• Journal of Communications and Networks
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• v.3 no.4
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.157-169
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• 1999

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.419-428
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• 2007

The space of periodic Boehmians with $\Delta$-convergence is a complete topological algebra which is not locally convex. A family of Boehmians $\{T_\lambda\}$ such that $T_0$ is the identity and $T_{\lambda_1+\lambda_2}=T_\lambda_1*T_\lambda_2$ for all real numbers $\lambda_1$ and $\lambda_2$ is called a one-parameter group of Boehmians. We show that if $\{T_\lambda\}$ is strongly continuous at zero, then $\{T_\lambda\}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for $\{T_\lambda\}$.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.35-38
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• 1995

Let A be a symmetric positive definite Cartan matrix. As in [4], we denote by U the quantum group arising from A and $U_\lambda$ be the corresponding quantum group at a root of unity $\lambda$. In [4], Lusztig constructed irreducible highest weight $U_\lambda$-modules $L_\lambda(z)$ for $z \in Z^n$ and showed that $L_\lambda(z)$ is of finite dimension over C if and only if $z \in (Z^+)^n$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1033-1041
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• 2016

We show that, for any non-zero integers ${\lambda}$, ${\mu}$, ${\nu}$, ${\xi}$, class-preserving automorphisms of the group $$G({\lambda},{\mu},{\nu},{\xi})={\langle}a,b,t:b^{-1}a^{\lambda}b=a^{\mu},t^{-1}a^{\nu}t=b^{\xi}{\rangle}$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G({\lambda},{\pm}{\lambda},{\nu},{\xi})$ is residually finite.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.337-346
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• 2002

Complete diallel crosses using group divisible design with m=2 or n=2 and ${\lambda}_1$<${\lambda}_2$ as parameter designs become A-optimal, D-optimal designs. In case of ${\lambda}_2$=${\lambda}_1$+1, this blocked complete diallel crosses become generalized optimal designs.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• Korean Journal of Remote Sensing
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• v.23 no.4
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• pp.311-321
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• 2007

The diffuse attenuation coefficient for down-welling irradiance $K_d({\lambda})$, which is the propagation of down-welling irradiance at wavelength ${\lambda}$ from surface to a depth (z) in the ocean, and underwater visibility are important optical parameters for ocean studies. There have been several studies on $K_d({\lambda})$ and underwater visibility around the world, but only a few studies have focused on these properties in the Korean sea. Therefore, in the present study, we studied $K_d({\lambda})$ and underwater visibility around the coastal area of the Yellow Sea, and developed $K_d({\lambda})$ and underwater visibility algorithms for ocean color satellite sensor. For this research we conducted a field campaign around the Yellow Sea from $19{\sim}22$ September, 2006 and there we obtained a set of ocean optical and environmental data. From these datasets the $K_d({\lambda})$ and underwater visibility algorithms were empirically derived and compared with the existing NASA SeaWiFS $K_d({\lambda})$ algorithm and NRL (Naval Research Laboratory) underwater visibility algorithm. Such comparisons over a turbid area showed small difference in the $K_d({\lambda})$ algorithm and constants of our result for underwater visibility algorithm showed slightly higher values.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.657-668
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• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• Journal of Korean Neurosurgical Society
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• v.55 no.5
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• pp.267-272
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• 2014

Objective : Differentiation of demyelination in white matter from axonal damage can be determined using diffusion tensor imaging (DTI). In this study using meningioma patients an attempt was made to evaluate the relationship between preoperative weakness and the changes of diffusion parameters in the corticospinal tract (CST) using DTI. Methods : Twenty-six patients with meningioma were enrolled in this study. Eleven of them suffered from objective motor weakness and were classified as Group 1. The remaining 15 patients did not present motor weakness and were classified as Group 2. Fiber tractography and CST diffusion parameters were obtained using DTIStudio. The ratios (lesion side mean value/contralateral side mean value) of CST diffusion parameters were compared with 1.0 as a test value using a one-sample t-test. Results : In Group 1, fractional anisotropy (FA), tensor trace (TT), and radial diffusivity (RD, ${\lambda}2$ and ${\lambda}3$) of the CST were significantly different between two hemispheres, but axial diffusivity (AD, ${\lambda}1$) of the CST was not significantly different between two hemispheres. In Group 2, FA and ${\lambda}3$ of CST did not differ significantly between the hemispheres. In Group 2, TT, ${\lambda}1$, and ${\lambda}2$ of CST in the ipsilateral hemisphere were significantly higher than those of the unaffected hemisphere. However, the differences were small. Conclusion : Motor weakness was related to a low FA and high TT resulting from increased RD of the CST fibers. CST diffusion changes in patients with weakness are similar to those for demyelination.