• Honam Mathematical Journal
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• v.29 no.3
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• pp.475-480
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• 2007

In this paper we find the point at which the rational B$\'{e}$zier curve has the given tangent direction. We also analyze the geometric properties of the point of quadratic rational B$\'{e}$zier curve.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.215-236
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• 1994

The purpose of the present paper is to study generic submanifolds of a Sasakian space form with nonvanishing parallel mean curvature vector field such that the shape operator in the direction of the mean curvature vector field commutes with the structure tensor field induced on the submanifold. In .cint. 1 we state general formulas on generic submanifolds of a Sasakian manifold, especially those of a Sasakian space form. .cint.2 is devoted to the study a generic submanifold of a Sasakian manifold, which is not tangent to the structure vector. In .cint.3 we investigate generic submanifolds, not tangent to the structure vector, of a Sasakian space form with nonvanishing parallel mean curvature vactor field. In .cint.4 we discuss generic submanifolds tangent to the structure vector of a Sasakian space form and compute the restricted Laplacian for the shape operator in the direction of the mean curvature vector field. As a applications of these, in the last .cint.5 we prove our main results.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.927-939
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• 2007

This paper concerns dynamics of a wheel-axle set on a tangent track which was already published in a book titled "Dynamics of Railway Vehicle Systems" authored by Garg and Dukkipati [1], pointing out several missing terms and erroneous parts in the derived expressions on the conventional governing equations of motion. It is indicated that the x-direction components of normal forces at left and right wheel-rail contact points in the equilibrium axis were missed. Another point is that in deriving the creepages the disturbed velocity components in both x and y directions in the equilibrium axis should not be disregarded in the first term of the numerators. When considering the creepage in the y direction in the body coordinate system, the second term of lateral velocity at the contact point also cannot be neglected. Besides, the hyper-assumptions in the final expressions of vertical components of normal forces at left and right wheel-rail contact points have been recovered in reaching the final stage of analytical model development. Finally it is noteworthy that the process of applying creep theory is deemed to contain a little bit inconsistencies and ambiguities to be clear.

• Journal of Ocean Engineering and Technology
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• v.13 no.4 s.35
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• pp.169-173
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• 1999

In this paper some modifications for Lu's inverse method of fairing process are presented. The object function is changed and additional constraints for hull curve foiling is proposed. The newly introduced minimizing object function is the sum of the distances between the two curve's positions at the same parameter values instead of the sum of the distances between two vertices. The new one is better to represent the physical meaning of the object function, the smaller differences between two curves. In ship hull fairing the end tangent of curve has to be fined in some cases, so the additional constraint is considered to preserve the direction of end tangent. The sample results are shown.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• The Journal of the Korea Contents Association
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• v.9 no.2
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• pp.97-105
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• 2009

This paper presents a combination of the generalized Cascade Correlation and generalized Recurrent Cascade Correlation learning algorithms. The new network will be able to grow with vertical or horizontal direction and with recurrent or without recurrent units for the quick solution of the pattern classification problem. The proposed algorithm was tested learning capability with the sigmoidal activation function and hyperbolic tangent activation function on the contact lens and balance scale standard benchmark problems. And results are compared with those obtained with Cascade Correlation and Recurrent Cascade Correlation algorithms. By the learning the new network was composed with the minimal number of the created hidden units and shows quick learning speed. Consequently it will be able to improve a learning capability.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Journal of Broadcast Engineering
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• v.16 no.3
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• pp.501-509
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• 2011

In this paper, we propose an edge profile adaptive bi-directional diffusion interpolation method which consists of shock filter and level set. In recent years many interpolation methods have been proposed but all methods have some degrees of artifacts such as blurring and jaggies. To solve these problems, we adaptively apply shock filter and level set method where shock filter enhances edge along the normal direction and level set method removes jaggies artifact along the tangent direction. After the initial interpolation, weights of shock filter and level set are locally adjusted according to the edge profile. By adaptive coupling shock filter with level set method, the proposed method can remove jaggies artifact and enhance the edge. Experimental results show that the average PSNR and MSSIM of our method are increased, and contour smoothness and edge sharpness are also improved.