• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.545-551
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• 1996

It is well known in the theory of distributions and proved in [GS, S] that $$ (i) (Bochner-Schwartz) Every positive definite (tempered) distribution is the Fourier transform of a positive tempered measure \mu. $$ $$ (ii) (Schwartz kernel theorem) Let B(\varphi, \psi) be a bilinear distribution. Then for some u \in D'(R^n \times R^n) B(\varphi, \psi) = u(\varphi(x)\bar{\psi}(y)) for every \varphi, \psi \in C_c^\infty. $$ $$ (iii) A translation invariant positive definite bilinear distribution B(\varphi, \psi) is of the form B(\varphi, \psi) = \smallint \varphi(x)\psi(x) d\mu(x) for every \varphi, \psi \in C_c^\infty (R^n), where \mu is a positive tempered measure.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.371-389
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• 2000

Working within classical distribution theory, we develop notions of multiplication and convolution for tempered distributions which are general enough to encompass the classical cases -such as pointwise multiplication of continuous functions or the convolution of $L^1$ functions- which most textbook treatments of distribution theory leave out. Pains are taken to develop a theory which satisfies the commutative and asociative laws.

• Proceedings of the Safety Management and Science Conference
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• 2009.11a
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• pp.471-481
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• 2009

This study is deal with the high frequency induction hardening (HF at $850^{\circ}C$, 120kHz & 50kW condition) SM45C steel. (1) The HF specimen which was tempered at $150^{\circ}C$, did not appear any tempering effect. A brittle fracture occurred at rounded area of the tensile specimen. AE amplitude distribution showed between 45~60dB. (2) The HF specimen which was tempered at $300^{\circ}C$, slip and fracture occurred at the hole area of the tensile specimen. As it passes the yield point, the AE energy increased intermittently and AE amplitude distribution showed between 70~85dB. In addition, after the maximum tensile load, it showed high amplitude and energy distribution. The AE amplitude showed between 45~70dB. (3) The HF specimen which was tempered at $450^{\circ}C$, a brittle fracture occurred as if it is torn in the direction of $45^{\circ}$ on parallel area over the both sides of the tensile specimen, which led to several peak to be appeared in AE energy. It was found that the AE amplitude was relatively low and the AE energy was high.

• Journal of the Korean Society of Mechanical Technology
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• v.13 no.2
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• pp.93-100
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• 2011

This study deals with the high frequency induction hardening (HF at $850^{\circ}C$, 120kHz & 50kW condition) SM45C steel. (1) The HF specimen, which was tempered at $150^{\circ}C$, did not show any tempering effect. A brittle fracture occurred at rounded area of the tensile specimen. AE (acoustic emission) amplitude distribution showed between 45dB and 60dB. (2) A slip and fracture occurred at the hole area of the HF specimen which was tempered at $300^{\circ}C$. As they pass the yield point, the AE energy is increased intermittently and AE amplitude distribution exists between 70dB and 85dB. In addition, after imposing the maximum tensile load, AE signals showed high amplitude and energy distribution. The AE amplitude showed between 45dB and 70dB. (3) A brittle fracture occurred at HF specimen which was tempered at $450^{\circ}C$ as if it is torn in the direction of $45^{\circ}$ on parallel area over the both sides of the tensile specimen, which lead to several peak appeared in AE energy. It was found that the AE amplitude was relatively low and the AE energy was high.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.87-88
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• 1985

• Journal of Welding and Joining
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• v.11 no.4
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• pp.79-90
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• 1993

Shielded metal arc welding, one-ploe and two-pole submerged arc welding were accomplished to investigate microstructure changes on phase transformation behavior in $60kg/mm^2$ quenched and tempered high strength steel. Microstructures were examined by optical micrograph and TEM. In shielded metal arc welding (oxygen 250ppm), the inclusions were small size (0.3-0.5$\mu\textrm{m}$)and small in number. In submerged arc welding (oxygen 430-529ppm), the inclusions were larger(0.7-2$\mu\textrm{m}$) than that of shielded metal arc welding and large in number. Microstructure mainly depends on number and distribution of inclusions in fusion zone of weld metal. It was noticed that a limited number of inclusions favors the formation of acicular ferrite.

