47,198 research outputs found
The Largest Laplacian and Signless Laplacian H-Eigenvalues of a Uniform Hypergraph
In this paper, we show that the largest Laplacian H-eigenvalue of a
-uniform nontrivial hypergraph is strictly larger than the maximum degree
when is even. A tight lower bound for this eigenvalue is given. For a
connected even-uniform hypergraph, this lower bound is achieved if and only if
it is a hyperstar. However, when is odd, it happens that the largest
Laplacian H-eigenvalue is equal to the maximum degree, which is a tight lower
bound. On the other hand, tight upper and lower bounds for the largest signless
Laplacian H-eigenvalue of a -uniform connected hypergraph are given. For a
connected -uniform hypergraph, the upper (respectively lower) bound of the
largest signless Laplacian H-eigenvalue is achieved if and only if it is a
complete hypergraph (respectively a hyperstar). The largest Laplacian
H-eigenvalue is always less than or equal to the largest signless Laplacian
H-eigenvalue. When the hypergraph is connected, the equality holds here if and
only if is even and the hypergraph is odd-bipartite.Comment: 26 pages, 3 figure
Epoxy/Polycaprolactone Systems with Triple-Shape Memory Effect: Electrospun Nanoweb with and without Graphene Versus Co-Continuous Morphology
Triple-shape memory epoxy (EP)/polycaprolactone (PCL) systems (PCL
content: 23 wt %) with different structures (PCL nanoweb embedded in EP matrix and
EP/PCL with co-continuous phase structure) were produced. To set the two temporary
shapes, the glass transition temperature (Tg) of the EP and the melting temperature (Tm) of
PCL served during the shape memory cycle. An attempt was made to reinforce the PCL
nanoweb by graphene nanoplatelets prior to infiltrating the nanoweb with EP through
vacuum assisted resin transfer molding. Morphology was analyzed by scanning electron
microscopy and Raman spectrometry. Triple-shape memory characteristics were
determined by dynamic mechanical analysis in tension mode. Graphene was supposed to
act also as spacer between the nanofibers, improving the quality of impregnation with EP.
The EP phase related shape memory properties were similar for all systems, while those
belonging to PCL phase depended on the structure. Shape fixity of PCL was better without
than with graphene reinforcement. The best shape memory performance was shown by the
EP/PCL with co-continuous structure. Based on Raman spectrometry results, the
characteristic dimension of the related co-continuous network was below 900 nm
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