• 대한수학회지
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• 제33권3호
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• pp.651-655
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• 1996

Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.

• 대한수학회보
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• 제12권1호
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• pp.7-11
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• 1975

• Korean Journal of Mathematics
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• 제24권1호
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• pp.71-79
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• 2016

In this paper, we determine all positive integers which cannot be represented by a sum of four squares at least 9, and prove that for each N, there are nitely many positive integers which cannot be represented by a sum of four squares at least $N^2$ except $2{\cdot}4^m$, $6{\cdot}4^m$ and $14{\cdot}4^m$ for $m{\geq}0$. As a consequence, we prove that for each $k{\geq} 5$ there are nitely many positive integers which cannot be represented by a sum of k squares at least $N^2$.

• 한국통신학회논문지
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• 제37A권12호
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• pp.1031-1037
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• 2012

Tonelli-Shanks 알고리즘을 변형한 새로운 알고리즘을 통해 효율적으로 제곱근 및 세제곱근을 찾을 수 있는 방법을 연구하였다. 이 논문에서 소개하는 제곱근을 찾는 알고리즘은 Number Field Sieve에 응용할 수 있다. 큰 합성수를 인수분해하는데 가장 효율적인 알고리즘으로 알려진 Number Field Sieve (NFS)는 법 N에 대하여 공통근을 갖는 두 다항식 선택한 후에, sieving, linear algebra, square root 단계를 차례대로 거친다. NFS의 마지막 단계에서는 수체(Number Field)상에서 제곱근을 구하는 과정이 필요한데 이를 유한체(Finite Field)상으로 내려서 계산한 후 CRT(Chinese Remainder Theorem)을 이용하여 수체 상에서의 제곱근으로 복원하는 과정에서 제안된 알고리즘이 사용될 수 있다.

• Journal of information and communication convergence engineering
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• 제9권4호
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• pp.420-423
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• 2011

The paper is devoted to problem of spline modeling of multidimensional signals. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables.

• 대한조선학회논문집
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• 제57권2호
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• pp.114-123
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• 2020

A high-order potential-based panel method based on Green's theorem, with piecewise-linear dipole strength on triangular panels, is formulated for the analysis of potential flow around a three-dimensional wing. Previous low-order panel methods adopt square panels with piecewise-constant dipole strength, which results in inherent errors. Square panels can not represent a high curvature lifting body, such as propellers, since the four vertices of the square panel do not locate at the same flat plane. Moreover the piecewise-constant dipole strength induces inevitable errors due to the steps in dipole strength between adjacent panels. In this paper a high-order panel method is formulated to improve accuracy by adopting a piecewise linear dipole strength on triangular panels. Firstly, the square panels are replaced by triangular panels in order to increase the geometric accuracy in representing the shape of the object with large curvature. Next, the step difference of the dipole strength between adjacent panels is removed by adopting piecewise-linear dipole strength on the triangular panels. The calculated results by the present method is compared with analytical ones for simple non-lifting geometries, such as ellipsoid. The results for an elliptic wing with zero thickness at finite angle of attack are compared with Jordan's results. The comparison shows reasonable agrements for the both lifting and non-lifting bodies.

• International Journal of Contents
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• 제3권4호
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• pp.26-29
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• 2007

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables. Future work: application area such as digital contents like animation, game graphic.