• 대한수학회지
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• 제54권1호
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• pp.267-280
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• 2017

In this paper, we study analytic and geometric properties of the solution q(z) to the differential equation q(z) + zq'(z)/q(z) = h(z) with the initial condition q(0) = 1 for a given analytic function h(z) on the unit disk |z| < 1 in the complex plane with h(0) = 1. In particular, we investigate the possible largest constant c > 0 such that the condition |Im [zf"(z)/f'(z)]| < c on |z| < 1 implies starlikeness of an analytic function f(z) on |z| < 1 with f(0) = f'(0) - 1 = 0.

• Steel and Composite Structures
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• 제16권4호
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 춘계학술대회 논문집
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• pp.143-148
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• 1995

A study on the generation of optimum tool path for machining the concave parts is discussed. Above all, the various cutting factors and their relationships are considered. Then optimum tool path for concave parts is generated on these cutting variables and their relationships. It is difficult for existing CAD/CAM systems tomachine the concave parts. For cutting the part even the experienced craft must give many attentions and muchtime since it needs consideration of various cutting conditions and geometric properties. The optimum tool path for the concave part is generated onnot only geometric properties byut also cutting conditions. We choose, as variables, feed and cutting direction for productivity, diameter of tool and constant(stable) cutting force for machining accuracy. The results are verified through simulation of the index of performance and cutting force.

• 소성∙가공
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• 제12권4호
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• pp.328-333
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• 2003

Ball indentation tests have been used to estimate the mechanical properties of materials by several investigators. In this study, load-depth curves from ball indentation tests were analyzed using the geometric conditions of the contact between ball and specimen. A series of numerical calculations and experimental results showed that the contact load-depth curves could be simplified by linear functions. Once we obtained the contact indentation depth from linearizing the experimental indentation curves, the estimation process of the flow properties became straight-forward and the scatter of results could be drastically reduced.

• International Journal of CAD/CAM
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• 제8권1호
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• pp.11-20
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• 2009

The conventional methods of boundary-conformed 2D surfaces generation usually yield some problems. This paper deals with two boundary-conformed 2D surface generation methods, one conventional approach, the linear Coons method, and a new method, boundary-conformed interpolation. In this new method, unidirectional 2D surface has been generated using some of the geometric properties of the given boundary curves. A method of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacements include weighted combination of angle bisector and linear displacement vectors at all the data-points of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from its parents. This unidirectional process has been extended to bi-directional parameterization by superimposing two sets of unidirectional curves generated from both boundary pairs. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries. This algorithm is more robust than the linear Coons method and capable of resolving the 2D boundary-conformed parameterization problems.

• Steel and Composite Structures
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• 제44권1호
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• pp.91-104
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• 2022

The purpose of the present work is to study the parametric nonlinear vibration behavior of three layered symmetric laminated plate. In the analytical formulation; both normal and shear deformations are considered in the core layer by means of the refined higher-order zig-zag theory. Harmonic balance method in conjunction with Galerkin procedure is adopted for simply supported laminate plate, to obtain its natural and damping properties. For these aims, a set of complex amplitude equations governed by complex parameters are written accounting for the geometric nonlinearity and viscoelastic damping factor. The frequency response curves are presented and discussed by varying the material and geometric properties of the core layer.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.737-749
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• 2022

We investigate the geometric properties of 𝜂_*-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric 𝜂_*-Ricci soliton on an α-LS manifold is an 𝜂_*-Einstein manifold. Further, we study 𝜑_*-symmetric 𝜂_*-Ricci solitons on such manifolds. We prove that 𝜑_*-Ricci symmetric 𝜂_*-Ricci solitons on an α-LS manifold are also 𝜂_*-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

• 한국수학사학회지
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• 제36권1호
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• pp.1-17
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• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• Wind and Structures
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• 제20권2호
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• pp.249-274
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• 2015

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

• 천문학회보
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• 제43권2호
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• pp.44.4-45
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• 2018

(4179) Toutatis (Toutatis hereafter) is one of the Near-Earth Asteroids which has been studied most rigorously not only via ground-based photometric, spectroscopic, polarimetric, and radar observations, but also via the in-situ observation by the Chinese Chang'e-2 spacecraft. However, one of the most fundamental physical properties, the geometric albedo, is less determined. In order to derive the reliable geometric albedo and further study the physical condition on the surface, we made photometric observations of Toutatis near the opposition (i.e., the opposite direction from the Sun). We thus observed it for four days on 2018 April 7-13 using three 1.6-m telescopes, which consist of the Korean Microlensing Telescope Network (KMTNet). Since the asteroid has a long rotational period (5.38 and 7.40 days from Chang'e-2, Zhao et al., 2015), the continuous observations with KMTNet matches the purpose of our photometric study of the asteroid. The observed data cover the phase angle (Sun-asteroid-observer's angle) of 0.65-2.79 degree. As a result, we found that the observed data exhibited the magnitude changes with an amplitude of ~0.8 mag. We calculated the time-variable geometrical cross-section using the radar shape model (Hudson & Ostro 1995), and corrected the effect from the observed data to derive the geometric albedo. In this presentation, we will present our photometric results. In addition, we will discuss about the regolith particles size together with the polarimetric properties based on the laboratory measurements of albedo-polarization maximum.