• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.68-72
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• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.

• Journal for History of Mathematics
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• v.11 no.1
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• pp.36-41
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• 1998

In the Chosun Dynasty Nam, Byung-Gil(another name is Nam, Sang-Gil alias Won-Sang; 1820-1869) made a research comparing Chinese traditional mathematics with western mathematics, which missionaries who came to China at the end of Ming Dynasty introduced. He particularly studied fundamental differences between Chinese and western methods to solve algebraic equations. He wrote an article "Moo-Ee-Hae", in which he insisted that the two methods are eventually same though they are different in the고 expressions. His article has big significance as the first mathematic paper in the history of Korean mathematics.thematics.

• Korean Journal of Crystallography
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• v.9 no.1
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• pp.39-43
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• 1998

The well-known geometries showing the relation between the angular coordinates of a plane normal and a Laue diffraction spot have been improved. The Bernalte's algebraic equations for the lines in the Greninger and Leonhardt charts have been alternatively derived in more intuitive and perspicuous ways than his original derivation.

• Journal of the Korean Society of Safety
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• v.19 no.4 s.68
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• pp.155-160
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• 2004

A simply supported rectangular thin plate with temperature distribution varying over the thickness is analyzed. Since the thermal deflections are large compared to the plate thickness during bending and membrane stresses are developed md as such a nonlinear stress analysis is necessary. For the geometrically nonlinear, large deflection behavior of the plate, the classical von Karman equations are used. These equations are solved numerically by using the finite difference method. An iterative technique is employed to solve these quasi-linear algebraic equations. The results obtained from the suggested method are presented and discussed.

• Nuclear Engineering and Technology
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• v.24 no.3
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• pp.319-328
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• 1992

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.469-497
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• 2016

In this research, we develop a systematic learning the materials on constructibility of cubic roots. We propose two sets of materials: one is based on concepts of field, vector space, minimal polynomial in abstract algebra, another based on properties of cubic roots in elementary algebra. We assess the validity, applicability, defects and merits of developed materials through prospective teachers, in-service teachers, and professionals. It could be expected that materials be used for advanced secondary students, mathematics majoring college students and mathematics teachers. Furthermore, we may expect the materials be useful for understanding and solving the (un)constructibility problems.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.1
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• pp.139-146
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• 2003

In this paper we demonstrate a cryptanalysis of the stream cipher LILI-128. Our approach to analysis on LILI-128 is to solve an overdefined system of multivariate equations. The LILI-128 keystream generato $r^{[8]}$ is a LFSR-based synchronous stream cipher with 128 bit key. This cipher consists of two parts, “CLOCK CONTROL”, pan and “DATA GENERATION”, part. We focus on the “DATA GENERATION”part. This part uses the function $f_d$. that satisfies the third order of correlation immunity, high nonlinearity and balancedness. But, this function does not have highly nonlinear order(i.e. high degree in its algebraic normal form). We use this property of the function $f_d$. We reduced the problem of recovering the secret key of LILI-128 to the problem of solving a largely overdefined system of multivariate equations of degree K=6. In our best version of the XL-based cryptanalysis we have the parameter D=7. Our fastest cryptanalysis of LILI-128 requires $2^{110.7}$ CPU clocks. This complexity can be achieved using only $2^{26.3}$ keystream bits.

• School Mathematics
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• v.17 no.3
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• pp.391-405
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• 2015

This study was aimed to investigate how students' relational thinking about equations could be formed by exploring web-based balance. The researchers developed 3 groups of 4 typed 12 equation problems of (a+b+c = d+ _ ) to test 24 4th graders. Pretest and post-test were conducted using Eye-tracker for investigating their eye movements. The researchers interviewed students who were not having distinct strategies to look into their cognitive process. As a result, we can conclude web-based balance helped students to get the concept of the equal sign and to form the relational thinking by the process of comparing both sides, right and left on the basis of fulcrum on balance.

• Korean Journal of Optics and Photonics
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• v.18 no.1
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• pp.19-23
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• 2007

We derived analytically the generalized curvature linear equation useful in the initial optical design of a two-mirror system with finite object distance, including an infinite object distance from paraxial ray tracing and Seidel third order aberration theory for coma coefficient. These aberration coefficients for finite object distance were described by the curvature, the inter-mirror distance, and the effective focal length. The analytical equations were solved by using a computer with a numerical analysis method. Two useful linear relationships, determined by the generalized curvature linear equations relating the curvatures of the two mirrors, for the cancellation of each aberration were shown in the numerical solutions satisfying the nearly zero condition ($<10^{-10}$) for each aberration coefficient. These equations can be utilized easily and efficiently at the step of initial optical design of a two-mirror system with finite object distance.