Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has duality-type {l, n} if l is the valency of its vertices and n is the valency of its faces. Here, we study some properties of this duality index in oriented regular hypermaps and we prove...

highlighting the driving cause and its strict relationship with the formal cause and especially the final cause in the intrinsic elements of natural justice has caused the duality of reason and natural justice in the thinking of the proponents of the reason as the source. since the same emphasis makes the full understanding of the mechanisms of natural justice and its content for the human wisd...

We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data sets. Our applications to graphs include new, tangle-type, duality theorems for tree-width, path-width, and tree-decompositions of small adhesion. Conversel...

We will show that the duality for regular weight system introduced by K. Saito can be interpreted as the duality for the orbifoldized Poincare polynomial χ(W,G)(y, ȳ). Introduction In [A], Arnold discovered a strange duality among the 14 exceptional singularities. This was interpreted by Dolgachev, Nikulin and Pinkham in terms of the duality between algebraic cycles and transcendental cycles on...

Electric-magnetic duality and higher dimensional analogues are obtained as symmetries in generalized coset constructions, similar to the axial-vector duality of twodimensional coset models described by Roček and Verlinde. We also study global aspects of duality between p-forms and (d−p−2)-forms in d-manifolds. In particular, the modular duality anomaly is governed by the Euler character as in f...