• Journal of Korean Society of Rural Planning
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• v.15 no.2
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• pp.27-42
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• 2009

This study has intended to evaluate the subjective landscape of rural region using additive integration index calculation model in Seondong region, Gochang-gun, Jeollabuk-do, Korea. This study consists of the following three steps. First, this study defmed the rural landscape using survey and developed the estimating equation for rural landscape assessment index. Second, this study set up assessment units and assessment indicators, then estimated mean of representative landscape adjectives in accordance with them through residents-participatory evaluation. Third, this study calculated rural landscape assessment index using additive integration index calculation model, and evaluated subjective landscape of rural region in accordance with space types and landscape fields through mapping methodology. The results of this study can be described as follows: 1) satisfaction level for landscape in accordance with village (urban area and residential area) was very high; 2) satisfaction level was very high in both Ye-Jeon reservoir and Hakwon farm, representative landscape resources of the study area.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).

• Journal of Communications and Networks
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• v.9 no.1
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• pp.11-17
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• 2007

In this paper, system performance of turbo trellis coded modulation (turbo TCM) is presented and analyzed through computer simulations over two typical channels, namely additive white Gaussian noise (AWGN) and Rayleigh fading channels. We use and compare different mapping strategies based on Ungerboeck partitioning (UP), block partitioning (BP), mixed partitioning (MP), Gray partitioning (GP), and Ungerboeck-Gray partitioning (UGP) of the signal constellation of the turbo TCM system. Furthermore, taking 8PSK modulation of turbo TCM as an example, our simulation results show that turbo TCM with UP can obtain better performance than turbo TCM with BP, MP, GP, and UGP in both AWGN and Rayleigh fading channels.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.287-301
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• 2011

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$(\ddag)\hspace{50}dk\;f\left(\frac{\sum_{j=1}^{dk}x_j}{dk}\right)=\displaystyle\sum_{j=1}^{dk}f(x_j)$$ if and only if the mapping $f$ : X ${\rightarrow}$ Y is Cauchy additive, and prove the Cauchy-Rassias stability of the functional equation ($\ddag$) in Banach modules over a unital $C^{\ast}$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^{\ast}$-algebras. As an application, we show that every almost homomorphism $h\;:\;\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h((k-1)^nuy)=h((k-1)^nu)h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and $n$ = 0,1,2,$\cdots$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^{\ast}$-algebras.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.707-721
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• 2013

In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0 in the sense of M. Mirmostafaee and M. S. Moslehian.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.59-71
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.99-107
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• 2017

Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the definition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the definition of biderivations and the statements of the results in [14], and prove the corrected theorems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.127-128
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• 2008

In this paper, we consider define fuzzy invex sets and fuzzy preinvex functions on the class of Choquet integrable functions, and interval-valued fuzzy invex sets and interval-valued fuzzy preinvex functions on the class of interval-valued Choquet integrals. And also we prove some properties of them.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.697-707
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• 2013

In this paper, we introduce the notion of permuting $n$-derivations in near-ring N and investigate commutativity of addition and multiplication of N. Further, under certain constrants on a $n!$-torsion free prime near-ring N, it is shown that a permuting $n$-additive mapping D on N is zero if the trace $d$ of D is zero. Finally, some more related results are also obtained.