• 정보보호학회논문지
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• 제33권3호
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• pp.375-381
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• 2023

완전동형암호는 암호화된 데이터에 대한 대수적 연산을 지원하며, 최근에는 최대값 함수 등의 비대수적 연산도 근사하는 방법이 연구되고 있다. 그러나 아직 4개 이상의 숫자에 대한 정밀한 맥스 풀링 근사 연구는 이루어지지 않았다. 본 연구에서는 최대값 함수 근사 다항식의 합성을 활용하여 정밀한 맥스 풀링 근사 기법을 제안하였으며, 이를 이론적으로 분석하여 높은 정밀도를 증명하였다. 실험 결과, 제안하는 근사 맥스 풀링은 1ms 이내의 작은 분할 실행 시간과 이론적 분석과 일치하는 높은 정밀도를 보여주었다.

• 한국정보과학회논문지:소프트웨어및응용
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• 제27권1호
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• pp.50-61
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• 2000

최근 원추곡선에 기반한 스테레오 비젼에 대한 연구가 주목을 받고 있는데, 이는 원추곡선이 행렬표현, 대응관계설정의 용이성, 그리고 실세계에서 쉽게 찾을 수 있다는 좋은 성질을 갖는다는 점에서 당연한 현상이라 여겨진다. 하지만, 일반적인 고차의 대수곡선에 대한 확장은 아직 성공적으로 이루어지지 못하고 있는 실정이다. 기약인 대수곡선 (irreducible algebraic curve)은 실세계에서 많지 않지만, 직선과 원추곡선은 무수히 많고, 따라서 이들의 곱으로 주어지는 높은 차수의 대수곡선도 무수히 많다. 본고에서는 2이상의 임의의 차수를 가지는 대수곡선을 calibration된 두 대의 카메라를 가지고 스테레오 문제를 푼다. 대응관계설정과 복원, 두 가지 문제 모두에 대한 closed form solution을 제시한다. $f_1,\;f_2,\;{\pi}$를 각각 두 이미지 곡선, 공간상의 평면이라 하고, $VC_P(g)$를 평면곡선 g와 점 P로 만들어지는 원추곡선이라 하면, $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ 의 관계를 이용하여 미지수인 평면 ${\pi}$의 계수들, $d_1,\;d_2,\;d_3$에 대한 다항 방정식들을 얻을 수 있다. 약간의 변형을 통하여 $d_1$에 대한 다항 방정식을 얻을 수 있고, 이 방정식의 유일한 양수해는 나머지 과정에서 매우 중요한 역할을 한다. 그 이후에는 $O(n^2)$개의 일변수 다항식에 대한 계산만으로 모든 스테레오 문제를 해결한다. 이는 과거의 여러 개의 다변수 다항식의 공통근을 구해야 했던 방법에 비교된다. synthetic 데이터와 실제 이미지에 대한 실험은 우리의 알고리듬이 옳음을 보여준다.

• Structural Engineering and Mechanics
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• 제14권3호
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• pp.263-285
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• 2002

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev's basis functions $R_{bf}$ based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Numerical results obtained by $R_{bf}$ functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표논문집(II)
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• 한국수학사학회지
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• 제15권3호
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• 한국소음진동공학회논문집
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• 제14권4호
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• pp.336-343
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• 2004

This paper reports the first known free vibration data for thin rectangular plates with V-notches. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets include (1) mathematically complete algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained, and (2) corner functions which account for the bending moment singularities at the sharp reentrant corner of the Y-notch. Extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of nondirectional frequencies for rectangular plates having the V-notch. In this paper, accurate frequencies and normalized contours of vibratory transverse displacement are presented for various notched plates, so that the effect of corner stress singularities may be understood.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.214-225
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• 1999

An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.

• Advances in nano research
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• 제6권3호
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• pp.257-278
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• 2018

Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading.

• 대한수학회지
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• 제41권4호
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• pp.717-735
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• 2004

A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which $2^a\;-\;2^b$ divides $n^a\;-\;n^b$ for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements ${\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}$ in the ring of integers A of a number field for which ${\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A$. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.