• 대한수학회지
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• 제32권2호
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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.

• Tuberculosis and Respiratory Diseases
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• 제42권2호
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• pp.165-174
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• 1995

연구배경: 운동유발성 천식은 운동에 의해서 기관지 수축이 나타나는 것으로, 일상생활에서 흔히 경험하는 천식발작의 형태로서, 특히 소아에서는 중요하다. 이러한 운동유발성 기관지 수축은 비특이적으로 발생된다는 점에서, 통상적으로 측정, 평가되는 histamine이나 metacholine에 의한 비특이적 기관지 반응도와 밀접한 관련을 생각할 수 있다. 비특이적 기관지 반응도 중 $PC_{20}$으로 표시되는 기도 민감도는 운동유발성 기관지 수축의 정도와 비례하는 것이 밝혀져 있으나, 또 다른 요소인 최대 기도 협착의 정도와 운동유발성 기관지 수축(EIB)의 정도와의 연관성에 대해서는 연구된 바 없다. 방법: 56명의 천식 환아에서 고농도의 methacholine 유발시험에서의 $PC_{20}$, 최대반응고원(MRP), 최대기도 협착(MAN)을 측정하고, 운동유발시험에서의 운동유발성 기관지수축을 측정하였다. 이들을 운동유발성 기관지 수축의 정도에 따라 3군으로 구분하여, 각군간의 $PC_{20}$, MRP, MAN의 차이를 알아보고 전체 대상에서 운동유발성 기관지 수축의 정도와 $PC_{20}$, MRP, MAN 각각과의 상관관계를 알아보았다. 결과: 1) 운동유발성 기관지 수축이 20% 이상인(+) EIB군의 $PC_{20}$은, 10% 이하인 (-)EIB의 $PC_{20}$보다 유의하게 낮았다(p<0.01). 2) 전체 대상에서 methacholine $PC_{20}$의 log치는 운동유발성 기관지수축의 정도와 유의한 역비례 관계를 나타내었다(r=-0.568, p<0.01). 3) 전체 56명중 36명에서 MRP를 구할수 있었는데 이들에서 MRP와 운동유발성 기관지 수축의 정도는 유의한 상관관계를 보였다(r=0.355, p<0.05). 4) (+)EIB인 군의 MAN은 (-)EIB군의 MAN보다 유의하게 높았다. 5) 전체 대상에서 MAN은 운동유발성 기관지 수축의 정도와 유의한 정비례 관계를 나타내었다(r=0.546, p<0.01). 결론: 운동유발성 기관지 수축의 정도는 methacholine유발검사로 측정된 $PC_{20}$과 뿐만 아니라 MAN의 정도와 유의한 상관관계를 나타내었다. 이같은 결과는 비록 특이적 기관지 반응도를 결정하는 2가지 요소가, 비록 서로 다른 기전이지만, 운동에 대한 반응을 결정하는 요인으로 중요하게 작용함을 암시한다. 또한 NSBR을 평가할때 $PC_{20}$뿐만 아니라 MRP혹은 MAN의 측정이 가능한 포함되어야 할것이다.

• 대한수학회보
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• 제56권6호
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• pp.1485-1495
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• 2019

The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional $Pr{\ddot{u}}fer$ domains. We prove that ${\mid}SStar(R){\mid}={\mid}Star(R){\mid}+{\mid}Spec(R){\mid}+ {\mid}Idem(R){\mid}$ where Idem(R) is the set of all nonzero idempotent prime ideals of R if and only if R is a $Pr{\ddot{u}}fer$ domain with Y -graph spectrum, that is, R is a $Pr{\ddot{u}}fer$ domain with exactly two maximal ideals M and N and $Spec(R)=\{(0){\varsubsetneq}P_1{\varsubsetneq}{\cdots}{\varsubsetneq}P_{n-1}{\varsubsetneq}M,N{\mid}P_{n-1}{\varsubsetneq}N\}$. We also characterize non-local $Pr{\ddot{u}}fer$ domains R such that ${\mid}SStar(R){\mid}=7$, respectively ${\mid}SStar(R){\mid}=14$.

• 대한수학회보
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• 제55권2호
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• pp.533-543
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• 2018

Under the symbol ${\Omega}$ is a combination of ${\phi}_i$ ($i=1,2,3,{\ldots},n$) which has a suitable growth condition, for dimension n = 2 and $n{\geq}3$, when the initial data f belongs to homogeneous Sobolev space, we obtain the global $L^q$ estimate for maximal operators generated by operators family $\{S_{t,{\Omega}}\}_{t{\in}{\mathbb{R}}}$ associated with solution to dispersive equations, which extend some results in [27].

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.329-336
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• 2010

In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M=N(Q) is essentially independent of choice of Q. 2) If f : M ${\rightarrow}$ M' is a maximal R-semimodule homomorphism, then $M/kerf_{(Q)}\;\cong\;M'$. 3) Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with $N{\subseteq}A$ if and only if $A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}$ is a subtractive subsemimodule of $M/N_{(Q)}$.

