We survey recent research on mixed-integer rounding (MIR) inequalities and a generalization, namely the two-step MIR inequalities defined by Dash and Günlük (2006). We discuss the master cyclic group polyhedron of Gomory (1969) and discuss how other subadditive inequalities, similar to MIR inequalities, can be derived from this polyhedron. Recent numerical experiments have shed much light on th...

We show that the effective field theory of low energy modes in dense QCD has positive Euclidean path integral measure. The complexity of the measure of QCD at finite chemical potential can be ascribed to modes which are irrelevant to the dynamics at sufficiently high density. Rigorous inequalities follow at asymptotic density. Lattice simulation of dense QCD should be possible using the quark d...

We show that the compatibility of individual preferences with equilibrium data sets consisting of finite numbers of observations of the price vector, individual incomes and aggregate demand, amounts to finding whether some set of linear inequalities has a solution. This characterization is then applied to the study of topological properties of equilibrium data sets compatible with specified pre...

How long should a Markov chain Monte Carlo algorithm be run? Using examples from statistical physics (Ehrenfest urn, Ising model, hard discs) as well as card shuffling, this tutorial paper gives an overview of a body of mathematical results that can give useful answers to practitioners (viz: seven shuffles suffice for practical purposes). It points to new techniques (path coupling, geometric in...

play an important role in approximation theory. Various generalizations in several directions are well-known; for a survey of these results see the recent monograph of P. Borwein and T. Erdélyi [2]. A number of papers study possible extensions of Markov-type inequalities to compact sets K ⊂ R when the geometry of K is known apriori (Cantor type sets, finitely many intervals, etc.; cf. W. Pleśni...

Abstract. This paper describes an algorithm for ”direct numerical integration” of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active disc...

if global trade were fair, it is argued, then international aid would be unnecessary and inequalities inherent to the economic system would be justifiable. here, we argue that while global trade is unfair, in part because richer countries set the rules, we believe that additional interventions must go beyond trade regulation and short-term aid to redress inequalities among countries that will p...

Let P be a linear, elliptic second order symmetric operator, with an associated quadratic form q, and let W be a potential such that the Hardy inequality λ0 ∫ Ω Wu 2 ≤ q(u) holds with (non-negative) best constant λ0. We give sufficient conditions so that the spectrum of the operator 1 W P is [λ0,∞). In particular, we apply this to several well-known Hardy inequalities: (improved) Hardy inequali...

We find sufficient conditions for a probability measure μ to satisfy an inequality of the type ∫ Rd fF ( f ∫ Rd f 2 dμ ) dμ ≤ C ∫ Rd f2c∗ ( |∇f | |f | ) dμ + B ∫ Rd f dμ, where F is concave and c (a cost function) is convex. We show that under broad assumptions on c and F the above inequality holds if for some δ > 0 and ε > 0 one has ∫ ε 0 Φ ( δc [ tF ( 1t ) Iμ(t) ]) dt <∞, where Iμ is the isop...

Given an arbitrary Petri net structure which may have uncontrollable and unobservable transitions and may be unbounded, the procedure described in this paper generates a supervisor for liveness enforcement. The supervisor is specified as a conjunction of linear marking inequalities. For all initial markings satisfying the linear marking inequalities, the supervised Petri net is live. Moreover, ...