• 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.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.225-231
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• 2019

In a previous paper, the authors of this paper studied $2{\times}2$ matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1, 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the $2{\times}2$ matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such $2{\times}2$ operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.489-494
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• 2018

The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of $2{\times}2$ operator matrices (Theorem 3.2).

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.195-206
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• 2007

We investigate the multiplicity of $2{\pi}$-periodic solutions of the nonlinear Hamiltonian system with perturbed polynomial and exponential potentials, $\dot{z}= JG^{\prime}(z)$, where $z:R{\rightarrow}R^{2n}$, $\dot{z}={\frac{dz}{dt}}$, $J=\(\array{0&-I\\I&0}\)$, I is the identity matrix on $R^n,G:R^{2n}{\rightarrow}R$, G(0, 0) = 0 and $G^{\prime}$ is the gradient of G. We look for the weak solutions $z=(p,q){\in}E$ of the nonlinear Hamiltonian system.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.95-113
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• 2018

A mathematical knot is an embedded circle in ${\mathbb{R}}^3$. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n - move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.379-383
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• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• Journal of Korean Vacuum Science & Technology
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• v.3 no.2
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• pp.101-106
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• 1999

The main consideration factor to design a magnetron of the sputtering system for TFT-LCD metallization is high sheet resistance (Rs) uniformity which is provided by the high target erosion and high current efficiency. The present study has developed a rectangular magnetron for TFT-LCD to bve considered full target erosion and high film uniformity. After an aluminum-2 at.% and alloy target was installed in a magnetron source and the film was deposited on the glass of 600${\times}$720 mm, the Rs uniformity of the deposited film was measured as functions of the magnet tilt and magnet scanning configuration. And the target erosion profile was observed with the target voltage. When sputtered at 4mtorr and 10kW, the magnet tilt for the high Rs uniformity of 8.38% was 7mm. The plasma voltage at the dwell home and end for full-face target erosion, when scanned the magnetron was 120% compared to the mean voltage of the other area.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.2
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• pp.147-153
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• 2007

The stability robustness problem of linear discrete-time systems with delayed time-varying perturbations is considered. Compared with continuous time system, little effort has been made for the discrete time system in this area. In the previous results, the bounds were derived for the case of non-delayed perturbations. There are few results for delayed perturbation. Although the results are for the delayed perturbation, they considered only the time-invariant perturbations. In this paper, the sufficient conditions for stability can be expressed as linear matrix inequalities(LMIs). The corresponding stability bounds are determined by LMI(Linear Matrix Inequality)-based algorithms. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed results.