• 대한수학회논문집
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• 제34권4호
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• pp.1049-1067
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• 2019

In this paper, we discuss the number of distinct fuzzy subgroups of the group ${\mathbb{Z}}_{p^n}{\times}{\mathbb{Z}}_{q^m}{\times}{\mathbb{Z}}_r$, m = 1, 2, 3 where p, q, r are distinct primes for any $n{\in}{\mathbb{Z}}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group G and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.

• East Asian mathematical journal
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• 제40권1호
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• pp.75-83
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• 2024

For a reduced, irreducible and nondegenerate curve C ⊂ ℙ^r of degree d, it was shown that the arithmetic genus g of C has an upper bound π₀(d, r) by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll S(0, 2) ⊂ ℙ³ which attain the maximal arithmetic genus.

• 대한수학회보
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• 제31권1호
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• pp.93-97
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• 1994

Previously T.Porter [3] has given a relative Chinese Remainder Theorem under the hypothesis that given ring R has at least one .tau.-closed maximal ideal (by his notation Ma $x_{\tau}$(R).neq..phi.). In this short paper we drop his overall hypothesis that Ma $x_{\tau}$(R).neq..phi. and give the proof and some related results with this Theorem. In this paper R will always denote a commutative ring with identity element and all modules will be unitary left R-modules unless otherwise specified. Let .tau. be a given hereditarty torsion theory for left R-module category R-Mod. The class of all .tau.-torsion left R-modules, dented by J is closed under homomorphic images, submodules, direct sums and extensions. And the class of all .tau.-torsionfree left R-modules, denoted by F, is closed under taking submodules, injective hulls, direct products, and isomorphic copies ([2], Proposition 1.7 and 1.10).

• The Korean Journal of Ecology
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• 제18권3호
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• pp.333-340
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• 1995

This study aims to examine how the amount of sample and changes in combustible temperature of living branches and leaves treated with high temperature are associated with combustible time of two coniferous trees, Pinus rigida (R) and Larix leptolepis (L), which are the main victims of forest fire. During the first thirty minutes at $80^{\circ}C$, moisture content of R was higher than that of L by 12%, but after four hours, the moisture content was both lowered by 4~5% and turned to highly combustible leaves. With living leaves, the maximal combustible temperature, regardless of heating temperature, turned out to be higher than normal temperature by $67~140^{\circ}C$, and that with living branches, it was higher by $113~207^{\circ}C$. Also, with living leaves (R, L), the duration time of combustion was as follows: 605, 906 seconds at $400^{\circ}C$ and 76, 227 seconds at $600^{\circ}C$, respectively. Concerning the relation between the amount of burnt fuel and maximal temperature, the more the former was, the higher the latter. The total amounts of combustion heat of living branches and living leaves were 1, 121 Cal (20.8%) and 1, 137 Cal (21.4%), respectively. The total amount of combustion heat increased in proportion to the amount of consumed fuel: 100 g of living leaves and branches gave rise to 128 Cal, whereas 300 g did 556 Cal, that was more than three times.

• Animal Bioscience
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• 제35권3호
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• pp.399-409
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• 2022

Objective: Follicle-stimulating hormone (FSH) is the central hormone involved in mammalian reproduction, maturation at puberty, and gamete production that mediates its function by control of follicle growth and function. The present study investigated the mutations involved in the regulation of FSH receptor (FSHR) activation. Methods: We analyzed seven naturally-occurring mutations that were previously reported in human FSHR (hFSHR), in the context of equine FSHR (eFSHR); these include one constitutively activation variant, one allelic variant, and five inactivating variants. These mutations were introduced into wild-type eFSHR (eFSHR-wt) sequence to generate mutants that were designated as eFSHR-D566G, -A306T, -A189V, -N191I, -R572C, -A574V, and -R633H. Mutants were transfected into PathHunter EA-parental CHO-K1 cells expressing β-arrestin. The biological function of mutants was analyzed by quantitating cAMP accumulation in cells incubated with increasing concentrations of FSH. Results: Cells expressing eFSHR-D566G exhibited an 8.6-fold increase in basal cAMP response, as compared to that in eFSHR-wt. The allelic variation mutant eFSHR-A306T was not found to affect the basal cAMP response or half maximal effective concentration (EC₅₀) levels. On the other hand, eFSHR-D566G and eFSHR-A306T displayed a 1.5- and 1.4-fold increase in the maximal response, respectively. Signal transduction was found to be completely impaired in case of the inactivating mutants eFSHR-A189V, -R572C, and -A574V. When compared with eFSHR-wt, eFSHR-N191I displayed a 5.4-fold decrease in the EC₅₀ levels (3,910 ng/mL) and a 2.3-fold decrease in the maximal response. In contrast, cells expressing eFSHR-R633H displayed in a similar manner to that of the cells expressing the eFSHR-wt on signal transduction and maximal response. Conclusion: The activating mutant eFSHR-D566G greatly enhanced the signal transduction in response to FSH, in the absence of agonist treatment. We suggest that the state of activation of the eFSHR can modulate its basal cAMP accumulation.