• Journal of Korean Society for Atmospheric Environment
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• v.20 no.6
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• pp.749-758
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• 2004

Nitrous oxide ($N_2$O) has been known as an important trace gas due to the greenhouse gas and the major source of stratospheric oxide of nitrogen (NO). Soil is the major source of $N_2$O in nature. The physicochemical characteristics of soils affect the emission of $N_2$O from soil. These physicochemical parameters are soil moisture, soil temperature, and soil N content. Since these parameters are correlated to the flux of $N_2$O from soil individually and compositely, there still remain many unknowns in the mechanism to produce $N_2$O in soil and the roles of such physicochemical parameters which affect the soil $N_2$O emission. Soil $N_2$O fluxes were measured at different levels in water filled pore space (WFPS), soil temperature and soil N contents from the same amounts of soils which were sampled from agriculturally managed upland field in a depth of ～30 cm at Kunsan. The soil $N_2$O flux measurements were conducted in a laboratory with a closed flux chamber system. The optimum soil moisture and soil temperature were observed at 60% of WFPS and ～13$^{\circ}C$. The soil $N_2$O flux increased as soil N contents increases during the whole experimental hours (up to 48 hours). However, average $N_2$O flux decreased after ～30 hours when organic carbon was mixed with nitrogen in the sample soils. It is suggested that organic carbon could be important for the emission of $N_2$O, and that the ratio of N to C needs to be identified in the process of $N_2$O soil emission.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1467-1480
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• 2015

Generalized Fibonacci and Lucas sequences ($U_n$) and ($V_n$) are defined by the recurrence relations $U_{n+1}=PU_n+QU_{n-1}$ and $V_{n+1}=PV_n+QV_{n-1}$, $n{\geq}1$, with initial conditions $U_0=0$, $U_1=1$ and $V_0=2$, $V_1=P$. This paper deals with Fibonacci and Lucas numbers of the form $U_n$(P, Q) and $V_n$(P, Q) with the special consideration that $P{\geq}3$ is odd and Q = -1. Under these consideration, we solve the equations $V_n=5kx^2$, $V_n=7kx^2$, $V_n=5kx^2{\pm}1$, and $V_n=7kx^2{\pm}1$ when $k{\mid}P$ with k > 1. Moreover, we solve the equations $V_n=5x^2{\pm}1$ and $V_n=7x^2{\pm}1$.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.4
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• pp.389-405
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• 1999

본 논문에서는 상호 연결망의 노드를 행렬로 표현하고 행렬연산을 이용하여 에지를 정의한 새로운 상호 연결망으로 행렬-스타 그래프를 제안한다. 행렬-스타 그래프는 널리 알려진 스타 그래프를 일반화한 그래프이다. 먼저, 행렬-스타 그래프의 노드를 2 $\times$ n 행렬로 표현한 행렬-스타 그래프 MS2,n 에 대하여 주요 망 척도인 분지수, 연결도, 확장성, 대칭성, 리우팅 ,지름 방송등을 분석한다. 다음으로, 행렬-스타 그래프 MS2,n의 노드를 2차원과 3차원으로 일반화한 행렬-스타 그래크 MSk,n과 MS k,n,p를 정의하고 행렬-스타그래프 MSk,n,p 의 라우팅 알고리즘과 지름을 분석한다. 상호연결망의 중요 망 척도중 하나는 망 비용이고 상호연결망의 망 비용은 그 연결망의 분지수와 지름의 곱으로 정의된다. star 그래프는 다른 상호 연결망보다 작은 망 비용을 갖는다. 최근에 제안된 Macro-Star 그래픈 star 그래프에 비해 상대적으로 망 비용이 작은 값을 갖는 연결망이다. (n2)!개의 노드를 갖는 행렬-스타 그래프 MSk,k,k(k={{{{ `^{ 3} SQRT { n$^2$} }}}} )와 ((n-1)2 + 1)!개의 노드를 갖는 Macro-Star 그래프 MS(n-1, n-1)의 망 비용은 행렬-스타그래프 MSk,k,k(k={{{{ `^{ 3} SQRT { n$^2$} }}}})는 O(n2,7)이고, Macro-Star 그래프 MS(n-1 , n-1)은 O(n3) 이다. 이는 행렬-스타 그래프가 스타 그래프와 Macro-Star 그래프보다 망비용이 우수함을 의미한다.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.331-360
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the sth powers of the positive divisors of a positive integer N and let $\tilde{\sigma}_s(N)={\sum}_{d|N}(-1)^{d-1}d^s$ with $d$, N, and s positive integers. Hahn [12] proved that $$16\sum_{k. In this paper, we give a generalization of Hahn's result. Furthermore, we find the formula ${\sum}_{k=1}^{N-1}\tilde{\sigma}_1(2^{n-m}k)\tilde{\sigma}_3(2^nN-2^nk)$ for $m(0{\leq}m{\leq}n)$.

