• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.161-170
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• 2022

For an arbitrary ample divisor A in smooth del Pezzo surface S of degree 2, we completely compute alpha invariant along curves when the ample divisor A is birational type.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• Clinical and Experimental Pediatrics
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• v.53 no.2
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• pp.136-145
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• 2010

Natural killer T (NKT) cell is a special type of T lymphocytes that has both receptor of natural killer (NK) cell (NK1.1, CD161c) and T cell (TCR) and express a conserved or invariant T cell receptor called $V{\alpha}14J{\alpha}18$ in mice or Va24 in humans. Invariant NKT (iNKT) cell recognizes lipid antigen presented by CD1d molecules. Marine-sponge-derived glycolipid, ${\alpha}-galactosylceremide$ (${\alpha}-GalCer$), binds CD1d at the cell surface of antigen-presenting cells and is presented to iNKT cells. Within hours, iNKT cells become activated and start to secrete Interleukin-4 and $interferon-{\gamma}$. NKT cell prevents autoimmune diseases, such as type 1 diabetes, experimental allergic encephalomyelitis, systemic lupus erythematous, inflammatory colitis, and Graves' thyroiditis, by activation with ${\alpha}-GalCer$. In addition, NKT cell is associated with infectious diseases by mycobacteria, leshmania, and virus. Moreover NKT cell is associated with asthma, especially CD4+ iNKT cells. In this review, I will discuss the characteristics of NKT cell and the association with inflammatory diseases, especially asthma.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.27-38
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• 2014

The notion of generalized (regular) (${\alpha},\;{\beta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${\alpha},\;{\beta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${\alpha},\;{\beta}$)-derivation and ${\alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${\alpha},\;{\beta}$)-derivations are proved.

• BMB Reports
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• v.47 no.5
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• pp.241-248
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• 2014

CD1 molecules belong to non-polymorphic MHC class I-like proteins and present lipid antigens to T cells. Five different CD1 genes (CD1a-e) have been identified and classified into two groups. Group 1 include CD1a-c and present pathogenic lipid antigens to ${\alpha}{\beta}$ T cells reminiscence of peptide antigen presentation by MHC-I molecules. CD1d is the only member of Group 2 and presents foreign and self lipid antigens to a specialized subset of ${\alpha}{\beta}$ T cells, NKT cells. NKT cells are involved in diverse immune responses through prompt and massive production of cytokines. CD1d-dependent NKT cells are categorized upon the usage of their T cell receptors. A major subtype of NKT cells (type I) is invariant NKT cells which utilize invariant $V{\alpha}14-J{\alpha}18$ TCR alpha chain in mouse. The remaining NKT cells (type II) utilize diverse TCR alpha chains. Engineered CD1d molecules with modified intracellular trafficking produce either type I or type II NKT cell-defects suggesting the lipid antigens for each subtypes of NKT cells are processed/generated in different intracellular compartments. Since the usage of TCR by a T cell is the result of antigen-driven selection, the intracellular metabolic pathways of lipid antigen are a key in forming the functional NKT cell repertoire.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.493-511
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• 2024

We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.198-208
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• 2024

In this paper, we find the conditions for a homogeneous Finsler space with an invariant infinite series (α, β)-metric to be of Berwald type. Also, we derive the necessary and sufficient condition for such a metric to be a Douglas metric.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.289-300
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• 2011

Let T(X) denote the semigroup (under composition) of transformations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = {${\alpha}\;{\in}\;T(X)\;:\;Y\;{\alpha}\;{\subseteq}\;Y$}. Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S($A^1$, A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.491-499
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• 2012

The hyperbolic metric is invariant under the action of M$\ddot{o}$bius maps and unbounded. For 0 < $r$ < 1, there is an r-lattice in the Bergman metric. Using this r-lattice, we get the measure ${\mu}_r$ and the Toeplitz operator $T^{\alpha}_{\mu}_r$ and we prove that $T^{\alpha}_{\mu}_r$ is bounded and $T^{\alpha}_{\mu}_r$ is compact under some condition.