Both the quality of the results of TEX s formula layout algorithm and the complexity of its description in the TEXbook are hard to beat The algorithm is verbally described as an imperative program with very complex control ow and complicated manipulations of the data structures representing formulae In a forthcoming textbook we describe TEX s formula layout algorithm as a functional program tra...

This is a report on an implemented system that allows the user to specify an argumentation semantics and that returns a logical encoding in the form of a parameterized propositional formula. When applied to a subset S of a given argumentation graph G, the instantiated formula is satisfiable if and only if S is an extension for G according to the argumentation semantics specified by the user.

We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U(N) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in t...

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components μ, of crossings c, and of Seifert circles s are related by a simple and elegant formu...

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways. The most famous of these results is Hall’s Theorem [6], characterizing when a bipartite graph has a matching that covers one partite set. Anderson [1] used Hall’s Theorem to prove Tutte’s 1Factor Theorem ...

<p style='text-indent:20px;'>In this paper, we consider a mixed boundary value problem with double phase partial differential operator, an obstacle effect and multivalued reaction convection term. Under very general assumptions, existence theorem for the under consideration is proved by using surjectivity pseudomonotone operators together approximation method of Moreau-Yosida. Then, intro...