• Journal of Drive and Control
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• v.16 no.3
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• pp.51-58
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• 2019

The objective of this study was to investigate a simulation technology for the AM field based on ANSYS Inc.. The introduction of metal 3D printing AM process, and the examining of the present status of AM process simulation software, and the AM process simulation processor were done in the previous study (part 1). This present study (part 2) examined the use of the AM process simulation processor, presented in Part 1, through direct execution of Topology Optimization, Ansys Workbench, Additive Print and Additive Science. Topology Optimization can optimize additive geometry to reduce mass while maintaining strength for AM products. This can reduce the amount of material required for additive and significantly reduce additive build time. Ansys Workbench and Additive Print simulate the build process in the AM process and optimize various process variables (printing parameters and supporter composition), which will enable the AM to predict the problems that may occur during the build process, and can also be used to predict and correct deformations in geometry. Additive Science can simulate the material to find the material characteristic before the AM process simulation or build-up. This can be done by combining specimen preparation, measurement, and simulation for material measurements to find the exact material characteristics. This study will enable the understanding of the general process of AM simulation more easily. Furthermore, it will be of great help to a reader who wants to experience and appreciate AM simulation for the first time.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.133-148
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• 2005

In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.565-576
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• 2003

In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].

• Corrosion Science and Technology
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• v.17 no.3
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• pp.129-137
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• 2018

The resistance to corrosion of additive manufactured (3D printing) Ti-6Al-4V alloys was investigated using micro-electrochemical tests. In terms of corrosion resistance, the acicular martensitic ${\alpha}^{\prime}$ phase in such additive manufactured Ti-6Al-4V was the focus of attention, and its behavior was distinct from that of conventional subtractive manufactured Ti-6Al-4V. To order to identify ${\alpha}^{\prime}$ phase, XRD tests were performed and micro Vickers hardness was measured for different grains (bright and dark grains) in the additive manufactured Ti-6Al-4V alloy. Micro-electrochemical tests were performed to measure corrosion resistance of bright and dark grains in the additive manufactured Ti-6Al-4V alloy with specially designed electrochemical micro-droplet cell. Critical pitting temperature (CPT) measurement was performed to evaluate the resistance to pitting corrosion of additive manufactured Ti-6Al-4V alloys with different volumes of ${\alpha}^{\prime}$ phase and subtractive manufactured Ti-6Al-4V alloy. The dark grains of the laminated Ti-6Al-4V alloy distributed broader than the bright grains measured with low microhardness. The dark grains of the Ti-6Al-4V alloy, which was rich in martensite ${\alpha}^{\prime}$, had lower general corrosion and pitting resistance than bright grains. As the fraction of martensite ${\alpha}^{\prime}$ phase increased, the resistance to the pitting corrosion decreased.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.295-306
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• 2021

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• Journal of Korean Society for Quality Management
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• v.24 no.1
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• pp.32-43
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• 1996

In this paper we develop nonparametric methods for regression analysis when the response variable is subject to censoring that arises naturally in quality engineering. This development is based on a general missing information principle that enables us to apply, via an iterative scheme, nonparametric regression techniques for complete data to iteratively reconstructed data from a given sample with censored observations. In particular, additive regression models are extended to right-censored data. This nonparametric regression method is applied to a simulated data set and the estimated smooth functions provide insights into the relationship between failure time and explanatory variables in the data.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.613-621
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• 2020

In this paper, we investigate the general solution and the Hyers-Ulam stability of n-variable additive functional equation of the form $${\Im}\(\sum\limits_{i=1}^{n}(-1)^{i+1}x_i\)=\sum\limits_{i=1}^{n}(-1)^{i+1}{\Im}(x_i)$$, where n is a positive integer with n ≥ 2, in Banach spaces by using the direct method.