• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.1008-1015
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• 2006

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.69-96
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• 2008

The purpose of this paper is to perceive the problems of current geometry education in the middle school mathematics, to develop some learning materials fitted for the mathematising activities based on Freudenthal's learning theories and to analyze the mathematising process followed by teaching-learning activities. For this purpose, we design activity-oriented learning materials for geometry based on Freudenthal's learning theories, and appropriate teaching-learning models are established for the middle school geometry at the 8-NA stage level according to the theory of van Hiele's geometry learning steps. After applied to the practical lessons, the effects of mathematical activities are analyzed.

• Bulletin of the Korean Chemical Society
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• v.15 no.8
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• pp.658-662
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• 1994

Ab initio and extended Huckel calculations have been applied to discuss the electronic structure, ring inversion barrier, and geometry of the $Cp_2TiS_3$ compound. The deformation of four membered ring in the planar geometry is originated from a second-order Jahn-Teller distortion due to the small energy gap between HOMO and LUMO on the basis of extended Huckel calculations. The puckered $C_s$ geometry is stabilized by the interaction of the $x^2-y^2$ metal orbital with the hybrid orbital in sulfur. Ab initio calculations have been carried out to explore the ring inversion process for the model $Cl_2TiS_3$ compound. We have optimized $C_s$ and $C_{2v}$ structures of the model compound at the RHF level. The energy barriers for the ring inversion are sensitive to the used basis set. With 4-31$G^*$ for the Cl and S ligands, the barriers are computed to be 8.41 kcal/mol at MP2 and 8.02 kcal/mol at MP4 level.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.535-546
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• 2005

We study on intuitive verification and rigor proof which are in geometry of Korean and Russian $7\~8$ grade's mathematics textbooks. We compare contents of mathematics textbooks of Korea and Russia laying stress on geometry. We extract 4 proposition explained in Korean mathematics textbooks by intuitive verification, analyze these verification method, and compare these with rigor proof in Russian mathematics textbooks.

• Proceedings of the SAREK Conference
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• 2005.11a
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• pp.281-287
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• 2005

This study investigates the pressure drop and heat transfer characteristics of heat exchanger according to the combination of fin configuration and fin pitch of each row by the similitude experiments with the finned-tube geometry scaled as large as four times Finned-tube heat exchanger has 2 rows, and fin geometry consists of two cases, louver-louver and louver-slit. Fin pitch is varied with three types in each case, 6-6 mm, 8-8 mm and 8-6 mm. Results show that total heat transfer can be occurred evenly at each row by varying the fin pitch of 1st row and 2nd row. Heat transfer rate and pressure drop characteristics change according to the combination for fin geometry and fin pitch.

• Korean Journal of Materials Research
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• v.4 no.7
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• pp.792-797
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• 1994

Force fields of syndiotactic isoregic PVF crystal have been extracted by optimizing a structure of 2,4,6-trifluoroheptane with ab initio Quantum mechanical method with 6-31G * * basis set, and applied to calculate the structure parameters and elastic constants of the material. The cell parameters turned out to be 5.205$\AA$, of a axis(chain axis), 8.457$\AA$, of b axis and 4.621$\AA$ of c axis. These parameters are in fair agreement with those of the atactic X-ray structure(5.04$\AA$, 8.57$\AA$, and 4.95$\AA$,respectively). The young's modulus of defect free syndiotactic PVF crystal was computed to be 267 GPa comparable to those of polyvinilidene fluoride(277-293 GPa) and polyethylene(264-337 GPa) crystals. Bulk modulus value obtained at optimum geometry is more than twice greater than that obtained at experimental geometry due to large difference of elastic compliance constant (especially Sgj element) at these two different geometries.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.4
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• pp.132-139
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• 2002

In GMAW(Gas Metal Arc Welding) processes, bead geometry (penetration, bead width and height) is a criterion to estimate welding quality. Bead geometry is affected by welding current, arc voltage and travel speed, shielding gas, CTWD (contact-tip to workpiece distance) and so on. In this paper, welding process variables were selected as welding current, arc voltage and travel speed. And bead geometry was reasoned from the chosen welding process variables using neuro-fuzzy algorithm. Neural networks was applied to design FL(fuzzy logic). The parameters of input membership functions and those of consequence functions in FL were tuned through the method of learning by backpropagation algorithm. Bead geometry could be reasoned from welding current, arc voltage, travel speed on FL using the results learned by neural networks. On the developed inference system of bead geometry using neuro-furzy algorithm, the inference error percent of bead width was within $\pm$4%, that of bead height was within $\pm$3%, and that of penetration was within $\pm$8%. Neural networks came into effect to find the parameters of input membership functions and those of consequence in FL. Therefore the inference system of welding quality expects to be developed through proposed algorithm.

• 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.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.8
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• pp.24-31
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• 2001