• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.685-697
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• 2014

In this paper, we prove that there are no pseudo null Bertrand curve with curvature functions $k_1(s)=1$, $k_2(s){\neq}0$ and $k_3(s)$ other than itself in Minkowski spacetime ${\mathbb{E}}_1^4$ and by using the similar idea of Matsuda and Yorozu [13], we define a new kind of Bertrand curve and called it pseudo null (1,3)-Bertrand curve. Also we give some characterizations and an example of pseudo null (1,3)-Bertrand curves in Minkowski spacetime.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.381-392
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• 2007

In 1906, da Rios, a student of Leivi-Civita, wrote a master's thesis modeling the motion of a vortex in a viscous fluid by the motion of a curve propagating in $R^3$, in the direction of its binormal with a speed equal to its curvature. Much later, in 1971 Hasimoto showed the equivalence of this system with the non-linear Schr$\ddot{o}$dinger equation (NLS) $$q_t=i(q_{ss}+\frac{1}{2}{\mid}q{\mid}^2q$$. In this paper, we use the same idea as Terng used in her lecture notes but different technique to extend the above relation to the case of $R^3$, and obtained an analogous equation that $$q_t=i[q_{ss}+(\frac{1}{2}{\mid}q{\mid}^2+1)q]$$.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.481-494
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• 2008

Iteration functions $K_m(z)$ and $U_m(z)$, $m{\geq}2$are defined recursively using the determinant of a matrix. We show that the fixed-iterations of $K_m(z)$ and $U_m(z)$ converge to a simple zero with order of convergence m and give closed form expansions of $K_m(z)$ and $U_m(z)$: To show the convergence, we derive a recursion formula for $L_m$ and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is $L_m(z)/(f^{\prime})^m$, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• 한국소음진동공학회논문집
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• 제14권9호
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• pp.837-845
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• 2004

A variable friction damper for vehicle driveline has been proposed. This new torsional damper system uses a solenoid as an actuator to vary friction force of the damper. To verify the idea of using a solenoid in a variable damper system, the test fixture and the dampers are made and tested. Also, to find out the range of damper friction forces that influence the vehicle driveline vibration, a mathematical model of the driveline had been developed and simulated. Test and simulation results show that, within electric current used in the vehicle electric system, the solenoid can develop enough friction force that will surpass resonance in the driveline of 1.5 L Gasoline engine vehicle during acceleration.

• 한국CDE학회논문집
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• 제6권4호
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• 한국CDE학회논문집
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• 제7권4호
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• pp.269-279
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• 2002

Geometric shape morphing is an interesting geometric operation that interpolates two geometric shapes to generate in-betweens. It is well known that Minkowski operations can be used to test and build collision-free motion paths and to modify shapes in digital image processing. In this paper, we present a new geometric modeling technique to control the morphing on geometric shapes based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extend this scheme into a Bezier-like control structure with multiple control shapes, which enables the interactive control over the intermediate shapes during the morphing sequence as in the traditional CAGD curve/surface editing. Moreover, we apply the theory of blossoming to our control structure, whereby our control structure becomes even more flexible and general. In this paper, we present mathematical models of control structure, their properties, and computational issues with examples.

• 대한산업공학회지
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• 제43권2호
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• pp.135-146
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• 2017

This paper considers redundancy optimization problems of multi-level systems and reviews existing papers which proposed various optimization models and used different algorithms in this research area. Three different mathematical models are studied: Multi-level redundancy allocation (MRAP), multiple multi-level redundancy allocation, and availability-based MRAP models. Many meta-heuristics are applied to find optimal solutions in the several optimization problems. We summarized key idea of meta-heuristics applied to the existing MARP problems. Two extended models (MRAP with interval reliability of units and an integrated optimization problem of MRAP and preventive maintenance) are studied and further research ideas are discussed.

• Journal of Information Display
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• 제4권3호
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• pp.29-34
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• 2003

At the paper the method of 3D holographic moving image reconstruction is discused. The main idea of this method is based on the substitution of optically created static hologram by equal diffraction array created by acoustical (AO) field which formed by bulk sound waves. Such sound field can be considered as dynamic optical hologram, which is electrically controlled. At the certain moment of time when the whole hologram already formed, the reference optical beam illuminates it, and due to acoustooptical interaction the original optical image is reconstructed. As the acoustically created dynamic optical hologram is electronically controlled, it can be used for moving 3-dimentional scene reconstruction in real time. The architecture of holographic display for moving scene reconstruction is presented at this paper. The calculated variant of such display laboratory model is given and discussed. The mathematical simulation of step by step images recording and reconstruction is given. The pictures of calculated reconstructed images are presented. The prospects, application areas, shortcomings and main problems are discussed.

• 전자통신동향분석
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• 제33권2호
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• pp.39-47
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• 2018

The fundamental problem of communication is that of transmitting a message from a source to a destination over a channel through the use of a transmitter and receiver. To derive a theoretically optimal solution, the transmitter and receiver can be divided into several processing blocks, with each component analyzed and optimized. The idea of machine learning (or deep learning) communications systems goes back to the original definition of the communi-cation problem, and optimizes the transmitter and receiver jointly. Although today's systems have been optimized over the last decades, and it seems difficult to compete with their performance, deep learning based communication is attractive owing to its simplicity and the fact that it can learn to communicate over any type of channel without the need for mathematical modeling or analysis.