• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.

• Journal of electromagnetic engineering and science
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• v.6 no.2
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• pp.135-145
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• 2006

This paper presents the theory, design, fabrication and characterization of the novel low actuation voltage capacitive shunt RF-MEMS switch using a corrugated membrane with HRS MEMS packaging. Analytical analyses and experimental results have been carried out to derive algebraic expressions for the mechanical actuation mechanics of corrugated membrane for a low residual stress. It is shown that the residual stress of both types of corrugated and flat membranes can be modeled with the help of a mechanics theory. The residual stress in corrugated membranes is calculated using a geometrical model and is confirmed by finite element method(FEM) analysis and experimental results. The corrugated electrostatic actuated bridge is suspended over a concave structure of CPW, with sputtered nickel(Ni) as the structural material for the bridge and gold for CPW line, fabricated on high-resistivity silicon(HRS) substrate. The corrugated switch on concave structure requires lower actuation voltage than the flat switch on planar structure in various thickness bridges. The residual stress is very low by corrugating both ends of the bridge on concave structure. The residual stress of the bridge material and structure is critical to lower the actuation voltage. The Self-alignment HRS MEMS package of the RF-MEMS switch with a $15{\Omega}{\cdot}cm$ lightly-doped Si chip carrier also shows no parasitic leakage resonances and is verified as an effective packaging solution for the low cost and high performance coplanar MMICs.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.12
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• pp.1152-1162
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• 2008

This paper deals with the State-Dependent Riccati Equation (SDRE) technique for the design of helicopter nonlinear flight controllers. Since the SDRE controller requires a linear system-like structure for nonlinear motion equations, a state-dependent coefficient (SDC) factorization technique is developed in order to derive the conforming structure from a general nonlinear helicopter dynamic model. Also on-line numerical methods of solving the algebraic Riccati equation are investigated to improve the numerical efficiency in designing the SDRE controllers. The proposed method is applied to trajectory tracking problems of the helicopter and computational tips for a real time application are proposed using a high fidelity rotorcraft mathematical model.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1189-1208
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• 2018

The aim of this paper is to study the class of ${\Lambda}$-constacyclic codes of length $2p^s$ over the finite commutative chain ring ${\mathcal{R}}_a=\frac{{\mathbb{F}_{p^m}}[u]}{{\langle}u^a{\rangle}}={\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}+{\cdots}+u^{a-1}{\mathbb{F}}_{p^m}$, for all units ${\Lambda}$ of ${\mathcal{R}}_a$ that have the form ${\Lambda}={\Lambda}_0+u{\Lambda}_1+{\cdots}+u^{a-1}{\Lambda}_{a-1}$, where ${\Lambda}_0,{\Lambda}_1,{\cdots},{\Lambda}_{a-1}{\in}{\mathbb{F}}_{p^m}$, ${\Lambda}_0{\neq}0$, ${\Lambda}_1{\neq}0$. The algebraic structure of all ${\Lambda}$-constacyclic codes of length $2p^s$ over ${\mathcal{R}}_a$ and their duals are established. As an application, this structure is used to determine the Rosenbloom-Tsfasman (RT) distance and weight distributions of all such codes. Among such constacyclic codes, the unique MDS code with respect to the RT distance is obtained.

• Journal of Astronomy and Space Sciences
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• v.34 no.1
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• pp.7-17
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• 2017

In South Korea, there are about 80 Global Positioning System (GPS) monitoring stations providing total electron content (TEC) every 10 min, which can be accessed through Korea Astronomy and Space Science Institute (KASI) for scientific use. We applied the computerized ionospheric tomography (CIT) algorithm to the TEC dataset from this GPS network for monitoring the regional ionosphere over South Korea. The algorithm utilizes multiplicative algebraic reconstruction technique (MART) with an initial condition of the latest International Reference Ionosphere-2016 model (IRI-2016). In order to reduce the number of unknown variables, the vertical profiles of electron density are expressed with a linear combination of empirical orthonormal functions (EOFs) that were derived from the IRI empirical profiles. Although the number of receiver sites is much smaller than that of Japan, the CIT algorithm yielded reasonable structure of the ionosphere over South Korea. We verified the CIT results with NmF2 from ionosondes in Icheon and Jeju and also with GPS TEC at the center of South Korea. In addition, the total time required for CIT calculation was only about 5 min, enabling the exploration of the vertical ionospheric structure in near real time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.5
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• pp.661-669
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• 1999

