12,418 research outputs found
Asymptotic enumeration of 2-covers and line graphs
In this paper we find asymptotic enumerations for the number of line graphs
on -labelled vertices and for different types of related combinatorial
objects called 2-covers.
We find that the number of 2-covers, , and proper 2-covers, , on
both have asymptotic growth where is the th Bell number, while the number of
restricted 2-covers, , restricted, proper 2-covers on , , and
line graphs , all have growth
In our proofs we use probabilistic arguments for the unrestricted types of
2-covers and and generating function methods for the restricted types of
2-covers and line graphs
Asymptotics for incidence matrix classes
We define {\em incidence matrices} to be zero-one matrices with no zero rows
or columns. A classification of incidence matrices is considered for which
conditions of symmetry by transposition, having no repeated rows/columns, or
identification by permutation of rows/columns are imposed. We find asymptotics
and relationships for the number of matrices with ones in these classes as
.Comment: updated and slightly expanded versio
Asymptotic enumeration of incidence matrices
We discuss the problem of counting {\em incidence matrices}, i.e. zero-one
matrices with no zero rows or columns. Using different approaches we give three
different proofs for the leading asymptotics for the number of matrices with
ones as . We also give refined results for the asymptotic
number of incidence matrices with ones.Comment: jpconf style files. Presented at the conference "Counting Complexity:
An international workshop on statistical mechanics and combinatorics." In
celebration of Prof. Tony Guttmann's 60th birthda
A note on higher-dimensional magic matrices
We provide exact and asymptotic formulae for the number of unrestricted,
respectively indecomposable, -dimensional matrices where the sum of all
matrix entries with one coordinate fixed equals 2.Comment: AmS-LaTeX, 9 page
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Solid Freeform Fabrication of Artificial Human Teeth
In this paper, we describe a solid freeform fabrication procedure for human dental
restoration via porcelain slurry micro-extrusion. Based on submicron-sized dental porcelain
powder obtained via ball milling process, a porcelain slurry formulation has been developed. The
formulation developed allows the porcelain slurry to show a pseudoplastic behavior and
moderate viscosity, which permits the slurry to re-shape to form a near rectangular cross section.
A well-controlled cross-section geometry of the extrudate is important for micro-extrusion to
obtain uniform 2-D planes and for the addition of the sequential layers to form a 3-D object.
Human teeth are restored by this method directly from CAD digital models. After sintering,
shrinkage of the artificial teeth is uniform in all directions. Microstructure of the sintered teeth is
identical to that made via traditional dental restoration processes.Mechanical Engineerin
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Laser Densification of Extruded Dental Porcelain Bodies in Multi-Material Laser Densification (MMLD) Process
In this study commercial dental porcelain powder was deposited via slurry extrusion and
laser densified to fabricate dental restorations in a Multi-Material Laser Densification (MMLD)
process. The processing conditions for laser densification of single lines and closed rings were
investigated in order to avoid warping and cracking. Multi-layer rings were also investigated to
study the dependence of bonding between layers on the laser densification conditions. The laser
densified rings showed no warping, and good bonding between layers could be achieved when
the laser densification condition was selected properly. The mechanism to achieve porcelain
rings without warping and cracking is discussed. The understanding developed will pave the way
for fabricating a physical dental restoration unit.Mechanical Engineerin
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