• 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.

• Bulletin of the Korean Chemical Society
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• v.25 no.6
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• pp.796-800
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• 2004

The structure of [Cu(tpen)]$(ClO_4)_2$ (tpen = N,N,N',N'-tetrakis(2-pyridylmethyl)-1,2-ethanediamine) has been identified by X-ray crystallography. The copper(II) ion is surrounded by two amine N atoms and three pyridine N atoms of the ligand, making a distorted trigonal-bipyramid. Among the six potential N donor atoms (two amine N and four pyridine N atoms), only one pyridine N atom remains uncoordinated. We examined structural changes on addition of $Cl^-$ to $[Cu(tpen)]^{2+}$(1). The addition of $Cl^-$ in methanol resulted in the formation of a novel dinuclear copper(II) complex $[Cu_2Cl_2(tpen)](ClO_4)_2{\cdot}H_2O$. The structure of the dinuclear complex was verified by X-ray crystallography. Each copper(II) ion in the dinuclear complex showed a distorted square planar geometry with two pyridine N atoms, one amine N atom and one $Cl^-$ ion.

• Korean Chemical Engineering Research
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• v.40 no.6
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• pp.746-751
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• 2002

Fluidized bed combustion is a coal combustion technology that can reduce both SOx and NOx emission; SOx is removed by limestone that is fed into the combustion chamber and the NOx is reduced by low temperature combustion in a fluidized bed combustor and air stepping, but $N_2O$ generation is quite high. $N_2O$ is not only a greenhouse gas but also an agent of ozone destruction in the stratosphere. The calcium oxide(CaO) is known to be a catalyst of $N_2O$ decomposition. This study of $N_2O$ decomposition reaction in fixed bed reactor packed over CaO bed has been conducted. Effects of parameters such as concentration of inlet $N_2O$ gas, reaction temperature, CaO bed height and effect of $CO_2$, NO, $O_2$ gas on the decomposition reaction have been investigated. As a result of the experiment, it has been shown that $N_2O$ decomposition reaction increased with the increasing fixed bed temperature. While conversion of the reaction was decreased with increasing $CO_2$ concentration. Also, under the present of NO, the conversion of $N_2O$ decomposition is decreased. From the result of kinetic study gained the heterogeneous reaction rate on $N_2O$ decomposition. In the case of $N_2O$ decomposition over CaO, heterogeneous reaction rate is. $\frac{d[N_2O]}{dt}=\frac{3.86{\times}10^9{\exp}(-15841/R)K_{N_2O}[N_2O]}{(1+K_{N_2O}[N_2O]+K_{CO_2}[CO_2])}$. In this study, it is found that the calcium oxide is a good catalyst of $N_2O$ decomposition.

• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Journal of KIISE:Databases
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• v.33 no.1
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• pp.12-31
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• 2006

The n-gram inverted index has two major advantages: language-neutral and error-tolerant. Due to these advantages, it has been widely used in information retrieval or in similar sequence matching for DNA and Protein databases. Nevertheless, the n-gram inverted index also has drawbacks: the size tends to be very large, and the performance of queries tends to be bad. In this paper, we propose the two-level n-gram inverted index (simply, the n-gram/2L index) that significantly reduces the size and improves the query performance while preserving the advantages of the n-gram inverted index. The proposed index eliminates the redundancy of the position information that exists in the n-gram inverted index. The proposed index is constructed in two steps: 1) extracting subsequences of length m from documents and 2) extracting n-grams from those subsequences. We formally prove that this two-step construction is identical to the relational normalization process that removes the redundancy caused by a non-trivial multivalued dependency. The n-gram/2L index has excellent properties: 1) it significantly reduces the size and improves the Performance compared with the n-gram inverted index with these improvements becoming more marked as the database size gets larger; 2) the query processing time increases only very slightly as the query length gets longer. Experimental results using databases of 1 GBytes show that the size of the n-gram/2L index is reduced by up to 1.9${\~}$2.7 times and, at the same time, the query performance is improved by up to 13.1 times compared with those of the n-gram inverted index.

• Bulletin of the Korean Chemical Society
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• v.22 no.7
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• pp.761-764
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• 2001