The Grishukhin inequality is a facet of the cut polytope CUT7 of the complete graph K7, for which no natural generalization to a family of inequalities has previously been found. On the other hand, the Imm22 Bell inequalities of quantum information theory, found by Collins and Gisin, can be seen as valid inequalities of the cut polytope CUT¤(K1,m,m) of the complete tripartite graph K1,m,m. They...

The main goal of this article is to show that many inequalities are not valid in operator theory become true if we add a separation condition on the spectra. applications include showing how monotone functions behave like and Choi-Davis inequality becomes for convex under condition.

Worldline quantum inequalities provide lower bounds on weighted averages of the renormalised energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally hyperbolic spacetime, we establish a worldline quantum inequality on the normal ordered energy density, valid for arbitrary smooth timelike trajectories of th...

are well known. When {Ij}j∈Z is the collection of dyadic intervals, i.e., I0 = {0} and Ij = sgn(j)[2 , 2) for |j| > 0, the estimate (1.2) is the classical Littlewood–Paley inequality which is valid (as well as the reverse estimate with ≥ in place of ≤) for all p ∈ (1,∞). If the Ij are disjoint intervals of equal length, then (1.2) holds if and only if p ∈ [2,∞); this was first proved by L. Carl...

Inequalities satisfied by the zeros of the solutions of second order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among o...

Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F (u1, . . . , um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i 6= j. This paper...

In this paper, we prove that the inequality [Γ(x + y + 1)/Γ(y + 1)]1/x [Γ(x + y + 2)/Γ(y + 1)]1/(x+1) < s x + y x + y + 1 is valid if and only if x+ y > y +1 > 0 and reversed if and only if 0 < x+ y < y + 1, where Γ(x) is the Euler gamma function. This completely extends the result in [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2009), no. 2, 967–970.] and thor...

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed integer linear programs. In 1998, Wolsey defined MIR inequalities differently. In some sense these definitions are equivalent. However, this note points out that the natural concepts of MIR closures derived from these two definitions are distinct. Dash, Günlük and Lodi made the same observation independently. Let S...

We consider testing about the slope parameter β when Y −Xβ is assumed to be an exchangeable process conditionally on X. This framework encompasses the semi-parametric linear regression model. We show that the usual Fisher’s procedure have non trivial exact rejection bound under the null hypothesis Rβ = γ. This bound derives from the Markov inequality and a close inspection of multivariate momen...

We study facets of the k-partition polytope Pk.+, the convex hull of edges cut by r-partitions of a complete graph for r < k, k 2 3. We generalize the hypermetric and cycle inequalities (see Deza and Laurent, 1992) from the cut polytope to Pk.,, k 2 3. We give some sufficient conditions under which these are facet defining. We show the anti-web inequality introduced by Deza and Laurent (1992) t...