• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.585-602
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• 2020

In this paper, we construct four infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O⁺(2n, 2^r). And we obtain two infinite families of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless' power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O⁺(2n, 2^r).

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1741-1752
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• 2008

Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1135-1144
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• 2014

A finite group G is called a SB-group if every subgroup of G is either s-quasinormal or abnormal in G. In this paper, we give a complete classification of those groups which are not SB-groups but all of whose proper subgroups are SB-groups.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.365-374
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• 2020

Given a noncompact semisimple Lie group G and its maximal compact Lie subgroup K such that the right multiplication of each element in K gives an isometry on G, consider a principal bundle G → G/K, which is a Riemannian submersion. We study the infinitesimal holonomy isometries. Given a closed curve at eK in the base space G/K, consider the holonomy displacement of e by the horizontal lifting of the curve. We prove that the correspondence is continuous.

• The Korean Journal of Physiology and Pharmacology
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• v.5 no.5
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• pp.373-380
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• 2001

The action of opioid on the hyperpolarization-activated cation current $(I_h)$ in substantia gelatinosa neurons were investigated by using whole-cell voltage-clamp recording in rat spinal brain slices. Hyperpolarizing voltage steps revealed slowly activating currents in a subgroup of neurons. The half-maximal activation and the reversal potential of the current were compatible to neuronal $I_h.$ DAMGO $(1\;{\mu}M),$ a selective- opioid agonist, reduced the amplitude of $I_h$ reversibly. This reduction was dose-dependent and was blocked by CTOP $(2\;{\mu}M),$ a selective ${\mu}-opioid$ antagonist. DAMGO shifted the voltage dependence of activation to more hyperpolarized potential. Cesium (1 mM) or ZD 7288 $(100\;{\mu}M)$ blocked $I_h$ and the currents inhibited by cesium, ZD 7288 and DAMGO shared a similar time and voltage dependence. These results suggest that activation of ${\mu}-opioid$ receptor by DAMGO can inhibit $I_h$ in a subgroup of rat substantia gelatinosa neurons.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.871-894
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• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1209-1251
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• 2015

The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group $Sol_1^4$, and more generally, the crystallographic groups of $Sol_1^4$. The maximal compact subgroup of Isom($Sol_1^4$) is $D_4={\mathbb{Z}}_4{\rtimes}{\mathbb{Z}}_2$. We shall exhibit an infra-solvmanifold of $Sol_1^4$ whose holonomy is $D_4$. This implies that all possible holonomy groups do occur; the trivial group, ${\mathbb{Z}}_2$ (5 families), ${\mathbb{Z}}_4$, ${\mathbb{Z}}_2{\times}{\mathbb{Z}}_2$ (5 families), and ${\mathbb{Z}}_4{\rtimes}{\mathbb{Z}}_2$ (2 families).

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.45-49
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• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.289-300
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• 1995

Every group G has a unique maximal normal locally nilpotent subgroup $\Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 \leq R_1 \leq \ldots$ in which $R_{\alpha+1}/R_\alpha = \{Phi(G/R_\alpha)$ for each ordinal $\alpha and R_\beta = \cup_{\alpha<\beta}R_\alpha$ for each limit ordinal $\beta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.

• Journal of Oral Medicine and Pain
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• v.24 no.1
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• pp.37-47
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• 1999

This study was performed to investigate the factors related to vibration of temporomandibular joint during mandibular opening movement. For this study, 144 patients with temporomandibular disorders were randomly selected. Angle's classification, lateral guidance pattern, range of maximal mouth opening, preferred chewing side, and affected side were investigated clinically. Mandibular torque rotational movement during opening was recorded with $BioEGN^{(R)}$ and vibration of temporomandibular joint during opening was recorded with $Sonopak^{(R)}$. After clinical diagnosis was made, visual analogue scale(VAS) was used for evaluation of clinical progress of the subject's chief complaints. The author calculated VAS treatment index(VAS Ti) from the record of VAS. The more VAS Ti was, the less remission of subjective symptom was, The data were analyzed with SAS/Stat program and the results of this study were as follows: 1. There were no significant difference in all the variables of joint vibration by age and sex. 2. Integral and peak amplitude in patients of Angle's class I were higher than those of class II or III patients. Integral in patients of group function was higher than that in patients of canine guidance or other types of lateral excursion. 3. As to Angle's classification or lateral guidance type, there were almost not significant difference between subgroup of same class or type and subgroup of different class or type on both sides. And there were also almost not difference between one side and the other side related to preferred chewing side or affected side. 4. Patients with disk displacement with reduction showed higher value of integral and peak amplitude than any other patients. 5. Joint vibration variables significantly correlated with VAS Ti of pain. with clinical range of mouth opening, and with ingredients of mandibular torque rotational movement.