• Nuclear Engineering and Technology
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• v.46 no.3
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• pp.413-422
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• 2014

Presented in this study are the variations of microstructures and mechanical properties with tempering and Post-Weld Heat Treatment (PWHT) conditions for SA508 Gr.4N steel used as Reactor Pressure Vessel (RPV) material. The blocks of model alloy were austenitized at the conventional temperature of $880^{\circ}C$ then tempered and post-weld heat treated at four different conditions. The hardness and yield strength decrease with increased tempering and PWHT temperatures, but impact toughness is significantly improved, especially in the specimens tempered at $630^{\circ}C$. The sample tempered at $630^{\circ}C$ with PWHT at $610^{\circ}C$ shows optimum mechanical properties in hardness, strength, and toughness, excluding only the transition property in the low temperature region. The microstructural observation and quantitative analysis of carbide size distribution show that the variations of mechanical properties are caused by the under-tempering and carbide coarsening which occurred during the heat treatment process. The introduction of PWHT results in the deterioration of the ductile-brittle transition property by an increase of coarse carbides controlling cleavage initiation, especially in the tempered state at $630^{\circ}C$.

• Korean Journal of Metals and Materials
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• v.47 no.7
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• pp.406-415
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• 2009

A study was conducted on the effects of carbon, tungsten, and vanadium on the wear properties and surface roughness of four High Speed Steel (HSS) rolls manufactured by the centrifugal casting method. Hot-rolling simulation tests were carried out using a high-temperature wear tester capable of controlling speed, load, and temperature. HSS rolls contained a large amount (up to 25 vol.%) of carbides such as MC, $M_{2}C$, $M_{7}C_{3}$, and $M_{6}C$ carbides formed in the tempered martensite matrix. The matrix consisted mainly of lath tempered martensite when the carbon content in the matrix was small, and contained a considerable amount of plate tempered martensite when the carbon content increased. The high-temperature wear test results indicated that the wear properties and surface roughness of the rolls improved when the amount of hard MC carbides formed inside solidification cells increased. The rolls distribution was also homogeneous. The best wear properties and surface roughness were obtained from a roll where a large amount of MC carbides was homogeneously distributed in the lath tempered martensite matrix. The proper contents of carbon equivalent, tungsten equivalent, and vanadium were 2.0~2.3%, 9~10%, and 5~6%, respectively.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.81-91
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• 2001

The expansion of a distribution of $K^r_M^r(R)$ in terms of regular orthogonal wavelets is considered. The expansion of a distribution of $K^r_M^r(R)$ is shown to converge pointwise to the value of the distribution where is exists.

• Journal of the Korea institute for structural maintenance and inspection
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• v.27 no.2
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• pp.77-84
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• 2023

As the installation of solar panel accelerates, so does the number of solar panels reaching their end-of-life (EOL). However, the EOL solar panels is becoming a concern, as they contain potentially hazardous materials and are not easily recycled. Coping strategies such as effective collection, disposal, and recycling methods will be important to manage the growing number of EOL solar panels in the coming years.Therefore, many studies have focused on the development of EOL solar panel recycling technology. One recycling technology for EOL solar panels applicable to the construction field is the application of extracted tempered glass from EOL solar panels as construction materials. This study summarized the EOL solar panel disassembly technology and evaluated the mechanical properties of mortar using extracted tempered glass as fine aggregate. The results showed that when tempered glass was used as a fine aggregate in mortar, the compressive strength, flexural strength, and macro pores in the 1-3 ㎛ with 200-300 ㎛ range were affected, regardless of the disassembly technology of EOL solar panels. Especially, we found that the mechanical performance of mortar using chemically treated tempered glass was noticeably decreased due to changes in the chemical composition of the extracted tempered glass resulting from the removal of K₂O and CuO due to chemical reactions. Meanwhile, it was found that when fly ash was used as a binder, the reduction of mechanical performance could be alleviated.