• 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.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.121-134
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• 2022

In this study, we obtain the spherical images of minimal curves in the complex space in ℂ⁴ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

• BMB Reports
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• v.44 no.2
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• pp.118-122
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• 2011

Most widely used secondary structure assignment methods such as DSSP identify structural elements based on N-H and C=O hydrogen bonding patterns from X-ray or NMR-determined coordinates. Secondary structure assignment algorithms using limited $C{\alpha}$ information have been under development as well, but their accuracy is only ~80% compared to DSSP. We have hereby developed SABA (Secondary Structure Assignment Program Based on only Alpha Carbons) with ~90% accuracy. SABA defines a novel geometrical parameter, termed a pseudo center, which is the midpoint of two continuous $C{\alpha}s$. SABA is capable of identifying $\alpha$-helices, $3_{10}$-helices, and $\beta$-strands with high accuracy by using cut-off criteria on distances and dihedral angles between two or more pseudo centers. In addition to assigning secondary structures to $C{\alpha}$-only structures, algorithms using limited $C{\alpha}$ information with high accuracy have the potential to enhance the speed of calculations for high capacity structure comparison.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.817-827
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• 2021

In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇_YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α²g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.

• Proceedings of the KWS Conference
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• 2003.11a
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• pp.45-48
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• 2003

Over the past few decades, there has been increasing research and commercial activity in invasive and non-invasive biomedical technology. One important challenge to developing these devices involves the increasing density of electrical interconnects. Resistance spot welding is limited in the density of interconnect based on either the size of welding head or the positional precision with which a weld can be made. Development of an automated laser microwelding system would permit the continued advancement of these important biomedical technologies. The objective of this work is to demonstrate the application of pseudo-pulse Nd:YAG laser technology as an alternative to resistance spot welding in performing electrical interconnection within biomedical products. To date, some experiments have been conducted by using a pseudo-pulse 1064 nm Nd:YAG laser, a successful weld of a 25 ${\mu}{\textrm}{m}$ diameter Pt/Ir wire to a 316 stainless steel shim can be made. Another application involves welding clips, which may be used for external interconnection, to electrodeposited nickel domes that make particular interconnections to specific insulated wires within a cable. These results show a great deal of promise for developing such a process.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.963-975
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• 2015

In this paper, we give a representation formula for an isotropic curve with pseudo arc length parameter and define the structure function of such curves. Using the representation formula and the Frenet formula, the isotropic Bertrand curve and k-type isotropic helices are characterized in the 3-dimensional complex space $\mathbb{C}^3$.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1309-1320
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• 2018

In this paper, we show that proper biharmonic spacelike curve ${\gamma}$ in Lorentzian Heisenberg space (${\mathbb{H}}_3$, g) is pseudo-helix with ${\kappa}^2-{\tau}^2=-1+4{\eta}(B)^2$. Moreover, ${\gamma}$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

• Journal of the Korean Magnetic Resonance Society
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• v.24 no.4
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• pp.136-142
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• 2020

Apolipoprotein B-100 (apo B-100), the main protein component that makes up LDL (Low density lipoprotein), consists of 4,536 amino acids and serves to combine with the LDL receptor. The oxidized LDL peptides by malondialdehyde (MDA) or acetylation in vivo were act as immunoglobulin (Ig) antigens and peptide groups were classified into 7 peptide groups with subsequent 20 amino acids (P1-P302). The biomimetic peptide P99 (KGTYG LSCQR DPNTG RLNGE) out of B-group peptides carrying the highest value of IgM antigens were selected for structural studies that may provide antigen specificity. Circular Dichroism (CD) spectra were measured for peptide secondary structure in the range of 190-260 nm. Experimental results show that P99 has pseudo α-helice and random coil structure. Homonuclear (COSY, TOCSY, NOESY) 2D-NMR experiments were carried out for NMR signal assignments and structure determination for P99. On the basis of these completely assigned NMR spectra and proton distance information, distance geometry (DG) and molecular dynamic (MD) were carried out to determine the structures of P99. The proposed structure was selected by comparisons between experimental NOE spectra and back-calculated 2D NOE results from determined structure showing acceptable agreement. The total Root-Mean-Square-Deviation (RMSD) value of P99 obtained upon superposition of all atoms were in the set range. The solution state P99 has mixed structure of pseudo α-helix and β-turn(Gln[9] to Thr[13]). These NMR results are well consistent with secondary structure from experimental results of circular dichroism. Structural studies based on NMR may contribute to the prevent oxidation studies of atherosclerosis and observed conformational characteristics of apo B-100 in LDL using monoclonal antibodies.

• 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.