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Comparative analysis of temperature effect on bandgap characteristics in 1D phononic crystals: Periodic versus quasiperiodic structures. [PDF]

open access: yesPLoS One
Heravi FJ   +9 more
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Infinite Euler Graphs

Canadian Journal of Mathematics, 1964
It is well known that for finite connected graphs the following are equivalent:(i)X is Euler (i.e., every vertex of X has positive even degree);(ii)X is traceable (i.e., the edges of X can be arranged in a sequence e1, . . . ,en such that ei ≠ ej if i ≠ j, and ei, ei+1 are adjacent, i = 1, . . .
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The Spectrum of an Infinite Graph

Canadian Journal of Mathematics, 2000
AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential)
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On self‐immersions of infinite graphs

Journal of Graph Theory, 2008
AbstractThe existence of an infinite graph which is not isomorphic to a proper minor of itself was proved by Oporowski. In the present note, it is shown that an analogous result holds when immersions are considered instead of minors. The question whether or not the same is true for weak immersions remains open. © 2008 Wiley Periodicals, Inc.
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Infinite Sets and Infinite Graphs

1985
E.C. MILNER: Let me begin with a problem due to Prikry and myself. First I’ll state a theorem concerning the depth of an ordered set. The depth of a partial order is the least ordinal γ such that does not embed γ*, the reverse of γ. For example vK has depth v+, if v ⪰ ω, κ ⪰ 2.
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The Cycle Space of an Infinite Graph

Combinatorics, Probability and Computing, 2005
Finite graph homology may seem trivial, but for infinite graphs things become interesting. We present a new ‘singular’ approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of $S^1$ in the space formed by the graph together with its ends. Our approach permits the extension to
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