved in general, while...
Some Common Themes in Visual Mathematical Art
Some Erdös-Szekeres Type Results About Point in Space.
Some extensions of the class of -convex bodies.
Some Extremal Results on Circles Containing Points.
Some Geometric Applications of Dilworth's Theorem.
Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.
Some geometric probability problems involving the Eulerian numbers.
Some geometric properties for a class of non-Lipschitz domains.
Some geometric properties of typical compact convex sets in Hilbert spaces
An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection from e to X has fixed cardinality n+1 ( arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection from e to X where X is a compact subset of .
Some inequalities between two polygons inscribed one in the other.
Some Inequalities for Planar Convex Figures.
Some inequalities for radial Blaschke-Minkowski homomorphisms
We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals.