A simple algorithm is described which determines the satisfiability over the reals of a conjunction of linear inequalities, none of which contains more than two variables. In the worst case the algorithm requires time O(WH#~Q~~+~ log n), where n is the number of variables and m the number of inequalities. Several considerations suggest that the algorithm may be useful in practice: it is simple ...

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

1.16. Again, I’ll only do the triangle inequality. Let x = (a1, . . . , an), y = (b1, . . . , bn), z = (c1, . . . , cn) be three points in Rn, then there is some integer j, 1 ≤ j ≤ n where the max occurs, so that d∞(x, y) = |aj − bj |. Hence, d∞(x, y) = |(aj−cj)+(cj−bj)| ≤ |aj−cj |+|cj−bj | But, |aj−cj | ≤ max{|a1− c1|, . . . , |an − cn|} = d∞(x, z), since it is one of the terms occurring in th...

In this paper, we give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Ã Lojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for...

We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below with the number of vertices minus the size of the graph’s shortest index code. We show that the Network Coding solvability of each specific multiple unicast n...

Abstract Consider the subspace $${{{\mathscr {W}}}_{n}}$$ W n of $$L^2({{\mathbb {C}}},dA)$$ L 2 ( C , d A )<...

We consider a polynomial programming problem P on a compact semi-algebraic set K ⊂ Rn, described by m polynomial inequalities gj(X) ≥ 0, and with criterion f ∈ R[X]. We propose a hierarchy of semidefinite relaxations in the spirit those of Waki et al. [9]. In particular, the SDP-relaxation of order r has the following two features: (a) The number of variables is O(κ2r) where κ = max[κ1, κ2] wit...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

We present an efficient algorithm to find an optimal integer solution of a given system of 2-variable equalities and 1-variable inequalities with respect to a given linear objective function. Our algorithm has worst-case running time in O(N) where N is the number of bits in the input.

Using classical univariate polynomial inequalities (Ehlich and Zeller, 1964), we show that there exist admissible meshes with O(n2) points for total degree bivariate polynomials of degree n on convex quadrangles, triangles and disks. Higher-dimensional extensions are also briefly discussed. Mathematics subject classification (2010): 41A10, 41A63, 65D10.