A spanning tree T in a finite planar connected graph G determines a dual spanning tree T * in the dual graph G * such that T and T * do not intersect. We show that it is not always possible to find T in G such that the diameters of T and T * are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.

We prove that for every integer g ≥ 0 and graph H, there exists a polynomial-time algorithm deciding whether an input graph of Euler genus at most g can be contracted to H. We introduce surface contractions and surface topological minors of embedded graphs. We prove that an embedded graph H is a surface contraction of an embedded graph G if and only if the geometric dual of H is a surface topol...

1. Let G be a locally compact and abelian group, Gl the dual group. Through this paper, "Ml will denote the set of all bounded Radon measure n on G; this set will be considered as a Banach algebra when provided with the customary norm as the dual of the space Co(G) defined below and with the ring product defined as convolution. If /iGM1, its Fourier transform is by definition the bounded and co...

We investigate possible preduals of the measure algebra M(G) of a locally compact group and the Fourier algebra A(G) of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak∗-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals C0...

Let G be a connected, simply-connected, almost simple algebraic group of simplylaced type over C and let σ be a diagram automorphism of G. Let Gσ = ((G)) be the L-dual of the fixed point subgroup of σ on the L-dual of G. In this paper we relate the character of a finite dimensional irreducible representation of the disconnected algebraic group G〈σ〉 (generated by G and σ) on the connected compon...

In this paper we express the velocity-dependent, spin-dependent heavy quark potential Vq q̄ in QCD in terms of a Wilson loop W(G) determined by pure Yang-Mills theory. We use an effective dual theory of longdistance Yang-Mills theory to calculate W(G) for large loops, i.e., for loops of size R.RFT . @RFT is the flux tube radius, fixed by the value of the Higgs ~monopole! mass of the dual theory,...

Algebraic structure of codes over Fq , closed under arbitrary abelian group G of permutations with exponent relatively prime to q, called G-invariant codes, is investigated using a transform domain approach. In particular, this general approach unveils algebraic structure of quasicyclic codes, abelian codes, cyclic codes, and quasi-abelian codes with restriction on G to appropriate special case...