• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.37-45
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• 1980

The Riemannian space of recurrent curvature was defined and studied by Ruse [8] and Walker [10]. In 1963, $M{\acute{o}}or$ [4] generalised this idea for Finsler spaces and defined and studied Finsler spaces of recurrent curvature. These spaces for various curvature tensors have subsequently been studied by Mishra and Pande [1], Sen [9] and Misra [3] etc. The purpose of the present paper is to study Finsler space based on the recurrency of the curvature tensors derived from non-linear connections.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.261-278
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• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.

• Journal of the Optical Society of Korea
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• v.19 no.6
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• pp.658-664
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• 2015

Lens designers generally refer to flat image fields and attempt to minimize the field curvature. Present-day CMOS image sensors for mobile phone cameras, however, are not flat, but curved. Sometimes it is necessary to generate an intentional field curvature according to the degree and direction of the CMOS image-sensor’s curvature. This paper presents the degree of curvature of a CMOS image sensor measured using an interferometer, and proposes an effective compensation method that minimizes the net field curvature through optimizing the air gap between lens elements, which is demonstrated using simulations and experiments.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• Journal of the Korea Safety Management & Science
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• v.10 no.2
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• pp.85-94
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• 2008

The object of this study is to investigate the penetration characteristics according to the change of stacking sequences and curvature radius in the composite laminated shell. They are staked to [02/902]S and [0/902/0]s, their interlaminar number are two and four. We are manufactured to composite laminated shells with various curvature radius. Curvature radius of composite shell is 100, 150, 200mm and ${\infty}$(it's meaning flat-plate). In general, kinetic energy after impact-kinetic energy before impact increased linearly in all specimens. Absorbed energy increased linearly as the curvature increased, and absorbed energy of [02/902]S specimen, which is small interlaminar number, was higher than [0/902/0]s specimen.

• The Journal of Korea Robotics Society
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• v.15 no.2
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• pp.139-146
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• 2020

In this paper, the slope of the footplate is adjusted to compensate for the centrifugal force with a series elastic actuator (SEA) attached to the Segway's body to improve the cornering characteristics during turning. To ensure Segway's driving safety in the curvature motion, it is necessary to compensate for the centripetal force by tilting the footplate to generate inward force from gravity. When the footplate is tilted under the control of SEA, the vertical load on both wheels has been changed accordingly. The frictional force of the wheel has been changed by the change of the vertical force, which requires adjustment of driving torque to keep the curvature trajectory. That is, the driving torque has been controlled to keep the curvature trajectory considering the frictional force caused by the turning motion. Four SEAs are attached to the footplate to control the slope of the footplate and the real curvature motion has been demonstrated to verify the effects of SEAs in the high- speed curvature motion.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.8
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• pp.29-39
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• 1997

The clamp, as the structure which is used for supporting the pipe in the atomic power plant, is produced with a certain degree of anticlastic curvature in the current manufacturing process. In this study, the structural analysis of the clamp and the pipe was performed using ABAQUS. And the finite element modelling for the analysis was made by an HyperMesh. The contact forces which are transferred between the clamp and the pipe for the external force are changed according to the binding force of bolts and keeps the clamp tightly and protects the slipping between the clamp and the pipe. The clamps with the anticlastic curvature and with the flat curvature are considered in order to invest the anticlastic effect. In this study, another case is suggested. The present case does not have the stiffness ring on the end of the clamp but the suggested case has the ring. For the present case, the results showed that the equivalent stress is higher in the anticlastic curvature case than in the flat curvature case and the equivalent stresses on the pipe are almost the same as the binding force increses. For the suggested case, the result showed that the equivalent stress in the anticlastic curvature case decreases until some binding force and increases as the binding forces increase and is lower in some range than in the flat curvature case. From this study, the clamp with the anticlastic curvature in the suggested method is better than the clamp with the flat curvature and the optimal binding force are given.

• Journal of Korean Medicine Rehabilitation
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• v.20 no.1
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• pp.133-139
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• 2010

Objectives : The purpose of this study was to compare about quantity of pain and fatigue according to cervical spine curvature of patient with neck pain. Methods : Cervical spine curvature was measured using the sagittal radiography of the cervical spine, neck pain was evaluated using the VAS and neck fatigue was evaluated using fatigue symptom checklist. Based on four line Cobb's method, 51 subjects were divided into hypolordosis group, normal group, hyperlordosis group. Window version SPSS 12K was used for statistical analysis about relation between pain and cervical spine curvature of each group, also about between fatigue and cervical spine curvature of each group. Results : 1. A significant difference was not found between pain and cervical curvature of each group. 2. A significant difference was not found between fatigue and cervical curvature of each group. Conclusions : There was no relation between pain and cervical curvature of each group, also fatigue and cervical curvature.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.433-448
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• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.