• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.885-899
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• 2013

In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.231-247
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• 2023

In this study, we mean that timelike q-helices are curves whose q-frame fields make a constant angle with a non-zero fixed axis. We present the necessary and sufficient conditions for timelike curves via the q-frame to be q-helices in Lorentz-Minkowski 3-space. Then we find some results of the relations between q-helices and Darboux q-helices. Furthermore, we portray Darboux q-helices as special curves whose Darboux vector makes a constant angle with a non-zero fixed axis by choosing the curve as one of the types of q-helices, and also the general case.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.263-285
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• 2023

In this paper, we investigate the spherical indicatrices of a new relationship between Bertrand pair curves in Euclidean 3-space. We obtain necessary and sufficient conditions for this type of Bertrand pair curves to be slant helix, and provide an example.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.381-390
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• 2012

In this paper, we give some characterizations for a quaternionic general helix by means of curvatures of a curve in a 4-dimensional Euclidean space.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.939-949
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• 2016

In this paper, we give an algorithm to construct a space curve in Euclidean 3-space ${\mathbb{E}}^3$ from a plane curve which is called PDP-helix of order d. The notion of the PDP-helices is a generalization of a general helix and a slant helix in ${\mathbb{E}}^3$. It is naturally shown that the PDP-helix of order 1 and order 2 are the same as the general helix and the slant helix, respectively. We give a characterization of the PDP-helix of order d. Moreover, we study some geometric properties of that of order 3.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1109-1126
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• 2013

Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• Journal of Microbiology and Biotechnology
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• v.27 no.4
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• pp.775-784
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• 2017

A neutral xylanase (CcXyn) was identified from Coprinus cinereus. It has a single GH10 catalytic domain with a basic amino acid-rich extension (PVRRK) at the C-terminus. In this study, the wild-type (CcXyn) and C-terminus-truncated xylanase ($CcXyn-{\Delta}5C$) were heterologously expressed in Pichia pastoris and their characteristics were comparatively analyzed with aims to examine the effect of this extension on the enzyme function. The circular dichorism analysis indicated that both enzymes in general had a similar structure, but $CcXyn-{\Delta}5C$ contained less ${\alpha}-helices$ (42.9%) and more random coil contents (35.5%) than CcXyn (47.0% and 32.8%, respectively). Both enzymes had the same pH (7.0) and temperature ($45^{\circ}C$) optima, and similar substrate specificity on different xylans. They all hydrolyzed beechwood xylan primarily to xylobiose and xylotriose. The amounts of xylobiose and xylotriose accounted for 91.5% and 92.2% (w/w) of total xylooligosaccharides (XOS) generated from beechwood by CcXyn and $CcXyn-{\Delta}5C$, respectively. However, truncation of the C-terminal 5-amino-acids extension significantly improved the thermostability, SDS resistance, and pH stability at pH 6.0-9.0. Furthermore, $CcXyn-{\Delta}5C$ exhibited a much lower $K_m$ value than CcXyn (0.27 mg/ml vs 0.83 mg/ml), and therefore, the catalytic efficiency of $CcXyn-{\Delta}5C$ was 2.4-times higher than that of CcXyn. These properties make $CcXyn-{\Delta}5C$ a good model for the structure-function study of $({\alpha}/{\beta})_8$-barrel-folded enzymes and a promising candidate for various applications, especially in the detergent industry and XOS production.

• Proceedings of the Korea Crystallographic Association Conference
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• 2003.05a
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• pp.18-18
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• 2003

Thioredoxin (Trx) is a small redox protein that is ubiquitously distributed from achaes to human. In diverse organisms, the protein is involved in various physiological roles by acting as electron donor and regulators of transcription and apoptosis as well as antioxidants. Sequences of Trx within various species are 27～69% identical to that of E. coli and all Trx proteins have the same overall fold, which consists of central five β strands surrounded by four α helices. The N-terminal cysteine in WCGPC motif of Trx is redox sensitive and the motif is highly conserved. Compared with general cysteine, the N-terminal cysteine has low pKa value. The result leads to increased reduction activity of protein. Recently, novel thio.edoxin-related protein (TRP14) was found from rat brain. TRP14 acts as disulfide reductase like Trx1, and its redox potential and pKa are similar to those of Trx1. However, TRP14 takes up electrons from cytosolic thioredoxin reductase (TrxR1), not from the mitochondrial thioredoxin reductase (TrxR2). Biological roles of TES14 were reported to be involved in regulating TNF-α induced signaling pathways in different manner with Trx1. In depletion experiments, depletion of TRP14 increased TNF-α induced phosphorylation and degradation of IκBα more than the depletion Trx1 did. It also facilitated activation of JNK and p38 MAP kinase induced by TNF-α. Unlike Trx1, TRP14 shows neither interaction nor interference with ASK1. Here, we determined three-dimensional crystal structure of TRP14 by MAD method at 1.8Å. The structure reveals that the conserved cis-Pro (Pro90) and active site-W-C-X-X-C motif, which may be involved in substrate recognition similar to Trx1 , are located at the beginning position of strand β4 and helix α2, respectively. The TRP14 structure also shows that surface of TRP14 in the vicinity of the active site, which is surrounded by an extended flexible loop and an additional short a helix, is different from that of Trx1. In addition, the structure exhibits that TRP14 interact with a distinct target proteins compared with Trx1 and the binding may depend mainly on hydrophobic and charge interactions. Consequently, the structure supports biological data that the TRP14 is involved in regulating TNF-α induced signaling pathways in different manner with Trx1.