• Journal of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1515-1528
• /
• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1823-1834
• /
• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

• East Asian mathematical journal
• /
• v.8 no.2
• /
• pp.199-204
• /
• 1992

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.661-679
• /
• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Journal of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.987-998
• /
• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• Journal of KIISE:Software and Applications
• /
• v.33 no.1
• /
• pp.95-104
• /
• 2006

The Gradient Vector Flow (GVF) snake or active contour model offers the best performance for image segmentation. However, there are problems in classical snake models such as the limited capture range and the slow progress into concavity. This paper presents a new method for enhancing the performance of the GVF snake model by extending the external force fields from the neighboring fields and using a modified smoothing method to regularize them. The results on a simulated U-shaped image showed that the proposed method has larger capture range and makes it possible for the contour to progress into concavity more quickly compared with the conventional GVF snake model.

• Journal of the Korea Computer Graphics Society
• /
• v.30 no.2
• /
• pp.1-9
• /
• 2024

In this paper, we propose a new method to visualize different vector field patterns from density data. We use moving least squares (MLS), which is used in physics-based simulations and geometric processing. However, typical MLS does not take into account the nature of density, as it is interpolated to a higher order through vector-based constraints. In this paper, we design an algorithm that incorporates Monte Carlo-based weights into the MLS to efficiently account for the density characteristics implicit in the input data, allowing the algorithm to represent different forms of white noise. As a result, we experimentally demonstrate detailed vector fields that are difficult to represent using existing techniques such as naive MLS and divergence-constrained MLS.

• Journal of The Korean Astronomical Society
• /
• v.32 no.2
• /
• pp.127-136
• /
• 1999

In this study we present the study of solar active regions based on BOAO vector magnetograms and H$\alpha$ filtergrams. With the new calibration method we analyzed BOAO vector magnetograms taken from the SOFT observational system to compare with those of other observing systems. In this study it has been demonstrated that (1) our longitudinal magnetogram matches very well the corresponding Mitaka's magnetogram to the extent that the maximum correlation yields r=0.962 between our re-scaled longitudinal magnetogram and the Mitaka's magnetogram; (2) according to a comparison of our magnetograms of AR 8422 with those taken at Mitaka solar observatory their longitudinal fields are very similar to each other while transverse fields are a little different possibly due to large noise level; (3) main features seen by our longitudinal magnetograms of AR 8422 and AR 8419 and the corresponding Kitt Peak magnetograms are very similar to each other; (4) time series of our vector magnetograms and H-alpha observations of AR 8419 during its flaring (M3.1/1B) activity show that the filament eruption followed the sheared inversion line of the quadrupolar configuration of sunspots, indicating that the flare should be associated with the quadrupolar field configuration and its interaction with new filament eruption. Finally, it may be concluded that the Solar Flare Telescope at BOAO works normally and it is ready to do numerous observational and theoretical works associated with solar activities such as flares.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.853-867
• /
• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• Korean Journal of Computational Design and Engineering
• /
• v.12 no.1
• /
• pp.58-73
• /
• 2007

This paper described a method for the construction of a surface through a set of nonuniform scattered points. When the shift vectors of some points as constraints on the original surface are given, those of the other points should be computed to make the new surface. To keep up the look-see and smoothness with the original surfaces, the proper relationship should be formulated between the shifts of the constraint points and those of the other points. Vector fields for 3 dimensional shift of a point on the surface are made based in the constraint shifts. Vector fields for 3 dimensional shift of a point on the surface are made based on the constraint shifts. Multilevel B-spline approximation technique was used to construct the vector field. The technique uses coarse-to-fine hierarchy of control lattices. The developed method was applied to shoe sole design system especially for grading. Using this system, a shoe sole can be modified effectively.