Oscillatory properties of strongly superlinear differential equations with deviating arguments |
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Authors: | M.K Grammatikopoulos Y.G Sficas V.A Staikos |
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Affiliation: | Department of Mathematics, University of Ioannina, Ioannina, Greece |
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Abstract: | We regard a graph G as a set {1,…, v} together with a nonempty set E of two-element subsets of {1,…, v}. Let p = (p1,…, pv) be an element of nv representing v points in n and consider the realization G(p) of G in n consisting of the line segments [pi, pj] in n for {i, j} ?E. The figure G(p) is said to be rigid in n if every continuous path in nv, beginning at p and preserving the edge lengths of G(p), terminates at a point q ? nv which is the image (Tp1,…, Tpv) of p under an isometry T of n. We here study the rigidity and infinitesimal rigidity of graphs, surfaces, and more general structures. A graph theoretic method for determining the rigidity of graphs in 2 is discussed, followed by an examination of the rigidity of convex polyhedral surfaces in 3. |
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