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Hexagonal Systems, I

2002
In this chapter, we give the classification of hexagonal systems as formulated in Theorem 17.6. Our goal is to show that the list of hexagonal systems described in (15.14) and summarized in Figure 2 on page 148 is complete.
Jacques Tits, Richard M. Weiss
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Minimum Covering for Hexagon Triple Systems

Designs, Codes and Cryptography, 2004
The authors have recently obtained a complete solution to the problem of constructing perfect \(k\)-fold hexagon triple systems and perfect maximum packings of \(3k\)-fold \(K_n\) with hexagon systems [Discrete Math. 279, 325--335 (2004; Zbl 1043.05021)].
Selda Küçükçifçi   +1 more
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Perfect matchings in hexagonal systems

Combinatorica, 1984
A hexagonal system (HS) is a finite connected plane graph with no cut- vertices in which every interior region is a hexagonal unit cell. The author provides a simple and fast algorithm for finding a perfect matching (PM) in an HS if it exists. He also characterizes the set of all PM's in a given HS.
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Design of hexagonal multiplexer for communication system

Proceedings of the International Conference & Workshop on Emerging Trends in Technology - ICWET '11, 2011
In this paper, hexagonal loop resonator filter with, without perturbation and tri-band hexagonal multiplexer of high selectively and compact size are presented. The tri-band multiplexer topology is based on the hexagonal loop resonators of different size which capacitive coupled from a single input.
R. Kumar, G. A. Edae
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Hexagonal and rhombohedral systems

1967
Fig. 24 and Tables 5, 6 and 7 provide for calculations and stereographic projections for hexagonal crystals over a wide range of axial ratios.† Rhombohedral lattices referring to these hexagonal axes include the three cubic lattices with the axial ratios given in Table 5. In Fig.
K. W. Andrews, D. J. Dyson, S. R. Keown
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Hexagons for systems thinking

European Journal of Operational Research, 1992
Abstract This article describes an approach to bridging the gap between the generalist thinking of decision makers and the specialism of modellers by concentrating on the preliminary issue conceptualisation stage of modelling. A new type of visual facilitation is described using hexagons as a flexible mapping technique to bridge the gap between ...
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Isomorphic Hexagonal Systems

2002
In Chapter 15, we described six families, or types, of hexagonal systems; they are summarized in Figure 2 on page 148. In Chapter 30, we showed that every hexagonal system belongs to one of these families and in (35.13), we showed that two hexagonal systems give rise to isomorphic Moufang hexagons if and only if they are similar as defined in (29.36 ...
Jacques Tits, Richard M. Weiss
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Hexagons and squares in a passive nonlinear optical system

Physical Review A, 1994
Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern.
, Geddes, , Indik, , Moloney, , Firth
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Hexagon-Diamond Grid System for Motion Tracking

2009 Third UKSim European Symposium on Computer Modeling and Simulation, 2009
Based on the block-matching motion vector estimation techniques, a grid system using the block-based technique is proposed for motion tracking in video sequences. The technique is known as hexagon-diamond grid system (HDGS). The HDGS has a large hexagon and small diamond search pattern based on block-matching motion tracking characteristics.
Singh Sarban Singh Ranjit   +3 more
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A small embedding for partial hexagon systems [PDF]

open access: possibleAustralas. J Comb., 1997
Let \(n\) be a nonnegative integer. An \(m\)-cycle system of order \(n\) is a pair \((S, C)\), where \(S\) is an \(n\)-set and \(C\) is a set of \(m\)-cycles of the complete graph \(K_n\), with vertex set \(S\), that partition the edge set of \(K_n\). A generalization is a partial \(m\)-cycle system \((X, P)\), where \(P\) is a set of edge-disjoint \(m\
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