• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.509-531
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• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• Korean Journal of Mathematics
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• 제32권2호
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• 대한수학회논문집
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• 제11권3호
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• pp.797-805
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• 1996

We provide a new proof of the following fact using least area surfaces : If the fundamental group of a $P^2$-irreducible closed 3-manifold M contains a finitely generated nontrivial normal subgroup of infinite index, then M has a finite cover which is a closed surface bundle over $S^1$ , unless N is free.

• Computers and Concrete
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• 제29권4호
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• pp.247-253
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• 2022

In this study, the problem of discontinuous contact in two functionally graded (FG) layers resting on a rigid plane and loaded by two rigid blocks is solved by the finite element method (FEM). Separate analyzes are made for the cases where the top surfaces of the problem layers are metal, the bottom surfaces are ceramic and the top surfaces are ceramic and the bottom surfaces are metal. For the problem, it is accepted that all surfaces are frictionless. A two-dimensional FEM analysis of the problem is made by using a special macro added to the ANSYS package program The solution of this study, which has no analytical solution in the literature, is given with FEM. Analyzes are made by loading different Q and P loads on the blocks. The normal stress (σy) distributions at the interfaces of FG layers and between the substrate and the rigid plane interface are obtained. In addition, the starting and ending points of the separations between these surfaces are determined. The normal stresses (σx, σy) and shear stresses (τxy) at the point of separation are obtained along the depth. The results obtained are shown in graphics and tables. With this method, effective results are obtained in a very short time. In addition, analytically complex and long problems can be solved with this method.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2011년도 제40회 동계학술대회 초록집
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• pp.310-310
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• 2011

Morphological evolution of amorphous carbon film is investigated by molecular dynamics simulation. Here, energetic carbon atoms (75 eV) are deposited on the diamond (001) substrate to find effect of incidence angles. At normal and near-normal incidences ($0^{\circ}{\sim}30^{\circ}$) atomically smooth surfaces are observed during their growth. However, rough surfaces emerge and develop into a ripple structure at grazing incidences ($60^{\circ}{\sim}70^{\circ}$). The different growth modes according to the incidence angles can be described by impact-induced displacements of atoms. Downhill transport along any sloped surfaces is predominant for the case of normal incidence. As the incidence angles become grazing, uphill transport is allowed along the surfaces, which have smaller slopes than incidence angle, so the surface features can be amplified. Impact-induced transport and self-shadowing effect can be responsible to the initial growth of seeding structures at a grazing incidence, which would be grown up as tilted columnar structures in further depositions.

• Journal of Computational Design and Engineering
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• 제2권3호
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• pp.129-136
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• 2015

This paper proposes a novel method for shape design of a Bezier surface with given boundary curves. The surface is defined as the minimizer of an extended membrane functional or an extended thin plate functional under the guidance of a specified normal field together with an initial prescribed surface. For given boundary curves and the guiding normal field, the free coefficients of a Bezier surface are obtained by solving a linear system. Unlike previous PDE based surface modeling techniques which construct surfaces just from boundaries, our proposed method can be used to generate smooth and fair surfaces that even follow a specified normal field. Several interesting examples are given to demonstrate the applications of the proposed method in geometric modeling.

• 대한전자공학회논문지
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• 제27권1호
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• pp.120-129
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• 1990

In this paper, 3-dimensional object segmentation and classification are proposed. Planar object is segmented surface using jump boundary and internal boundary. Curved object is segmented surfaces by maximin clustering method. Segmented surfaces are classified by depth trends and angle measurement of normal vectors. Classified surfaces are merged according to adjacent surfaces and compared to Guassian curvature and mean curvature method. The proposed methods have been successfully applied to the synthetic range images and shows good classification.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.121-126
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• 2008

A plane strain problem of a crack on interface between an isotropic elastic conductor and a transversely isotropic piezoelectric ceramics is considered. The problem is reduced to system integrodifferential equations on the interface. These equations relate the normal and tangential components of the crack opening vector with distribution of normal and shear stresses on the crack surfaces. It therefore make it possible to obtain an exact solution as a function of the loading applied to the crack surfaces. As an example, some analytical solutions of the crack problem are given.

• 호남수학학술지
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• 제39권3호
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• pp.363-377
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

• PNF and Movement
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• 제15권3호
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• pp.311-316
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• 2017

Purpose: Flatfeet are one of the risk factors of foot dysfunction and postural imbalance. The purpose of this study was to compare the limitation of stability (LOS) for the center of gravity (COG) between flatfeet and neutral feet on stable and unstable support surfaces. Methods: The study included 26 healthy, adult male participants: 14 with normal feet and 12 with flatfeet. The subjects were asked to incline the trunk maximumly to the left, right, anterior, and posterior directions and were asked to keep their feet on the floor with the knee extension. The subjects had 30 seconds of rest time between the tasks. The LOS (anterior, posterior, left, right) of COG was measured by Balance Trainer (BT4, Hur-labs, Tampere, Finland). An independent t- test was used to compare the LOS of COG between flatfeet and normal feet on stable and unstable support surfaces, respectively. Results: The LOS of the flatfeet group was generally decreased on stable support surfaces as compared to that of neutral feet, but it was not significantly different (p>0.05), while the LOS of the flatfeet group was significantly decreased compared to that of neutral feet on unstable support surfaces (p<0.05). Conclusion: This study suggested that the LOS of individuals with flatfeet may be decreased on unstable support surfaces and the postural balance of the flatfeet group may easily be disturbed on an unstable support surface.