Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

Let Γ denote a distance-regular graph with diameter D and intersection numbers a2 > a1 = 0. We show that for each 1 ≤ d ≤ D−1, if Γ contains no parallelograms of lengths up to d+1 then Γ is d-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229]. By applying this result we show the nonexistence of distance-regular graphs with...

We consider the Gamma limit of the Abelian Chern-Simons-Higgs energy

We aim here at introducing a new point of view of the Laplacian of a graph, Γ. With this purpose in mind, we consider L as a kernel on the finite space V (Γ), in the context of the Potential Theory. Then we prove that L is a nice kernel, since it verifies some fundamental properties as maximum and energy principles and the equilibrium principle on any proper subset of V (Γ). If Γ is a proper se...

Let Γ denote an undirected, connected, regular graph with vertex set X, adjacency matrix A, and d+1 distinct eigenvalues.

We classify triangleand pentagon-free distance-regular graphs with diameter d ≥ 2, valency k, and an eigenvalue multiplicity k. In particular, we prove that such a graph is isomorphic to a cycle, a k-cube, a complete bipartite graph minus a matching, a Hadamard graph, a distance-regular graph with intersection array {k, k − 1, k − c, c, 1; 1, c, k − c, k − 1, k}, where k = γ(γ + 3γ + 1), c = γ(...

In this note, we present a Γ-convergence type result for ferromagnetic films. We propose a model of films for which we could ensure the strong convergence of minimizers when the exchange parameter vanishes. In this model, the plate thickness is kept constant and the magnetization stays constant in the thickness of the film.

We consider the Gamma limit of the Abelian Chern-SimonsHiggs energy

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...