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  • 1
    Electronic Resource
    Electronic Resource
    Improved bounds on the effective conductivity of high-contrast suspensions (1991)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 7118-7125 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Conventional upper and lower bounds on the effective conductivity σe of two-phase composite media diverge from one another in the infinite-contrast limits (α=∞ or 0). We have derived a generally nontrivial upper bound on σe for suspensions of identical spheres when the spheres are superconducting, i.e., the upper bound does not necessarily become infinite in the limit α→∞. Similarly, a generally nontrivial lower bound on σe is derived for the aforementioned suspension when the spheres are perfect insulators, i.e., the lower bound does not necessarily vanish in the limit α→0. The bounds are computed for two models: simple cubic arrays and random arrays of spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.347600
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  • 2
    Electronic Resource
    Electronic Resource
    A variational approach to the Steiner network problem (1991)
    Springer
    Annals of operations research 33 (1991), S. 481-499 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02071984
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  • 3
    Electronic Resource
    Electronic Resource
    Graham's problem on shortest networks for points on a circle (1992)
    Springer
    Algorithmica 7 (1992), S. 193-218 
    Details
    ISSN: 1432-0541
    Keywords: Graham's conjecture ; Steiner trees ; Spanning trees ; Variational approach ; Cocircular points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Suppose a configurationX consists ofn points lying on a circle of radiusr. If at most one of the edges joining neighboring points has length strictly greater thanr, then the Steiner treeS consists of all these edges with a longest edge removed. In order to showS is, in fact, just the minimal spanning treeT, a variational approach is used to show the Steiner ratio for this configuration is at least one and equals one only ifS andT coincide. The variational approach greatly reduces the number of possible Steiner trees that need to be considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01758758
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  • 4
    Electronic Resource
    Electronic Resource
    The steiner minimal network for convex configurations (1993)
    Springer
    Discrete & computational geometry 9 (1993), S. 323-333 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract SupposeX is a convex configuration with radius of maximum curvaturer and at most one of the edges joining neighboring points has length strictly greater thanr. We use the variational approach to show the Steiner treeS coincides with the minimal spanning tree and consists of all these edges with a longest edge removed. This generalizes Graham's problem for points on a circle, which we had solved. In addition we describe the minimal spanning tree for certain convex configurations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189325
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  • 5
    Electronic Resource
    Electronic Resource
    The Steiner ratio conjecture for cocircular points (1992)
    Springer
    Discrete & computational geometry 7 (1992), S. 77-86 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A Steiner minimal treeS is a network of shortest possible length connecting a set ofn points in the plane. LetT be a shortest tree connecting then points but with vertices only at these points.T is called a minimal spanning tree. The Steiner ratio conjecture is that the length ofS divided by the length ofT is at least √3/2. In this paper we use a variational approach to show that if then points lie on a circle, then the Steiner ratio conjecture holds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187826
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  • 6
    Electronic Resource
    Electronic Resource
    On the Formation and Motion of Defects in Nematic Liquid Crystals (1993)
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 123-125 (Jan. 1993), p. 463-472 
    Details
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://www.tib-hannover.de/fulltexts/2011/0528/01/59/transtech_doi~10.4028%252Fwww.scientific.net%252FMSF.123-125.463.pdf
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  • 7
    Electronic Resource
    Electronic Resource
    Pattern formation in associative neural networks with weak lateral interaction (1994)
    Springer
    Biological cybernetics 70 (1994), S. 563-567 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A model is proposed for the formation of singularities in the director field of orientation-selective cells in the visual cortex. The model consists of a two-layer associative neural net. The forward connections converge to a continuum of steady states. The degeneracy is removed by lateral interactions. It is shown that in many cases the director field contains critical points which are identified as the vortex locations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00198809
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  • 8
    Electronic Resource
    Electronic Resource
    Pattern formation in associative neural networks with weak lateral interaction (1994)
    Springer
    Biological cybernetics 70 (1994), S. 563-567 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. A model is proposed for the formation of singularities in the director field of orientation-selective cells in the visual cortex. The model consists of a two-layer associative neural net. The forward connections converge to a continuum of steady states. The degeneracy is removed by lateral interactions. It is shown that in many cases the director field contains critical points which are identified as the vortex locations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050059
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  • 9
    Electronic Resource
    Electronic Resource
    Cusp structures of alternating links (1992)
    Springer
    Inventiones mathematicae 109 (1992), S. 473-494 
    Details
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An alternating link ℒ Г is canonically associated with every finite, connected, planar graph Γ. The natural ideal polyhedral decomposition of the complement of ℒ Г is investigated. Natural singular geometric structures exist onS 3−ℒ Г , with respect to which the geometry of the cusp has a shape reflecting the combinatorics of the underlying link projection. For the class of ‘balanced graphs’, this induces a flat structure on peripheral tori modelled on the tessellation of the plane by equilateral triangles. Examples of links containing immersed, closed π1-injective surfaces in their complements are given. These surfaces persist after ‘most’ surgeries on the link, the resulting closed 3-manifolds consequently being determined by their fundamental groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01232034
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  • 10
    Electronic Resource
    Electronic Resource
    On the economics of the performing arts in the Soviet Union and the USA: A comparison of data (1992)
    Springer
    Journal of cultural economics 16 (1992), S. 1-24 
    Details
    ISSN: 1573-6997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Art History , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00231286
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