• Journal of the Korean Mathematical Society
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• v.55 no.4
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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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• v.20 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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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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• v.55 no.3
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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.

• Journal of the Korean Society of Food Science and Nutrition
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• v.22 no.4
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• pp.405-411
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• 1993

Several studies have shown that phytol isolated from perilla leaf and small water dropwort (Oenanthe javanica (BL) D.C., wild type) extract reveal antirumor activities. In the present study we investigated the effect of phytol and the small water dropwort extract on the T subset in the sarcoma 180-transplanted mice in order to elucidate the immunological mechanism of antiturmor activity of these substances. The results obtained from the experiment were as follows : When phytol was injected into the sarcoma-180 transplanted mice (control), the levels of T cell and T subset by inoculation of the tumor cells were enhanced, but that of T cells in case of small water dropwort extract was similar to the control. Asialo GM1$^{＋}$ cells were increased when phytol or small water dropwort extract with injected into tumor-transplanted mice. In normal mice the number of asialo GM1$^{＋}$ cells increased with phytol injection and decreased with small water dropwort extract injection. L3T4$^{＋}$/Lyt-2$^{＋}$cell ratios were decreased when phytol was injected into tumor-transplanted mire, but increased in case of small water dropwort extract injection. In normal mice the ratios showed large decreases with phytol or small water dropwort extract injection. These results indicate that phytol or small water dropwort extract ran activate the proliferation of natural killer cells that are effector cells in tumor-bearing mice.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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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 ${\kappa}{\geq}5$.

• The Mathematical Education
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• v.26 no.1
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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:

• Journal of the Korean Mathematical Society
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• v.40 no.5
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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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• v.24 no.1
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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.