The evolutionary structure of a tip vortex in the initial period have been investigated by the two-dimensional LDV system. Circumferential and axial components of mean velocities, their turbulences and Reynolds stresses were measured by the phase averaging technique at seven different wake ages within one revolution of the rotor. Core growth was also analyzed. It was resulted that circumferential velocity components showed a Rankine combined vortex shape and their circulation profiles viewed in the radial direction were close to the n = 2 model of Vatistas' algebraic formula, while axial velocity components seemed to have the Gaussian profiles In these measured ranges with the base width of three times of core radii. Peaks of circumferential velocities and core radii showed distinct asymmetric behaviors before the wake age of $150^{\circ}$ over inboard and outboard sides of the slipstream, but they became symmetric afterwards. Turbulence profiles which had two peaks Inside the core radii in the earlier wake age were also changed to single peaks after $150^{\circ}$. These trends imply that the tip vortex was barely mature at this wake age.

• Korean Journal of Optics and Photonics
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• v.20 no.6
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• pp.319-327
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• 2009

We introduce a new design technique by treating a two-group zoom lens system with a wide angle of view. First, the concept of the global optimization is introduced in the initial design stage, and from this, the global design technique is completed by analyzing and summarizing large quantities of modern design data. That is, we define the global structure function to achieve a new conceptual design technique for global optimization. And the function is put in a simple form by referring lots of patent data, manipulated with other algebraic equations, and solved finally such that we obtain the global solution region. The global solution region corresponds to the global optimization and suggests insightful systematized directions for the design of two-group zoom lens systems. These directions are attractive compared to global optimization.

• International Journal of Contents
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• v.7 no.4
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• pp.56-63
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• 2011

Quantum mechanics is a branch of physics for a mathematical description of the particle wave, and it is applied to information technology such as quantum computer, quantum information, quantum network and quantum cryptography, etc. In 1936, Garrett Birkhoff and John von Neumann introduced the logic of quantum mechanics (quantum logic) in order to investigate projections on a Hilbert space. As another type of quantum logic, orthomodular implication algebra was introduced by Chajda et al. This algebra has the logical implication as a binary operation. In pure mathematics, there are many algebras such as Hilbert algebras, implicative models, implication algebras and dual BCK-algebras (DBCK-algebras), which have the logical implication as a binary operation. In this paper, we introduce the definitions and some properties of those algebras and clarify the relations between those algebras. Also, we define the implicative poset which is a generalization of orthomodular implication algebras and DBCK-algebras, and research properties of this algebraic structure.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.267-278
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• 2009

As a survey-type article, the paper reviews the recent results on a (generalized) universal covering space in digital covering theory. The recent paper [19] established the generalized universal (2, k)-covering property which improves the universal (2, k)-covering property of [3]. In algebraic topology it is well-known that a simply connected and locally path connected covering space is a universal covering space. Unlike this property, in digital covering theory we can propose that a generalized universal covering space has its intrinsic feature. This property can be useful in classifying digital covering spaces and in studying a shortest k-path problem in data structure.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1247-1258
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• 1995

Input-output decoupling is well-known to be effective in the control of the nonlinear systems. This paper points out some problems of this technique in applications, and obtains a new digital input-output decoupling feedback law by using the inherent structure of the system. The effectiveness (accuracy) of our new control technique are confirmed by simple computer simulations. Finally, a digital compensator is also designed. The problems we study are of importance in the field of nonlinear control of robots, aerospace navigation, and vehicular control. The methodology to be employed involves both algebraic and geometric aspects of the systems.