• Honam Mathematical Journal
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• v.27 no.3
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• pp.389-397
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• 2005

Let K be an absolutely real abelian number field with $G=Gal(K/{\mathbb{Q}})$. Let E be a subfield of K and ${\Delta}=Gal(K/E)$. Let $C_K$ and $C_E$ be the group of circular units of K and E respectively. In [G], Greither has shown that if G is cyclic then $C_K^{\Delta}=C_E$. In this paper we show that the same result holds in function field case.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.515-525
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• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

• International Journal of Advanced Culture Technology
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• v.6 no.3
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• pp.44-52
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• 2018

The purpose of this study was to assess the effects and find the correlation of LOTCA-G and SS-QOL on the cognitive function and quality of life of elderly stroke patients. The time period of the experiment was from March 1, 2018 to March 30, 2018, and the study sample was composed of 102 stroke out-patients who participated in the rehabilitation center in G-city and received treatment of LOTCA-G and SS-QOL. The raw scores of the cognitive function of the elderly stroke patients varied depending on their gender, age, education, and marital status, but the differences were not statistically significant. Second, the raw scores of the quality of life of the elderly stroke patients varied depending on their gender, age, education, and marital status, but only marital status showed significance (p <0.01). The elderly stroke patients' cognitive function and the quality of life showed a statistically significant correlation (p <0.01). LOTCA-G and SS-QOL generally showed significant correlation even among sub-categories, but energy, one of the sub-categories of quality of life, did not show significant correlation with any of the other sub-categories of cognitive function. By combining the study results, it was possible to see that there were high levels of correlation between cognitive function and quality of life in elderly stroke patients shown through LOTCA-G and SS-QOL. Based on this study, if the raw scores of cognitive function and quality of life could be validated and various basic data could be provided for increasing quality of life, it can be considered that the stroke patients' quality of life will be improved.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.77-87
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• 1996

For any map $v:X{\rightarrow}Y$, the generalized Gottlieb set $G({\Sigma}A;X,v,Y)$ with respect to v is a subgroup of $[{\Sigma}A,Y]$. If $v:X{\rightarrow}Y$ has a left homotopy inverse $u:X{\rightarrow}Y$, then for any $f{\in}G({\Sigma}A;X,v,Y)$, $g{\in}G({\Sigma}A;X,u,Y)$, the function spaces $L({\Sigma}A,X;uf)$ and $L({\Sigma}A,X;g)$ have the same homotopy type.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.27-33
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• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.551-563
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• 2011

Let ${\kappa}$ be a positive integer and let G be a simple graph with vertex set V(G). A function f : V (G) ${\rightarrow}$ {-1, 1} is called a signed total ${\kappa}$-dominating function if ${\sum}_{u{\in}N({\upsilon})}f(u){\geq}{\kappa}$ for each vertex ${\upsilon}{\in}V(G)$. A set ${f_1,f_2,{\ldots},f_d}$ of signed total ${\kappa}$-dominating functions of G with the property that ${\sum}^d_{i=1}f_i({\upsilon}){\leq}1$ for each ${\upsilon}{\in}V(G)$, is called a signed total ${\kappa}$-dominating family (of functions) of G. The maximum number of functions in a signed total ${\kappa}$-dominating family of G is the signed total k-domatic number of G, denoted by $d^t_{kS}$(G). In this note we initiate the study of the signed total k-domatic numbers of graphs and present some sharp upper bounds for this parameter. We also determine the signed total signed total ${\kappa}$-domatic numbers of complete graphs and complete bipartite graphs.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.7 s.98
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• pp.697-708
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• 2005

The forward link of the 3G CDMA system may become limited under the increasing of the number of users. The conventional channelization code, Walsh code, has not enough sizes f3r much possible users, therefore, the quasi orthogonal function(QOF), which process optimal crosscorrelation with Walsh code, is considered. In this paper, we investigate quasi orthogonal function on Jacket matrices, which can lead lower correlations values and better performance in 3G CDMA system. Moreover, to simplify the detector and improve the BER performance, a novel detection for QOF CDMA system is proposed. Finally, the simple recursive generation of the bent sequences for QOF mask function is discussed.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.55-82
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• 2019

Given ${\sigma}:G{\rightarrow}G$ an involutive automorphism of a semigroup G, we study the solutions and stability of the following functional equations $$f(x{\sigma}(y))=f(x)g(y)+g(x)f(y),\;x,y{\in}G,\\f(x{\sigma}(y))=f(x)f(y)-g(x)g(y),\;x,y{\in}G$$ and $$f(x{\sigma}(y))=f(x)g(y)-g(x)f(y),\;x,y{\in}G$$, from the theory of trigonometric functional equations. (1) We determine the solutions when G is a semigroup generated by its squares. (2) We obtain the stability results for these equations, when G is an amenable group.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.4A
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• pp.291-300
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• 2002

In this paper, a way of constituting optimized S box and G function was suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over GF(2$\^$8/) which has neither a fixed point, whose input and output are the same except 0 and 1, nor an opposite flexed number, whose output is one's complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes diffusive linear transform with 4 S-box outputs using the matrix of 4$\times$4 over GF(2$\^$8/). G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, there can be no weak input, where a fried point, an opposite fried point, and output can be two's complement of input, and the construction of hardware can be made easy. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.