• 대한수학회보
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• 제58권3호
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• pp.593-602
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• 2021

We use a kind of modified Hurwitz class numbers to express the number of representing a positive integer by some ternary quadratic forms such as the sum of three squares, and the Fourier coefficients of weight 2 modular forms of prime level with trivial character.

• 대한수학회보
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• 제58권4호
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• pp.829-836
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• 2021

In this paper, we consider several domination parameters like perfect domination number, locating-domination number, open-locatingdomination number, etc. in the Mycielski graph M(G) of a graph G. We found upper bounds for locating-domination number of M(G) and computational formulae for perfect locating-domination number and open locating-domination number of M(G). We also showed that the perfect domination number of M(G) is at least that of G plus 1 and that for each positive integer n, there exists a graph G_n such that the perfect domination number of M(G_n) is equal to that of G_n plus n.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2011년도 정기총회 및 추계학술대회 논문집
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• pp.1246-1250
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• 2011

This paper considers the container storage problem determining storage position of inbound containers in a container yard at a rail freight terminal. The objective of the problem is to minimize the total number of rehandles when storing/retrieving containers onto/from stacks in the yard. Rehandle implies the temporary removal from and placement back onto the stack to retrieval a target container. In order to solve the problem, we formulate the problem as a binary integer program.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.797-820
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• 2019

For every tree T, we introduce a topological invariant, called the T-cross-index, for connected graphs. The T-cross-index of a graph is a non-negative integer or infinity according to whether T is a tree basis of the graph or not. It is shown how this cross-index is independent of the other topological invariants of connected graphs, such as the Euler characteristic, the crossing number and the genus.

• 대한산업공학회지
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• 제10권1호
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• pp.3-10
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• 1984

A materials acquisition planning (MAP) problem that involves the determination of how much to order of a number of different items from a number of different suppliers is considered. This particular problem is modelled as a nonlinear mixed integer programming problem. A solution procedure based upon the partition of variables is developed to handle the MAP problem. This solution procedure utilizes a modified Hooke-Jeeves Pattern Search procedure along with a linear programming simplex algorithm. An example problem is presented and the results of applying the suggested solution procedure to this problem are reported.

• East Asian mathematical journal
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• 제28권2호
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• 한국수학교육학회지시리즈A:수학교육
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• 제15권1호
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• pp.18-21
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• 1976

Lagrange proved that any positive integer is the sum of at most four squares. We consider a elliptic function f$_{\alpha}$(v│$\tau$) of periods 1. $\tau$ derived from $\theta$-functions. From the important number-theoretical interpretation (equation omitted) we obtain $A_4$(n) the number of representations entations of n as a sum of 4-squares.m of 4-squares.

• 대한수학회보
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• 제59권5호
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• pp.1279-1287
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• 2022

A partition of n is complete if every positive integer from 1 to n can be represented by the sum of its parts. The concept of complete partitions has been extended in several ways. In this paper, we consider the number of k-relaxed r-complete partitions of n and the number of double-complete partitions of n.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.187-198
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• 2022

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer n. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic n-roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for n = 16, 18 support the results.

• 한국인터넷방송통신학회논문지
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• 제12권5호
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• pp.185-189
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• 2012

큰 반소수 n=pq의 소인수 p,q를 직접 찾는 것은 현실적으로 거의 불가능하여 대부분의 소인수분해 알고리즘은 $a^2{\equiv}b^2$(mod n)의 제곱합동을 찾아 p=GCD(a-b,n),q=GCD(a+b,n)의 소인수를 찾는 간접 방법을 적용하고 있다. 제곱합동 a,b을 찾는 다양한 방법이 제안되었지만 100자리 이상인 RSA 수에 대해서는 적용이 쉽지 않다. 본 논문에서는 $xa={\lceil}\sqrt{zn}{\rceil}\;or\;{\lceil}\sqrt{zn}{\rceil}+z+z=1,2,{\cdots}$로 설정하고 $(xa)^2{\equiv}(yb)^2$(mod n)을 찾는 간단한 방법을 제안한다. 제안된 알고리즘은 19 자리 수 까지는 제곱합동을 빠르게 찾는데 성공하였으나 39 자리 수에 대해서는 실패하였다.