• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.489-496
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• 2012

In this paper, we introduce the notions of Smarandache weak BE-algebra, Q-Smarandache filters and Q-Smarandache ideals. We show that a nonempty subset F of a BE-algebra X is a Q-Smarandache filter if and only if $A(x,y){\subseteq}F$, which A($x,y$) is a Q-Smarandache upper set The relationship between these notions are stated and proved.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.821-827
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• 2012

In this paper, we prove that for all odd prime powers $q$ there exist MDS(maximum distance separable) self-dual codes over $\mathbb{F}_{q^2}$ for all even lengths up to $q+1$. Additionally, we prove that there exist MDS self-dual codes of length four over $\mathbb{F}_q$ for all $q$ > 2, $q{\neq}5$.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Journal of the Korean earth science society
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• v.28 no.6
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• pp.720-732
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• 2007

For the Seoul metropolitan area and the eastern Kyeongsang Basin, we simultaneously calculated $Q_P^{-1}$ and $Q_S^{-1}$ by applying the extended coda-normalization method for 98 seismograms of local Earthquakes. As frequency increases from 1.5 Hz to 24 Hz, the result decreased from $(4.0{\pm}9.2){\times}10^{-3}$ to $(4.1{\pm}4.2){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.5{\pm}5.6){\times}10^{-3}$ to $(3.4{\pm}1.3){\times}10^{-4}$ for $Q_S^{-1}$ in Seoul Metropolitan Area. The result of eastern Kyeongsang basin also decreased from $(5.4{\pm}8.8){\times}10^{-3}$ to $(3.7{\pm}3.4){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.7{\pm}4.2){\times}10^{-3}$ to $(3.5{\pm}1.6){\times}10^{-4}$ for $Q_S^{-1}$. If we fit a frequency-dependent power law to the data, the best fits of $Q_P^{-1}$ and $Q_S^{-1}$ are $0.005f^{-0.89}$ and $0.004f^{-0.88}$ in Seoul metropolitan Area, respectively. The value of $Q_P^{-1}$ and $Q_S^{-1}$ in the eastern Kyeongsang basin are $0.007f^{-1.02}$ and $0.006f^{-0.99}$, respectively. The $Q_S^{-1}$ value of the eastern Kyeongsang basin is almost similar to Seoul metropolitan area. But the $Q_P^{-1}$ value of the eastern Kyeongsang basin is a little higher than that of Seoul metropolitan area. This may be that the crustal characteristics of the eastern Kyeongsang basin is seismologically more heterogeneous. However, these $Q_P^{-1}$ values in Korea belong to the range of seismically stable regions all over the world.

• Journal of the Korean Geophysical Society
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• v.9 no.3
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• pp.199-207
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• 2006

Fukuoka earthquake on March 20, 2005 showed the potential hazard of large events out of S. Korea. From the viewpoint of seismic hazard, seismic amplitude decrease Q-1 is very important. Related to the crustal cracks induced by the earthquakes, the value of Q-1- high Q-1 regions are more attenuating than low Q-1 regions - shows a correlation with seismic activity; relatively higher values of Q-1 have been observed in seismically active areas than in stable areas. For the southeastern and central S. Korea, we first simultaneously estimated QP-1 and QS-1 by applying the extended coda-normalization method to KIGAM and KNUE network data. Estimated QP-1 and QS-1 values are 0.009 f-1.05 and 0.004 f-0.70 for southeastern S. Korea and 0.003 f -0.54 and 0.003 f -0.42 for central S. Korea, respectively. These values agree with those of seismically inactive regions such as shield. The low QLg-1 value, 0.0018f -0.54 was also obtained by the coda normalization method. In addition, we studied QLg-1 by applying the source pair/receiver pair (SPRP) method to both domestic and far-regional events. The obtained QLg-1 for all Fc is less than 0.002, which is reasonable value for a seismically inactive region.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.731-745
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• 2013

In this paper, we investigate uniqueness problems of certain types of $q$-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where $q$-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function $f$ and a non-zero complex constant $q$, $E(S_j,f)=E(S_j,{\Delta}_qf)$ for $j=1,2$ imply $f(z)=t{\Delta}_qf$, where $t^n=1$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $f(z)$ and $t{\Delta}_qf$.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• The Korean Journal of Ecology
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• v.14 no.3
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• pp.231-241
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• 1991

The analyses of correlation, enviromental gradient, continuum and polar ordination methods were used for studing on relationships between forest vegetation and their habitats in Mt. changan, chagsu-gun, korea. influencing correlation of moisture index to the main 41species from the study area they were composed of several groups by leading species of quercus mongoulica, that of carpinus tschonoskii and that of fraxinus mandshurica. On the other hand, it was found three communities in different habitats by environmental gradient i.e. each community of f. mandshurica, mangnolia sieboldii and hydrangea serrata for. acuminata have occurred in moist place, that of c. teschonoskii and q. serrata, in mesic and that of q. mongolica, q.variabilis, rhododendron schlippenbachii, in dry. in addition an occupied distribution area was investigated according to continuum index e.g. cornus controversa,betula costata,q. variabilis, q. serrata and q. mongolica over altitudinal 800m were distributed to a habitat were forming climax by q. mongolica, and/or c. controversa, f. mandshurica, q. serrata and c. tschonoskii under altitudinal 800m were done, by g. tschonoskii. while the forest vegetation of the area was classified into 6 communities such as q. mongolica community, q. variabilis community,q. serrata community, g. tschonoskii community,c. controversa community and f. mandshurica community by means of polar ordination analysis and these have come under the influence of environmental factors.

• Journal of the Korean earth science society
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• v.22 no.6
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• pp.500-511
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• 2001

For the southeastern Korea aound the Yangsan fault we measured Q$_P^{-1}$ and Q$_S^{-1}$ simultaneously by using the extended coda-normalization method for seismograms registered at 9 stations deployed by KIGAM. We analyzed 707 seismograms of local earthquakes that occurred between December 1994 and February 2000. From seismograms, bandpass filtered traces were made by applying Butterworth filter with frequency-bands of 1${\sim}$2, 2${\sim}$4, 4${\sim}$8, 8${\sim}$16 and 16${\sim}$32 Hz. Estimated Q$_P^{-1}$ and Q$_S^{-1}$ values decrease from (7${\pm}$2)${\times}$10$^{-3}$ and (5${\pm}$4)${\times}$10$^{-4}$ at 1.5 Hz to (5${\pm}$4)${\times}$10$^{-3}$ and (5${\pm}$2)${\times}$10$^{-4}$ at 24 Hz, respectively. By fitting a power-law frequency dependent to estimated values over the whole stations, we obtained 0.009 (${\pm}$0.003)f$^{-1.05({\pm}0.14)$ for Q$_P^{-1}$ and 0.004 (${\pm}$0.001)f$^{-0.75({\pm}0.14)$) for Q$_S^{-1}$, where f is frequency in Hz.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.287-303
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• 1999

The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s $\in$] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.