• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.535-549
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• 2020

In this paper, we introduce the geometry of contact CR submanifolds and radical transversal lightlike submanifolds of Sasaki-like almost contact manifolds with B-metric. We obtain some new results that establish a relationship between these two submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1027-1034
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• 2015

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1095-1103
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• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• Proceedings of the KSR Conference
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• 2006.11b
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• pp.1483-1487
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• 2006

In electric railway, image monitoring using high speed camera provides reliable, timely information of wear and geometry status, important in taking decisions for overhead contact wire maintenance. The contribution of this research is the development of a simple real-time monitoring system for use in measurement subsystem of contact wire and geometry of overhead contact wire in electric railway. The system has been consists of a high speed CMOS camera with resolution $1024{\times}1280$ pixels, line type laser source and PC-based image acquisition system with PCI Express slot. Vision acquisition software have been used in application programming interface for image acquisition, display, and storage with a frequency of sampling of 500 acquisitions per second.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.543-559
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• 2002

In this paper we formulate the linear theory for compressible fluids in cylindrical geometry with small perturbation at the material interface. We derive the first order equations in the smooth regions, boundary conditions at the shock fronts and the contact interface by linearizing the Euler equations and Rankine-Hugoniot conditions. The small amplitude solution formulated in this paper will be important for calibration of results from full numerical simulation of compressible fluids in cylindrical geometry.

• Journal of Korean Ophthalmic Optics Society
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• v.18 no.1
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• pp.75-84
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• 2013

Purpose: Changes of refractive correction value in different age group were investigated. Regarding the inhibitive effects against myopia progression after wearing reverse geometry contact lenses and myopia control lenses (MC lenses), the effects after wearing single vision lenses were compared. Methods: We organized children between the ages of six and fifteen into three groups by age, and distributed fifty-seven reverse geometry contact lenses, fifty-six MC lenses and seventy-eight single vision lenses among them to be worn. Group 1 consisted of children aged ten and under, Group 2 consisted of children between the ages of eleven and fifteen, and Group 3 represents all of the study participants. The aim of this study was to learn the inhibitive effects against myopia progression attained by changes of refractive correction value and to verify their statistical significance at twelve months and under, thirteen to twenty-four months and twenty-five to thirty-six months. Results: Changes of refractive correction value by each length of use in Group 3 were as follows. For the age group of under twelve months, participants using the reverse geometric contact lens showed no change, while those using the MC or single vision lens had significant changes (P<0.05) of $-0.36{\pm}0.10$ D and $-0.67{\pm}0.52$ D, respectively. Users of all three lens types displayed significant change (P<0.05), in the age group of between thirteen and twenty-four months, of $0.18{\pm}0.49$ D, $0.60{\pm}0.42$ D and $1.37{\pm}0.72$ D for users of the reverse geometry contact lens, the MC lens and the single vision lens, respectively. There were significant changes (P<0.05) of $0.29{\pm}0.61$ D, $0.93{\pm}0.57$ D and $1.72{\pm}0.78$ in the same respective order as the above in the age group of twenty-five to thirty-six months. Refractive correction value showed changes with different age group. Group 1 displayed significant changes (P<0.05) of $0.29{\pm}0.73$ D, $1.07{\pm}0.59$ D and $1.75{\pm}0.74$ D for users of the reverse geometry contact lens, MC lens and single vision lens, respectively, up to thirty-six months of lens wearing; Group 2, also up to thirty-six months, displayed significant changes (P<0.05) of $0.28{\pm}0.42$ D, $0.75{\pm}0.49$ D and $1.70{\pm}0.84$ D in the same respective order, and changes in refractive correction for the age group under ten years was significantly greater (P<0.05) for the age group of eleven and older. Conclusions: The results found in this study demonstrate that there were no changes of refractive correction value for the case of wearing reversing geometry contact lens up to twelve month or less. MC lens showed less changes in variations of visual acuity for all users which might be resulted in inhibiting progression of myoptia. When both reverse geometry contact lens and the MC lens are wearing for the period from 13 to 36 month, both lens showed less changes in variation of visual acuity for all users. The results suggested that the less changes in variation of visual acuity of both lens had an effect on inhibiting progression of myopia.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.2
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• pp.59-64
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• 2001

The distribution of current in the conductors influenced by the armature geometry and velocity is an important parameter for determining performance of an electromagnetic launcher(EML). the electric current in the early launching stage tends to flow on the outer surfaces of the conductors, resulting in very high local electric current density. However, the tendency for current to concentrate on the surface is driven by the velocity skin effect later in launching stage. The high current density produces high local heating and, consequently, increases armature wear which causes several defects on EML system. This paper investigates the effects of rail/armature geometry on current density distribution, launcher inductance gradient (L'), and contact force. Three geometrical parameters are used here to characterize the railgun system. These are the ratio of contact length to root length, relative position of contact leading edge to root trailing edge, and the ratio of rail overhang to the rail height. The distribution of current density, L', contact force between various configurations of the armature and the rail are analyzed and compared by using the EMAP3D program.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.27-36
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• 2014

Similar to the essential components of many mechanical systems, the geometrical properties of the teeth of spiral bevel gears greatly influence the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show a unique advantage in transmission due to their constant spiral angle property. However, a mathematical model suitable for accurate digital modeling, differential geometrical characteristics, and related contact analysis methods for tooth surfaces have not been deeply investigated, since such gears are not convenient in traditional cutting manufacturing in the gear industry. Accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed in this study, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry; actually, the tooth surface is a parametric surface defined on a parallelogrammic domain. Equivalence proof of the tooth surface geometry is then given in order to greatly simplify the mathematical model. As major factors affecting the lubrication, surface fatigue, contact stress, wear, and manufacturability of gear teeth, the differential geometrical characteristics of the tooth surface are summarized using classical fundamental forms. By using the geometrical properties mentioned, manufacturability (and its limitation in logarithmic spiral bevel gears) is analyzed using precision forging and multiaxis freeform milling, rather than classical cradle-type machine tool based milling or hobbing. Geometry and manufacturability analysis results show that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multiaxis freeform milling also need to be solved in a further study.