• 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.

• Korean Journal of Biological Psychiatry
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• v.1 no.1
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• pp.79-87
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• 1994

For the purpose of evaluating the human leukocyte antigen(HLA) disease-association with bipolar disorder, HLA class I and class II allelic frequencies were assessed in 37 bipolar patients and were compared to the data from normal population. HLA class 1 typing was performed with microlymphocytotoxicity method while class II(DRB1) genotyping with reverse dot blot hybridization and sandwich method. Statistical analysis consisted of relative risk, Haldane's modified relative risk, Fisher's exact test and Bonferoni's corrected P. The results were as follows : 1) Bipolar patients showed increased allelic frequency of HLA A3 which has statistical significance. 2) Allelic frequencies of HLA B7, B14 and B54 were higher, while those of B51 and B55 were lower in bipolar patients, but they were not statistically significant. 3) Both of increased frequencies of DR2 in bipolar patients and DR15 in normal controls had statistical significance. The results of the present study suggested that some of HLA allelic types might be associated with bipolar disorder. To clarify the genetic influence of HLA to bipolar disorder, we should do consecutive study of bipolar disorder with new information about HLA system including alleles.

• Journal of the Korean Society of Food Culture
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• v.13 no.4
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• pp.293-305
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• 1998

According to economical status, under-nutrition and over-nutrition coexist in preschool children in Korea. Subjects consumed more than RDA in most nutrients, and children in of the upper income class tended to have more nutrients than those of the low income class. Especially in case of energy, protein, fat, vitamin $B_2$, and P there were significant differences among the different classes. The mean calorie compositions of carbohydrates, protein and fat were $57{\sim}59:\;16{\sim}17:\;26{\sim}27$ and fat calorie percentage was higher than quantity recommended for Korean adults. Energy, protein, Fe, vitamin A, $B_1$ and C intakes were taken mostly from plant food sources. In the upper income class group, intakes of protein and vitamin $B_2$ from animal food sources were higher than in any other income classes. Intakes of iron, vitamin A, $B_1$ and C were largely provided by plant food group. Especially 44-45% of vitamin A were taken from vegetable and fruits group, which indicated that about 50% of vitamin A intake was the form of ${\beta}-carotene$. Also compared with other groups, in the upper income class group, the intakes of energy, protein, Ca, p, vitamin $B_1$ and vitamin $B_2$ from cereal and potatoes were significantly lower, and those of Ca and P from milks and meats, fishes & eggs were significantly higher(p<0.05). The mean fat intake in all subjects was $38{\sim}43g/day$. Regardless of income class, oleic acid($6.6{\sim}8.4g$) and linoleic acid($6.7{\sim}8.1g$) were the most abundant fatty acids contained in the diet. The upper class group consumed significantly more total saturated fatty acids and total monounsaturated fatty acids(p<0.05). In polyunsaturated fatty acids, there were no differences between 3 different income classes, but intakes of total ${\omega}6$ fatty acids in the upper class tended to be higher and those of total o3 fatty acids in low class tended to be higher. Therefore, ${\omega}6/{\omega}3$ tended to be higher in the upper class group. Regardless of income classes, P/M/S and ${\omega}6/{\omega}3$ ratios in all subjects were $0.9{\sim}l.3/1.0{\sim}1.1/1.0$ and $5.2{\sim}7.4/1.0$, respectively and were in a desirable range. Cholesterol intake of subject was 184-218 mg/day, which was comparable to the value of Korean adult intake.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.865-877
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• 2013

The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal{M}$, as the disjoint union of the braid groups $\mathcal{B}$ does. We give a concrete and geometric meaning of the braidings ${\beta}_{r,s}$ in $\mathcal{M}$. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we can define an obvious map ${\phi}\;:\;B_g{\rightarrow}{\Gamma}_{g,1}$. We show that this map ${\phi}$ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor ${\Phi}\;:\;\mathcal{B}{\rightarrow}\mathcal{M}$, the integral homology homomorphism induced by ${\phi}$ is trivial in the stable range.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.61-74
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• 2006

Let G be a simple graph and let G denote its complement. We say that $\bar{G}$ is integral if its spectrum consists of integral values. In this work we establish a characterization of integral graphs which belong to the class $\bar{{\alpha}K_{a,a}\cup{\beta}K_{b,b}}$, where mG denotes the m-fold union of the graph G.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.539-547
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• 2005

The class of b-open sets in the sense of $Andrijevi{\acute{c}}$ ([3]), was discussed by El-Atik ([9]) under the name of ${\gamma}-open$ sets. This class is closed under arbitrary union. The aim of this paper is to use ${\Lambda}-sets$ and ${\vee}-sets$ due to Maki ([15]) some topologies are constructed with the concept of b-open sets. $b-{\Lambda}-sets,\;b-{\vee}-sets$ are the basic concepts introduced and investigated. Moreover, several types of near continuous function based on $b-{\Lambda}-sets,\;b-{\vee}-sets$ are constructed and studied.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) which consists of functionals F of the form : $$F(x)={\int}_H\;{\exp}\{i(h,x)^{\sim}\}df(h),\;x{\in}B$$ where $({\cdot}{\cdot})^{\sim}$ is a stochastic inner product between H and B, and $f$ is in $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.391-401
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• 2012

B. C. Berndt has found a transformation formula for a large class of functions, which comes from a transformation formula for a more general class of Eisenstein series. In this paper, using his formula which is 'twisted' by change of variables, we find a class of infinite series identities.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.59-65
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• 1996

In this paper, we study spaces admitting cs-semistratification and cs-semistratifications with (CF) property. The class of cs-semistratifiable spaces lies between the class of k-semistratifiable spaces and that of semistratifiable spaces which lie between the class of semi-metric spaces and the class of spaces in which closed sets are $G_{\sigma}$ and really differs from the classes of stratifiable spaces.