• 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.

• Journal of Biomedical Engineering Research
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• v.14 no.1
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• pp.51-62
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• 1993

An experimental study was performed for the preparation of living skin-equivalent by the using collagen gel contraction with human fibroblasts as neodermls and cultured human keratinocytes as neoderm is . The results were as follows ; 1) The rate of collagen gel contraction was dependent on the number of fibroblasts into the lattice and collagen contraction was progressed according to the increment of the number of the cells. 2) The rate of collagen gel contraction was progressed according to the decrement of the contraction of the collagen. 3) The rate of gel contraction was progressed according to the increment of serum concentration in the fixed concentration of the fibroblasts and collagen. 4) The lattice contraction was decreased according to the increment of the population doublings of the fibroblasts. 5) Macroscopically, the artificial dermis was gray white in color and tissue-like consistency and elas- ticity. 6) Microscopically, three dimensionally contracted artificial dermis showed more dense fibroblasts and its newly formed collagen fibrils in the matrix than one dimensionally contracted one. 7) Finally prepared skin-equivalent showed good attachment of living stratified keratinocytes to the dermal equivalent microscopically. It has been proposed that newly formed skin-equivalent is suitable for the graft of extensively and deeply burned patients. Shortening of the manufacturing period of skin-equivalent and development of conservation technique as a readily usable state are to be solved for our ongoing works.

• Korean Journal of Metals and Materials
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• v.50 no.10
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• pp.703-710
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• 2012

The effects of the ordering reaction on high temperature mechanical behavior is investigated by tensile tests at $2{\times}10^{-2}/s-3.3{\times}10^{-5}/s$ up to $745^{\circ}C$. The tensile deformed region is examined by differential scanning calorimeter (DSC), TEM, and high resolution neutron diffraction (HRPD). The results showed that a plateau of tensile strength appeared at $150-500^{\circ}C$ whereas the elongation minimum occurred at about $600^{\circ}C$. This suggests that the occurrence of a plateau does not cause the elongation minimum. The temperature of the elongation minimum decreases with the strain rate. HRPD results show a lattice contraction in the tensile deformed specimen at the temperature of the plateau occurring region. The plateau of tensile strength, the lattice contraction, and the occurrence of serration appeared in the same temperature region.

• 한국신재생에너지학회:학술대회논문집
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• 2011.05a
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• pp.150.2-150.2
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• 2011

Unlike non-ionic clathrate hydrates stably formed by van der Waals interaction between a guest molecule and a surrounding host framework, ionic clathrate hydrates are stabilized by ionic interaction between an ionic guest molecule and the host water-framework. Here, we firstly described the stable entrapment of the superoxide ions in ${\gamma}$-irradiated $Me_4NOH+O_2$ hydrate. Owing to peculiar direct guest-guest ionic interaction, the lattice structure of ${\gamma}$-irradiated $Me_4NOH+O_2$ hydrate shows significant change of lattice contraction behavior even at relatively high temperature(120K). Particularly, we note that ionic-induced dimensional change is much greater than thermal-induced change. Such findings are expected to provide useful information for a better understanding of unrevealed nature of clathrate hydrate fields.

• Proceedings of the PSK Conference
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• 2000.10a
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• pp.146.1-146.1
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• 2000

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.24-29
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• 2002

In this paper, the microstructure and the dielectric properties of Sr$\_$1-x/CaxTiO$_3$(0$\leq$x$\leq$0.2)-based grain boundary layer ceramics were investigated. The sintering temperature and time were 1420∼152 0$\^{C}$ and 4 hours in N$_2$ gas, respectively. The average grain size and the lattice constant were decreased with increasing content of Ca, but the average grain size was increased with increase of sintering temperature. The second phase foamed by the thermal diffusion of CuO from the surface leads to verb high apparent dielectric constant, $\xi$$\_$r/>50000 and low dielectric loss, tan$\delta$<0.05. X-ray diffraction patterns of Sr$\_$1-x/CaxTiO$_3$ exhibited cubic structure, and the peaks shifted upward and the peak intensity were decreased with x. This is due to the lattice contraction as Sr is replaced by Ca with a smaller ionic radius. The specimens treated thermal diffusion for 2hrs in 1150$\^{C}$ exhibited nonlinear current-voltage characteristic, and its nonlinear coefficient(a) was overt 7.

• Proceedings of the Korean Ceranic Society Conference
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• 2000.10a
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• pp.156.2-156
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• 2000

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.6
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• pp.591-597
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• 2013

Because most existing non-Newtonian models are not suitable for application to the lattice Boltzmann method, theoretical and numerical studies in this regard remain challenging. In this study, the hydrokinetic (HK) model was modified and applied to a 3D sudden contraction-expansion channel flow, and the characteristics of the HK model flow were evaluated to generate non-trivial predictions in three-dimensional strong shear flows. The HK model is very efficient for application to the lattice Boltzmann method because it utilizes the shear rate and relaxation time. However, the simulation would be unstable in a high shear flow field because the local relaxation time sharply decreases with an increase in the shear rate in a strong shear flow field. In the HK model, it may become necessary to truncate the relaxation time and non-dimensional parameter to obtain stable numerical results.

• 한국초전도학회:학술대회논문집
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• v.14
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• pp.62-62
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• 2004

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.24 no.12
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• pp.955-961
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• 2011

We investigated the physical properties of stoichiometric and non-stoichiometric oxide doped complex perovskite, $Ba(Zn_{1/3}Ta_{2/3})O_3$ ceramics and their impacts on the microwave dielectric performances using various characterization techniques such as X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and network analyzer. According to the measurement of lattice constant changes, anomalous lattice volume contraction of $ZrO_2$ doped $Ba(Zn_{1/3}Ta_{2/3})O_3$ sample only showed the dielectric quality factor enhancements, which was due to the lattice volume contraction as well as the 1:2 B-site cation ordering. In addition, NiO doping was useful to the stabilization of temperature coefficient of resonance frequency.