In a recent paper, Amini et al. introduced a general framework to prove duality theorems between tree decompositions and their dual combinatorial object. They unify all known ad-hoc proofs in one duality theorem based on submodular partition functions. This general theorem remains however a bit technical and relies on this particular submodularity property. Instead of partition functions, we pr...

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dual GI/M/1. In this note, we generalize this duality relation to GI/G/1 queues with modif...

In this note we prove the Serre duality theorem for the cohomology of coherent sheaves on a projective scheme. First we do the case of projective space itself. Then on an arbitrary projective scheme X, we show that there is a coherent sheaf ω◦ X , which plays the role in duality theory similar to the canonical sheaf of a nonsingular variety. In particular, if X is Cohen-Macaulay, it gives a dua...

Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities ...

We prove a duality theorem applicable to a a wide range of specialisations, as well as to some generalisations, of tangles in graphs. It generalises the classical tangle duality theorem of Robertson and Seymour, which says that every graph either has a large-order tangle or a certain low-width tree-decomposition witnessing that it cannot have such a tangle. Our result also yields duality theore...

Dual linear programs are very useful to obtain bounds on the optimal value of the primal linear programs using the following two duality theorems. Theorem 1.1. Weak duality: Let x be a feasible solution for (P ) and y be a feasible solution for (D). Then, cx ≥ by. Theorem 1.2. Strong duality: For the linear programs in Figure 1, exactly one of the following possibilities occurs: 1. Both (P ) an...

We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.

Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...

It is shown, in a completely general setting, that a theorem of the alternative is logically equivalent to a duality theorem linking two constrained optimization problems. A standard technique for proving a duality theorem linking two constrained optimization problems is to apply an appropriate theorem of the alternative, sometimes called a transposition theorem (see, e.g., Mangasarian [2], Roc...