• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.259-263
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• 1996

Let G be a topological group and X a G space. For a given nonequivariant vector bundle over X there does not always exist a G equivariant vector bundle structure. In this paper we find some sufficient conditions for nonequivariant real line bundles to have G equivariant vector bundle structures.

• 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.51 no.1
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• pp.67-76
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• 2014

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${\bullet}$ X is a divergence-free vector field satisfying the shadowing property. ${\bullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${\bullet}$ X is an expansive divergence-free vector field. ${\bullet}$ X has no singularities and is Anosov.

• Journal of Multimedia Information System
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• v.4 no.4
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• pp.249-254
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• 2017

Digital vector maps must be compressed effectively for transmission or storage in Web GIS (geographic information system) and mobile GIS applications. This paper presents a polyline compression method that consists of polyline feature-based hybrid simplification and second derivative-based data compression. Experimental results verify that our method has higher simplification and compression efficiency than conventional methods and produces good quality compressed maps.

• Structural Engineering and Mechanics
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• v.2 no.2
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• pp.125-139
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• 1994

A vector algorithm for calculating the stiffness matrices of reinforced concrete shell elements is presented. The algorithm is based on establishing vector lengths equal to the number of elements. The computational efficiency of the proposed algorithm is assessed on a Cray Y-MP supercomputer. It is shown that the vector algorithm achieves scalar-to-vector speedup of 1.7 to 7.6 on three moderate sized inelastic problems.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.8
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• pp.1977-1983
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• 1998

An algorithm-based fault tolerant scheme for the vector convolution is proposed employing the positive and negative checksum vectors that are defined in this paper based on the encoder vector. The proposed scheme is implemented on the aray processor, and then the amount of redundancy is examined thrugh the complexity analysis.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.203-207
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• 2008

In [1], Mishra and Wang established relationships between vector variational-like inequality problems and non-smooth vector optimization problems under non-smooth invexity in finite-dimensional spaces. In this paper, we generalize recent results of Mishra and Wang to infinite-dimensional case.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.103-112
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• 2022

A definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. The formulas for Euclidean norm of the fractional vector cross product of two vectors, and for fractional triple vector cross product are obtained.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1358-1363
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• 1995

This paper presents a new learning method for a noise tolerant Fuzzy ART. In the conventional Fuzzy ART, the top-down and bottom-up weight vectors have the same value. They are updated by a fuzzy AND operation between the input vector and the current value of the top-down or bottom- up weight vectors. However, it can not prevent the abrupt change of the weight vector and can not achieve good performance for a noisy input vector. To solve the problems, we updated using the weighted sum of the input vector and the current value of the top-down vector. To achieve stability, the bottom-up weight vector is updated using the fuzzy AND operation between the newly learned top-down vector and the current value of the bottom-up vector. Computer simulations show that the proposed method prominently resolves the category proliferation problem without increasing the training epoch for stabilization in noisy environments.