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Digitale Medien

Large faces in 4-critical planar graphs with minimum degree 4 (1995)

Abbott, H. L. ; Hare, D. R. ; Zhou, B.

Springer

Combinatorica 15 (1995), S. 455-467

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ISSN: 1439-6912

Schlagwort(e): Primary 05C15 ; Secondary 05C35

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract We prove that the size of the largest face of a 4-critical planar graph with δ≥4 is at most one half the number of its vertices. Letf(n) denote the maximum of the sizes of largest faces of all such graphs withn vertices (n sufficiently large). We present an infinite family of graphs that shows $$\mathop {\lim }\limits_{n \to \infty } \frac{{f(n)}}{n} = \frac{1}{2}$$ .

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01192518

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Digitale Medien

A Contactless CCD Dilatometer for Foil Materials (1999)

Wang, H. ; Zhang, Y. Y. ; He, G. H. ; [weitere]

Springer

International journal of thermophysics 20 (1999), S. 743-753

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ISSN: 1572-9567

Schlagwort(e): CCD ; contactless ; dilatometer ; foil ; thermal expansion

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract A contactless, compact, low-cost dilatometer based on a laser-pulse thermal-conductivity apparatus has been developed to measure the linear thermal expansion of foil materials. The two sample-edge images are projected onto the array of a charge-coupled device (CCD). Changes in sample length are determined from measurements of the corresponding displacements of the sample-edge images focused on the CCD. The dilalometer performance was tested by comparing results of measurements of the thermal expansion for pure copper with published data. The linear thermal expansion of an L-16-type foil of 20-μm thickness, which is a candidate material for thermocontrol layers (in engineering), was measured with the apparatus.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1022685927689

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