• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.377-388
• /
• 2018

In this paper, we define new quaternionic associated curves called quaternionic principal-direction curves and quaternionic principal-donor curves. We give some properties and relationships between Frenet vectors and curvatures of these curves. For spatial quaternionic curves, we give characterizations for quaternionic helices and quaternionic slant helices by means of their associated curves.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.183-200
• /
• 2015

In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.589-598
• /
• 2023

Magnetic curves are the trajectories of charged particals which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between β-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for γ-magnetic curves. Finally, we give an evaluation of what we did.

• Honam Mathematical Journal
• /
• v.44 no.1
• /
• pp.121-134
• /
• 2022

In this study, we obtain the spherical images of minimal curves in the complex space in ℂ⁴ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

• Honam Mathematical Journal
• /
• v.39 no.4
• /
• pp.603-616
• /
• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1994.04a
• /
• pp.691-700
• /
• 1994

Voronoi diagram of a set of geometric entities on a plane such as points, line segments, or arcs is a collection of Voronoi polygons associated with each entity, where Voronoi polygon of an entity is a locus of point which is closer to the associated entity than any other entity. Voronoi diagram is one of the most fundamental geometrical construct and well-known for its theoretical elegance and the wealth of applications. Various geometric problems can be solved with the aid of Voronoi diagram. For example, the maximum tool diameter of a milling cutter for rough cutting in a pocket can be easily found, and the pocketing tool path can be efficiently generated from Voronoi diagram. In PCB design, the design rule checking can be easily done via Voronoi diagram, too. This paper discusses an algorithm to construct Voronoi diagram of a simple polygon which consists of simple curves such as line segments as well as arcs in a plane with O(nlogn) time complexity by employing the divide and conquer scheme.

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.193-207
• /
• 1999

Let ${\gamma}$ : Ilongrightarrow R2 be a sufficiently smooth curve and $\sigma$${\gamma}$ be the affine arclength measure supported on ${\gamma}$. In this paper, we study the Lp - improving properties of the convolution operators T$\sigma$${\gamma}$ associated with $\sigma$${\gamma}$ for various curves ${\gamma}$. Optimal results are obtained for all finite type plane curves and homogeneous curves (possibly blowing up at the origin). As an attempt to extend this result to infinitely flat curves we give and example of a family of flat curves whose affine arclength measure has same Lp-improvement property. All of these results will be based on uniform estimates of damping oscillatory integrals.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.6 no.1
• /
• pp.255-262
• /
• 2002

This paper presents a statistical analysis of empirical fragility curves for bridge. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogoken Nanbu(Kobe) earthquake. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters(median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.

• School Mathematics
• /
• v.16 no.4
• /
• pp.827-845
• /
• 2014

This study aims to investigate how the university educational programs about quadratic curves are operated in relation to the high school curriculum and what their effects may be, and the degree of understanding for the prospective and current teachers of the mathematical content knowledge about quadratic curves. To solve this research questions, we randomly selected three universities and one high school. Then we investigated the curricula of each department of mathematics education, compared them with the high school curricula, and conducted surveys of the professors' and students' conception on how much mathematical content knowledge they need to know about quadratic curves. The study resulted in the following conclusions. First, the curriculum on the subject of quadratic curves in the college of education is closely connected to the high school programs. This study's results showed that the college of education's curriculum includes a series of lectures regarding quadratic curves, and that within them, the mathematical content about quadratic curves associated with high school mathematics was thoroughly covered. Also, a large number of students who attended the lecture reported a significant increase in their understanding in regards to the quadratic curves. Second, it is strongly recommended to strengthen the connection between the college of education's curriculum and the actual high school education field. The prospective teachers think that there is a substantial need to learn about the quadratic curves because it is closely connected with the high school curriculum. But they find it challenging to put what they were taught into practical use in the high school education field, and feel that an improvement in this area is much needed. Third, it is necessary to promote, encourage and support the voluntary efforts to expand the range of the content knowledge in quadratic curves to cover the academic content associated with the high school mathematics.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.83-96
• /
• 2013

Let K be a number field and fix a prime number $p$. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set $B_{K,p}$ of primes of K satisfying that any elliptic curve over K with $B_{K,p}$-reduction has no $p$-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with $B_{K,p}$-reduction and a $p$-torsion point. The action of the absolute Galois group on the $p$-torsion subgroup of E gives its associated Galois representation $\bar{\rho}_{E,p}$ modulo $p$. We also study the irreducibility and surjectivity of $\bar{\rho}_{E,p}$ for semistable elliptic curves with $B_{K,p}$-reduction.