• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.151-161
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• 1998

The odd spherical non-commutative tori $\mathbb{S}_{\omega}$ were defined in [2]. Assume that no non-trivial matrix algebra can be factored out of $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_{km}(\mathbb{C})$. It is shown that the tensor product of $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has the trivial bundle structure if and, only if km and 2d - 1 are relatively prime, and that the tensor product of $\mathbb{S}_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when km > 1.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.481-494
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• 2008

Iteration functions $K_m(z)$ and $U_m(z)$, $m{\geq}2$are defined recursively using the determinant of a matrix. We show that the fixed-iterations of $K_m(z)$ and $U_m(z)$ converge to a simple zero with order of convergence m and give closed form expansions of $K_m(z)$ and $U_m(z)$: To show the convergence, we derive a recursion formula for $L_m$ and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is $L_m(z)/(f^{\prime})^m$, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.41-48
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• 1993

Prime advantage of flexible manufacturing systems(FMS) is a flexibility. Flexibility is expected to prolong the service life of a manufacturing facility and enable it to respond quickly and economically to dynamic market change. The FMS loading decision is concerned with the allocation of operations and tools to machines subject to technological and capacity constraints of the system. Modern FMS loading problem has the multiple objectives such as processing cost, time and work load balance. We propose multi-objectives which could be used to formulate the loading/routeing problem and sequencing decision which should be adopted for each part type in order to maximize the machine flexibility by Hamming distance matrix based on Incidance matrix. Finally, a numerical example is provided to illustrate the proposed model.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.533-538
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• 2022

Cryptography is one of the most essential developing areas, which deals with the secure transfer of messages. In recent days, there are more number of algorithms have been evolved to provide better security. This work is also such an attempt. In this paper, an algorithm is presented for encryption and decryption which employs the matrix Q^p* and the well- known equation x² - py² = 1 where p is a prime.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.2
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• pp.189-196
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• 1994

Quality assurance in the process of manufacturing high strengh bolt sets used in the frictional joints of structures in one of important concern to users as well as to manufactures. In case of occurrences of either defective or low-quality products, even if they are quite rare, some systematic means of localizing the cause-characteristics and matching to corresponding production process is necessary. Control chart of torque factor is the primary indicatir in finding defectiveness of the products. Use of correlation diagrams ofnhardness of the bolt set presents in part a way of screening the cause. Retest data of the bolt set provide additional ideas of localizing the cause, for which theoretical background is presented in this regard. A process-characteristics matrix relating the causes of low quality to the corresponding process of manufacturing, which is of prime importance for the feedback control of production, is also proposed. Finally general features of control to assure quality of the set is described.

• Journal of the Korean Society for Heat Treatment
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• v.11 no.2
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• pp.99-110
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• 1998

The effects of pre-heat treatment(Q/T) on microstructure and hardness of SCM435 structural steel nitrided by micro-pulse plasma was investigated. The quenching and tempering temperatures for obtaining matrix hardness of SCM435 steel on range of HRC30 to HRC40 desired for machine parts were about $860^{\circ}C$ and $500^{\circ}C$ respectively. The case depth of SCM435 nitrided at $480^{\circ}C$ for 5 hours was independent of pre-heat treatment condition and was approximately $150{\mu}m$. However, hardness and compactness of nitrified layer on Q/T treated specimen were more heigher than annealed specimen. The case depth increased linearly with the increase of nitriding temperature, however, the hardness of nitrified layer decreased with the temperature. Phase mixture of ${\gamma}^{\prime}$-phase($Fe_4N$) and ${\varepsilon}$-phase($Fe_3N$) were detected by XRD analysis in the nitrified layer formed at optimum nitriding condition, and only single ${\gamma}^{\prime}$-phase was detected in the nitrified layer formed at higher nitriding temperature such as $540^{\circ}C$. The optimum nitriding temperature was approximately $480^{\circ}C$ which is lower than tempering temperature for preventing softening behavior of SCM435 matrix during nitriding process and the surface hardness of nitrified layer obtained by optimum preheat treatment condition was about Hv930.

• Journal of Powder Materials
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• v.20 no.4
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• pp.264-268
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• 2013

Nickel-based superalloy IN 713C powders have been consolidated by hot isostatic pressing (HIPing). The microstructure and mechanical properties of the superalloys were investigated at the HIPing temperature ranging from $1030^{\circ}C$ to $1230^{\circ}C$. When the IN 713C powder was heated above ${\gamma}^{\prime}$ solvus temperature (about $1180^{\circ}C$), the microstructure was composed of the austenitic FCC matrix phase ${\gamma}$ plus a variety of secondary phases, such as ${\gamma}^{\prime}$ precipitates in ${\gamma}$ matrix and MC carbides at grain boundaries. The yield and tensile strengths of HIPed specimens at room temperature were decreased while the elongation and reduction of area were increased as the processing temperature increased. At $700^{\circ}C$, the strength was similar regardless of HIPing temperature; however, the ductility was drastically increased with increasing the temperature. It is considered that these properties compared to those of cast products are originated from the homogeneity of microstructure obtained from a PM process.

• Transactions of Materials Processing
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• v.27 no.6
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• pp.339-346
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• 2018

This study investigated the microstructure and wear properties of extruded hyper-eutectic Al-Si (15wt.%) alloy in an engine oil environment. The wear mechanism of the material was also analyzed and compared to conventional gray cast iron. In microstructural observation results of Al-15wt.%Si alloy, primary Si phase ($45.3{\mu}m$) and eutectic Si phase ($3.1{\mu}m$) were found in the matrix, and the precipitations of $Mg_2Si({\beta}^{\prime})$, $Al_2Cu({\theta}^{\prime})$ and $Al_6(Mn,Fe)$ were also detected. In the case of gray cast iron, ferrite and pearlite were observed. It was also observed that flake graphite ($20-130{\mu}m$) were randomly distributed. Wear rates were lower in the Al-Si alloy as compared to those of gray cast iron in all load conditions, confirming the outstanding wear resistance of Al-15wt.%Si alloy in engine oil environment. In the $4kg_f$ condition, the wear rate of gray cast iron was $6.0{\times}10^{-5}$ and that of Al-Si measured $0.8{\times}10^{-5}$. The microstructures after wear of the two materials were analyzed using scanning electron microscope (SEM) and electron backscatter diffraction (EBSD). The primary Si and eutectic Si of Al-Si alloy effectively mitigated the abrasive wear, and the Al matrix effectively endured to accept a significant amount of plastic deformation caused by wear.

• Transactions of Materials Processing
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• v.8 no.3
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• pp.259-259
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• 1999

TiC ceramic particulate-reinforced titanium matrix composites were fabricated and the resultant densification, microstructure, and static and dynamic mechanical properties were studied. Comparing Ti with TiH₂powders as host materials for TiC ceramic reinforcement by pressureless vacuum sintering, TiH₂-started composites showed better sinterability and resistance to both elastic and plastic deformation than Ti-started ones. When TiH₂and TiH₂-45 vol.%TiC samples were hot pressed, TiH₂matrices transformed to alpha prime Ti and alpha Ti phase, respectively. It is interpreted that the diffusion of an alpha stabilizer carbon from TiC into the matrix is one of the plausible reasons far such a microstructural difference. The 0.2% offset yield strengths of the hot pressed TiH₂and TiH₂-45 vol.%TiC samples were 1008 and 1446 MPa, respectively, in a static compressive mode (strain rate of 1×$10^{-3}$/s). Dynamic compressive strengths of the samples were 1600 and 2060 MPa, respectively, at a strain rate of 4×10³/s.