• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.9
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• pp.802-809
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• 2005

A hybrid genetic algorithm is proposed for the problem of generating laser torch paths to cut a stock plate nested with free-formed parts each having a set of sub-parts. In the problem, the total unproductive travel distance of the torch is minimized. The problem is shown to be formulated as a special case of the standard travelling salesman problem. The hybrid genetic algorithm for solving the problem is hierarchically structured: First, it uses a genetic algorithm to find the cutting path f3r the parts and then, based on the obtained cutting path, sequence of sub-parts and their piercing locations are optimally determined by using a combined genetic and heuristic algorithms. This process is repeated until any progress in the total unproductive travel distance is not achieved. Computational results are provided to illustrate the validity of the proposed algorithm.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.111-117
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• 2022

Let p_a,b,m(n) be the number of integer partitions of n with more parts congruent to a modulo m than parts congruent to b modulo m. We prove that p_a,b,m(n) ≥ p_b,a,m(n) whenever 1 ≤ a < b ≤ m. We also propose some conjectures concerning series with nonnegative coefficients in their expansions.

• Journal of Powder Materials
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• v.16 no.5
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• pp.358-362
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• 2009

Ti$_{50}$Cu$_{20}$Ni$_{20}$Al$_{10}$ quaternary amorphous alloy was prepared by high-energy ball milling process. A complete amorphization was confirmed for the composition of Ti$_{50}$Cu$_{20}$Ni$_{20}$Al$_{10}$ after milling for 30hrs. Differential scanning calorimetry showed a large super-cooled liquid region ($\Delta$T$_x$ = T$_x$ T$_g$, T$_g$ and T$_x$: glass transition and crystallization onset temperatures, respectively) of 80 K. Prepared amorphous powders of Ti$_{50}$Cu$_{20}$Ni$_{20}$Al$_{10}$ were consolidated by spark-plasma sintering. Densification behavior and microstructure changes were investigated. Samples sintered at higher temperature of 713 K had a nearly full density. With increasing the sintering temperature, the compressive strength increased to fracture strength of 756 MPa in the case of sintering at 733 K, which showed a 'transparticle' fracture. The samples sintered at above 693 K showed the elongation maximum above 2%.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.3
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• pp.115-122
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• 2011

The critical role played by manufacturing performance measurement systems in achieving competitive success is increasingly recognized. Developing an integrated performance measurement model is significant for strategic management. This study consist of several principal steps. Performance criteria from the literature and an questionnaire were utilized prior to building the performance model. The AHP(Analytic Hierarchy Process) is utilized to evaluate the weight of each criterion when generating the performance measurement model for Korea automobile parts manufacturing company. AHP analysis showed clear difference in the priority between 5 criteria and 24 sub-criteria in terms of manufacturing performance of Korean automobile parts manufacturing company. The result of priority evaluation in the 5 criteria of 2nd level was ranked quality, cost, delivery, employee, flexibility. And the critical sub-criteria in the 24 sub-criteria of 3rd level was ranked claim rate, process defect rate, outsourcing parts defect rate, ability to quality management innovation, claim cost, etc.

• Journal of Powder Materials
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• v.16 no.1
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• pp.9-15
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• 2009

Amorphization and crystallization behaviors of $Ti_{50}Cu_{50}Ni_{20}Al_{10}$ powders during high-energy ball milling and subsequent heat treatment were studied. Full amorphization obtained after milling for 30 h was confirmed by X-ray diffraction and transmission electron microscope. The morphology of powders prepared using different milling times was observed by field-emission scanning electron microscope. The powders developed a fine, layered, homogeneous structure with prolonged milling. The crystallization behavior showed that the glass transition, $T_g$, onset crystallization, $T_x$, and super cooled liquid range ${\Delta}T=T_x-T_g$ were 691,771 and 80 K, respectively. The isothermal transformation kinetics was analyzed by the John-Mehn-Avrami equation. The Avrami exponent was close to 2.5, which corresponds to the transformation process with a diffusion-controlled type at nearly constant nucleation rate. The activation energy of crystallization for the alloy in the isothermal annealing process calculated using an Arrhenius plot was 345 kJ/mol.

• Corrosion Science and Technology
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• v.22 no.6
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• pp.447-456
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• 2023

In this work, we performed a comparative study examining two coatings on Ti Gr.1 for use in fuel cell bipolar plates. The coatings consisted of carbon black as the conductor along with acrylic polymer and Ti Sol-Gel binder as the binder. Ti Sol-Gel that had precipitated as TiO₂ in areas impregnated between carbon black gaps, thereby acting as a binder for carbon black and serving as a polymer coating. Neither of the coatings peeled off during the 90° bend test to check formability. The contact resistance of the TiO₂ coating was found to be lower than that of the polymer binder coating. Moreover, due to coating shrinkage (denser) that occurred during the heat treatment process, the TiO₂ binder coating showed almost the same level of corrosion resistance, as measured by potentiostatic and EIS tests, despite being thinner than the polymer coating. However, both the polymer binder coating and the TiO₂ binder coating had many pores and irregularities internally (around 10 ~ 100 nm) and on the surface (0.1 ~ 2 ㎛). We considered that these pores and irregularities contributed to the lower corrosion resistance.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• Tribology and Lubricants
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• v.35 no.6
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• pp.356-361
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• 2019

The friction and wear between machine components directly influence the energy loss and failure in various machines. Therefore, there is always a demand for finding methods to reduce friction and wear. Of the possible methods, lubrication is a widely used method for reducing friction and wear. In the case of lubrication, it is important to analyze the tribological behavior in the boundary lubrication because most of friction and wear occurs in the boundary lubrication regime. Cast iron has been regarded as a good material for industrial applications due to the excellent mechanical properties and high productivity. Especially, nodular cast iron is a material that shows better mechanical properties and wear-resistance compared with cast iron due to inclusion of spheroidal graphite. In this work, we investigated the tribological characteristics of nodular cast iron with respect to different counter parts in boundary lubrication regime. Sliding tests were conducted with SUJ2, ZrO₂, Si₃N₄ balls as counter parts using a pin-on-disk type tribotester. The results showed different friction and wear behaviors with different counter parts. The case of ZrO₂ showed the lowest wear rate in specimen and no significant ball wear. In case of SUJ2, it showed similar wear rate with ZrO₂ case in specimen and the highest friction coefficient. The case of Si₃N₄ showed the lowest friction coefficient, 33% lower than the case of SUJ2. It showed 16.9 times larger wear rate in specimen and 43% larger wear rate in ball compared to that of the SUJ2 case.

• Journal of the Korean Society for Heat Treatment
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• v.31 no.4
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• pp.165-170
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• 2018

W, Fe, and carbon powders were mechanical alloyed to produce $W_{35}Fe_{43}C_{22}$ ternary alloy powders containing nanocrystal W embedded within amorphous matrix. When the powder samples were heated to the primary crystallization temperature of $735^{\circ}C$, most parts of their amorphous region were fully crystallized to [W,Fe]-rich $M_6C$ carbides. Interestingly, a little portion of the carbides changes to stoichiometric line compounds ($M_{12}C$ and $W_6Fe_7$) and a solution phase (Fe-rich bcc), and remaining parts of the crystallites were amorphized again. The resulting microstructure was retained even by cyclic heating between room temperature of $1,200^{\circ}C$, and thus we found that the amorphous structure can be irreversibly formed at above glass transition temperature.