• 대한수학회지
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• 제55권4호
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• pp.797-808
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• 2018

In [1], the authors generalize the concept of the class group of an integral domain $D(Cl_t(D))$ by introducing the notion of the S-class group of an integral domain where S is a multiplicative subset of D. The S-class group of D, $S-Cl_t(D)$, is the group of fractional t-invertible t-ideals of D under the t-multiplication modulo its subgroup of S-principal t-invertible t-ideals of D. In this paper we study when $S-Cl_t(D){\simeq}S-Cl_t(D_T)$, where T is a multiplicative subset generated by prime elements of D. We show that if D is a Mori domain, T a multiplicative subset generated by prime elements of D and S a multiplicative subset of D, then the natural homomorphism $S-Cl_t(D){\rightarrow}S-Cl_t(D_T)$ is an isomorphism. In particular, we give an S-version of Nagata's Theorem [13]: Let D be a Krull domain, T a multiplicative subset generated by prime elements of D and S another multiplicative subset of D. If $D_T$ is an S-factorial domain, then D is an S-factorial domain.

• IMMUNE NETWORK
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• 제20권1호
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• pp.2.1-2.19
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• 2020

Acute viral infection or vaccination generates highly functional memory CD8 T cells following the Ag resolution. In contrast, persistent antigenic stimulation in chronic viral infection and cancer leads to a state of T-cell dysfunction termed T-cell exhaustion. We and other have recently identified a novel subset of exhausted CD8 T cells that act as stem cells for maintaining virus-specific CD8 T cells in a mouse model of chronic lymphocytic choriomeningitis virus infection. This stem cell-like CD8 T-cell subset has been also observed in both mouse and human tumor models. Most importantly, in both chronic viral infection and tumor models, the proliferative burst of Ag-specific CD8 T cells driven by PD-1-directed immunotherapy comes exclusively from this stem cell-like CD8 T-cell subset. Therefore, a better understanding of the mechanisms how CD8 T-cell subsets are regulated during chronic viral infection and cancer is required to improve the current immunotherapies that restore the function of exhausted CD8 T cells. In this review, we discuss the differentiation of virus-specific CD8 T cells during chronic viral infection, the characteristics and function of CD8 T-cell subsets, and the therapeutic intervention of PD-1-directed immunotherapy in cancer.

• 대한수학회논문집
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• 제30권3호
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.507-514
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• 2015

Let D be an integral domain, t be the so-called t-operation on D, and S be a (not necessarily saturated) multiplicative subset of D. In this paper, we study the Nagata ring of S-Noetherian domains and locally S-Noetherian domains. We also investigate the t-Nagata ring of t-locally S-Noetherian domains. In fact, we show that if S is an anti-archimedean subset of D, then D is an S-Noetherian domain (respectively, locally S-Noetherian domain) if and only if the Nagata ring $D[X]_N$ is an S-Noetherian domain (respectively, locally S-Noetherian domain). We also prove that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D[X] is a t-locally S-Noetherian domain, if and only if the t-Nagata ring $D[X]_{N_v}$ is a t-locally S-Noetherian domain.

• 한국식품영양과학회지
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• 제22권4호
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• pp.405-411
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• 1993

본 연구는 녹황색채소류에서 추출되어 항암효과를 나타내는 활성 물질로 보고되어 있는 phytol과 들미나리 추출물을 sarcoma 180마우스에 주사한 후 적출한 비장세포내 T임프구와 T subset, 그리고 asialo GM1$^{＋}$세포를 정량하여 다음과 같은 결과를 얻었다. 1) 종양 마우스에 phytol 을 투여하였을 때 비장세포내의 T cell과 T-subset은 종양세포이식에 의해서 상승된 치를 더욱 증가시켰다. 그러나 들미나리추출물의 경우는 대동소이하였다. 2) Asialo GM1$^{＋}$세포는 종양마우스에 phytol이나 들미나리추출물을 주사하였을 때 모두 상승하였으며 정상마우스에 phytol 을 투여하였을 때도 대조군에 비하여 상승했지만 들미나리추출물을 작용시켰을 때는 저하되었다. 3) L3T4$^{＋}$/Lyt-2$^{＋}$세포비는 종양마우스에 phytol을 주사하였을 때 감소를 보였지만 정상 마우스에 투여하였을 때는 더욱 크게 낮아졌다. 그러나 들미나리추출물을 정상마우스에 투여 하였을때는 크게 감소하던 것이 종양마우스에 적요 시켰을 때는 증가현상을 보였다. 이상의 결과로 미루어 볼 때 phytol이나 들미나리추출물은 종양마우스에서 작용자 세포인 자연살해세포(natural killer cell)의 활성 인자로서 작용할 가능성이 높을 것으로 사료된다.

• 충청수학회지
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• 제7권1호
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• pp.87-95
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• 1994

Relationships between the prime ideals of a ring R and of a normalizing extension S have been studied by several authors. Relationships between the prime ideals of a ring R and of an intermediate normalizing extension T also have studied by several authors where $R{\subset}T{\subset}S$. In this note, some relationships between prime ideals of T and S are studied.

• 대한수학회지
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• 제48권3호
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• pp.599-626
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• 2011

Let T = (V,A) be a tournament. With every subset X of V is associated the subtournament T[X] = (X, A ${\cap}$ (X${\times}$X)) of T, induced by X. The dual of T, denoted by $T^*$, is the tournament obtained from T by reversing all its arcs. Given a tournament T' = (V,A') and a non-negative integer ${\kappa}$, T and T' are {$-{\kappa}$}-hemimorphic provided that for all X ${\subset}$ V, with ${\mid}X{\mid}$ = ${\kappa}$, T[V-X] and T'[V-X] or $T^*$[V-X] and T'[V-X] are isomorphic. The tournaments T and T' are said to be hereditarily hemimorphic if for all subset X of V, the subtournaments T[X] and T'[X] are hemimorphic. The purpose of this paper is to establish the hereditary hemimorphy of the {$-{\kappa}$}-hemimorphic tournaments on at least k + 7 vertices, for every ${\kappa}{\geq}5$.

• 한국수학교육학회지시리즈A:수학교육
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• 제26권1호
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• pp.41-45
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• 1987

In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

• 대한수학회지
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• 제40권5호
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• pp.757-768
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• 2003

In 1967, as an answer to the question of P. Erdos on a set of integers having distinct subset sums, J. Conway and R. Guy constructed an interesting sequence of sets of integers. They conjectured that these sets have distinct subset sums and that they are close to the best possible with respect to the largest element. About 30 years later (in 1996), T. Bohman could prove that sets from the Conway-Guy sequence actually have distinct subset sums. In this paper, we generalize the concept of subset-sum-distinctness to k-SSD, the k-fold version. The classical subset-sum-distinct sets would be 1-SSD in our definition. We prove that similarly derived sequences as the Conway-Guy sequence are k-SSD.

• East Asian mathematical journal
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• 제24권1호
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.