• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.215-219
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• 1995

The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].

• ETRI Journal
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• v.39 no.1
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• pp.1-12
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• 2017

In this paper, we present a new approach for the progressive compression of three-dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate-distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub-optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.315-321
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• 2009

Erd$\"{o}$s posed the problem of determining the minimum number g(n) such that any set of g(n) points in general position in the plane contains an empty convex n-gon. In 1978, Harborth proved that g(5) = 10. We reprove the result in a geometric approach.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.529-532
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• 1988

This paper proposes a graph matching algorithm based on simulated annealing, which assures the globally optimal solution for circuit partitioning for the placement in the rectilinear region occurring as a result of the pre-placement of some macro cells, or onto the nonplanar surface in some military or space applications. The circuit graph ($G_{C}$) denoting the circuit topology is formed by a hierarchical bottom-up clustering of cells, while another graph called region graph ($G_{R}$) represents the geometry of a planar rectilinear region or a nonplanar surface for circuit placement. Finding the optimal many-to-one vertex mapping function from $G_{C}$ to $G_{R}$, such that the total mismatch cost between two graphs is minimal, is a combinatorial optimization problem which was solved in this work for various examples using simulated annealing.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.08a
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• pp.277.2-277.2
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• 2013

Petri dishes and glass slides have been widely used as general substrates for in vitro mammalian cell cultures due to their culture viability, optical transparency, experimental convenience, and relatively low cost. Despite the aforementioned benefit, however, the flat two-dimensional substrates exhibit limited capability in terms of realistically mimicking cellular polarization, intercellular interaction, and differentiation in the non-physiological culture environment. Here, we report a protocol of culturing embryonic rat hippocampal neurons on the electro-spun polymeric network and the results from examination of neuronal cell behavior and network formation on this culture platform. A combinatorial method of laser-scanning confocal fluorescence microscopy and live-cell imaging technique was employed to track axonal outgrowth and synaptic connectivity of the neuronal cells deposited on this model culture environment. The present microfiber-based scaffold supports the prolonged viability of three-dimensionally-formed neuronal networks and their microscopic geometric parameters (i.e., microfiber diameter) strongly influence the axonal outgrowth and synaptic connection pattern. These results implies that electro-spun fiber scaffolds with fine control over surface chemistry and nano/microscopic geometry may be used as an economic and general platform for three-dimensional mammalian culture systems, particularly, neuronal lineage and other network forming cell lines.

• Journal of Radiation Protection and Research
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• v.26 no.2
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• pp.93-99
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• 2001

Voxel head phantom for overcoming the limitation of mathematical phantom in depleting anatomical details was constructed and example dose calculation for BNCT was performed. The repeated structure algorithm of the general purpose Monte Carlo code, MCNP4B was applied for yokel Monte Carlo calculation. Simple binary yokel phantom and combinatorial geometry phantom composed of two materials were constructed for validating the voxel Monte Carlo calculation system. The tomographic images of VHP man provided by NLM(National Library of Medicine) were segmented and indexed to construct yokel head phantom. Comparison of doses for broad parallel gamma and neutron beams in AP and PA directions showed decrease of brain dose due to the attenuation of neutron in eye balls in case of yokel head phantom. The spherical tumor volume with diameter, 5cm was defined in the center of brain for BNCT dose calculation in which accurate 3 dimensional dose calculation is essential. As a result of BNCT dose calculation for downward neutron beam of 10keV and 40keV, the tumor dose is about doubled when boron concentration ratio between the tumor to the normal tissue is $30{\mu}g/g$ to $3{\mu}g/g$. This study established the voxel Monte Carlo calculation system and suggested the feasibility of precise dose calculation in therapeutic radiology.