• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.849-866
• /
• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.2
• /
• pp.204-213
• /
• 2016

A differential game theory based approach is used to develop an automated maneuver generation algorithm for Within Visual Range (WVR) air-to-air combat of unmanned combat aerial vehicles (UCAVs). The algorithm follows hierarchical decisionmaking structure and performs scoring function matrix calculation based on differential game theory to find the optimal maneuvers against dynamic and challenging combat situation. The score, implying how much air superiority the UCAV has, is computed from the predicted relative geometry, relative distance and velocity of two aircrafts. Security strategy is applied at the decision-making step. Additionally, a barrier function is implemented to keep the airplanes above the altitude lower bound. To shorten the simulation time to make the algorithm more real-time, a moving horizon method is implemented. An F-16 pseudo 6-DOF model is used for realistic simulation. The combat maneuver generation algorithm is verified through three dimensional simulations.

• Communications of Mathematical Education
• /
• v.29 no.1
• /
• pp.131-155
• /
• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

• Structural Engineering and Mechanics
• /
• v.62 no.3
• /
• pp.345-355
• /
• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• Journal of the Korean Magnetic Resonance Society
• /
• v.19 no.3
• /
• pp.119-123
• /
• 2015

The thermodynamic properties and structural geometry of $KMgCl_3{\cdot}6H_2O$ were investigated using thermogravimetric analysis, differential scanning calorimetry, and nuclear magnetic resonance. The initial mass loss occurs around 351 K ($=T_d$), which is interpreted as the onset of partial thermal decomposition. Phase transition temperatures were found at 435 K ($=T_{C1}$) and 481 K ($=T_{C2}$). The temperature dependences of the spin-lattice relaxation time $T_1$ for the $^1H$ nucleus changes abruptly near $T_{C1}$. These changes are associated with changes in the geometry of the arrangement of octahedral water molecules.

• Journal for History of Mathematics
• /
• v.22 no.2
• /
• pp.13-26
• /
• 2009

Elie Cartan is one of the mathematicians whose works marked the development of geometry and algebra of 20th century. We illuminate his mathematical contributions which is familiar to the experts but is alien to most of the mathematicians in general. Also we elucidate some of his influences.

• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.273-278
• /
• 2012

Using a comparison of the Jacobi differential equations instead of volume comparison by Itokawa in [3], the focal radius is estimated under the suitable Ricci and mean curvature conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.231-241
• /
• 1991

Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.

• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.277-290
• /
• 1999

In this paper, we investigate the existence of a two dimensional surface in a four dimensional equiaffine space and characterize that surface.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.665-673
• /
• 2011

In this paper, we derive a set of the partial differential equations that characterize an inelastic flow of a curve in a 3-dimensional Galilean space. Also, we give necessary and sufficient condition for an inelastic flow.