• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.421-429
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• 2008

We consider a general semiparametric additive risk model that consists of three components. They are parametric, purely and smoothly nonparametric components. In parametric component, time dependent term is known up to proportional constant. In purely nonparametric component, time dependent term is an unknown function, and time dependent term in smoothly nonparametric component is an unknown but smoothly function. As an estimation method of this model, we use the weighted least square estimation by Huffer and McKeague (1991). We provide an illustrative example as well as a simulation study that compares the performance of our method with the ordinary least square method.

• Journal of Welding and Joining
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• v.33 no.6
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• pp.1-5
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• 2015

Additive Manufacturing defines the fabrication of objects by successive consolidation of materials, layer by layer, according to a three-dimensional design. The numerous technologies available today were recently standardized into seven categories based on the general method. Each technology has its own set of advantages and limitations. Though it very much depends on the field of application, major assets of additive manufacturing compared to conventional processing routes are the ability to readily offer complexity (in terms of intricate shape and customization) and significant reduction of waste. On the other hand, additive manufacturing often suffers of relatively low production rates. Anyhow, additive manufacturing technologies is being given outstanding attention. In particular, metal additive manufacturing emerges as of great significance in industries like aerospace, automotive and tooling. The trend progresses toward full production of high value finished products.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.291-305
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• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• Journal of Welding and Joining
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• v.32 no.4
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• pp.15-19
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• 2014

Additive manufacturing technology is taking great attentions in these days because the term 3D-printing became a hot issue as the next generation manufacturing paradigm. Especially, laser additive manufacturing is at the center of interest thanks to the accuracy compared to other heat sources. In this report, recent papers about laser additive manufacturing are analyzed and reviewed. General technology is specified into three different categories and they are laser sintering, laser melting and laser metal deposition. Similarities and differences are clearly described by detailed technologies and used materials type. Representative application examples are selected then future of this technology is expected through those applications. Additionally, market of laser additive manufacturing systems itself and application fields are also predicted based on present 3D-printing market and technical progressions.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.907-913
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• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.517-522
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• 2006

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the multi-additive functional equation $f(x1+x2,y1+y2,z1+z2)={\Sigma}_{1{\le}i,j,k{\le}2}\;f(x1,yj,zk)$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1759-1776
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• 2015

We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.563-572
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• 2005

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the additive-quadratic functional equation f(x + y, z + w) + f(x + y, z - w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w).

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.297-306
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• 2009

In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.