• Journal of The Korean Society of Integrative Medicine
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• v.7 no.3
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• pp.149-157
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• 2019

Purpose : This study aims to check the relationship between the size of curvature in scoliosis patients and the reduction rate of curvature after wearing a brace and the relationships of the size of curvature and correction angle with Body Mass Index (BMI). Methods : With 30 adolescent girls who had never worn a brace, their Cobb angle and BMI were measured before manufacturing braces, and their corrected Cobb angle was measured after wearing the manufactured scoliosis braces. Results : The size of the major curvature before wearing the brace and the reduction rate of the curvature after putting it on had a negative correlation in both the major curvature (r=-.465, p<.01) and the minor curvature (r=-.516, p<.01). The size of the minor curvature and the reduction rate of the minor curvature before and after putting it on also had a negative correlation (r=-.429, p<.05). As for the relationship between the size of curvature and BMI, they had a negative correlation in both the major curvature (r=-.141) and the minor curvature (r=-.123), and as for the relationship between the reduction rate of curvature and BMI after wearing the brace, they had a positive correlation in both the major curvature (r=.251) and the minor curvature (r=.136); however, it was not statistically significant (p>.05). Conclusion : In conclusion, the larger the size of curvature, the lower the reduction rate of curvature after wearing the brace became. The larger the size of curvature, the lower the BMI became. The higher the BMI, the higher the correction ratio of the brace became. Therefore, it is judged that it is necessary to provide early treatment and manage body composition before scoliosis progresses.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.537-557
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• 2021

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.149-161
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• 2019

In the present paper, we study curvature properties of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds satisfying $R({\xi},X).C=0$, $R({\xi},X).{\tilde{M}}=0$, $R({\xi},X).P=0$, $R({\xi},X).{\tilde{C}}=0$ and $R({\xi},X).H=0$, where $C,\;{\tilde{M}},\;P,\;{\tilde{C}}$ and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.53-60
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• 2010

The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.487-504
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• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.163-176
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• 2016

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.109-124
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• 2011

The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.67-72
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• 2011

This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.359-366
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• 2009

In this paper, we study a tube in a Euclidean 3-space satisfying some equation in terms of the Gaussian curvature, the mean curvature and the second Gaussian curvature.