• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.349-353
• /
• 2008

Using the recently developed ABS algorithm for solving linear Diophantine equations we introduce an algorithm for solving a system of m linear integer inequalities in n variables, m $\leq$ n, with full rank coefficient matrix. We apply this result to solve linear integer programming problems with m $\leq$ n inequalities.

• 충청수학회지
• /
• 제15권2호
• /
• pp.47-56
• /
• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• 대한수학회논문집
• /
• 제35권3호
• /
• pp.745-757
• /
• 2020

A set {a₁, a₂, …, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves E_k constructed by a Diophantine triple {F_2k, F_2k+2, 4F_2k+1F_2k+2F_2k+3}, and find all integer points on the elliptic curve under assumption that rank(E_k(ℚ)) = 2.

• 대한수학회보
• /
• 제23권2호
• /
• pp.155-160
• /
• 1986

Let X be a closed convex subset of a Banach space B and T:X.rarw.X a lipschitzian rotative map, i.e., such that ∥Tx-Ty∥.leq.k∥x-y∥ and ∥T$^{n}$ x-x∥.leq.a∥Tx-x∥ for some real k, a and an integer n>a. We denote by .PHI. (n, a, k, X) the family of all such maps. In [3], [4], K. Goebel and M. Koter obtained results concerning the existence of fixed points of T depending on k, a and n. In the present paper, the main results of [3], [4] are so strengthened that some information concerning the geometric estimations of fixed points are given.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2007년도 하계종합학술대회 논문집
• /
• pp.383-384
• /
• 2007

In this paper, we propose the new and simple method for sub-pixel block search algorithm by only using integer-pixel for motion estimation and compensation. In many papers, the fast search block match algorithms based on TSS have been proposed. However, these methods could be achieved a little reduction of the computational complexity. All of searching points by 1/4-pixel have own predicted integer-pixel SAD array. Therefor, if we know initial nine SAD values by integer, which is on the searching area of the reference frame, then we can find optimal searching point by 1/4-pixel, directly.

• Journal of Power Electronics
• /
• 제15권1호
• /
• pp.160-176
• /
• 2015

This paper presents a method of designing optimal integer- and fractional-order proportional-integral-derivative (FOPID) controllers for a boost converter to gain a set of favorable characteristics at various operating points. A Pareto-based multi-objective optimization approach called strength Pareto evolutionary algorithm (SPEA) is used to obtain fast and low overshoot start-up and dynamic responses and switching stability. The optimization approach generates a set of optimal gains called Pareto set, which corresponds to a Pareto front. The Pareto front is a set of optimal results for objective functions. These results provide designers with a trade-off look-up table, in which they can easily choose any of the optimal gains based on design requirements. The SPEA also overcomes the difficulties of tuning the FOPID controller, which is an extension to the classic integer-order PID controllers and potentially promises better results. The proposed optimized FOPID controller provides an excellent start-up response and the desired dynamic response. This paper presents a detailed comparison of the optimum integer- and the fractional-order PID controllers. Extensive simulation and experimental results prove the superiority of the proposed design methodology to achieve a wide set of desired technical goals.

• 한국통신학회논문지
• /
• 제24권9B호
• /
• pp.1697-1703
• /
• 1999

본 논문에서는 반화소 위치에서의 평균 절대 오차 (mean absolute difference; MAD)의 최소 범위를 이용한 고속 반화소 단위의 블록 정합 알고리듬을 제안한다. 제안한 방법에서는 반화소 단위의 MAD의 최소 범위를 화소 단위의 움직임 추정으로 얻어진 MAD들을 이용하여 구한 후, 반화소 단위의 MAD의 최소 범위가 화소 단위의 움직임 추정으로 구한 기준 MAD보다 작은 탐색점에 대해서만 블록 정합을 행하였다. 제안한 방법의 성능을 평가하기 위한 컴퓨터 모의 실험결과로부터 제안한 방법이 기존의 방법과 동일한 성능을 유지하면서도 많은 계산량을 줄일 수 있음을 확인할 수 있었다.

• 산업경영시스템학회지
• /
• 제20권43호
• /
• pp.25-36
• /
• 1997

The purpose of this paper is to structure a new integrated model that can minimize the total cost for the transportation and inventory systems between m origin points, where origin i has a supply of a commodity, such as distribution centers or warehouses, and n destination points, where destination j requires the commodity. In this case, demands of the destination points are assumed random variables which have a known probability distribution. We will find optimal distribution centers which transport the commodity to the destination points and suggest optimal inventory policy to the selected distribution center which find the optimal pair $$ and safety stock level that minimize total cost with back-ordered case. This new model is formulated as a 0-1 nonlinear integer programming problem. To solve the problem, this paper proposes heuristic computational procedures and program and provides numerical examples.

• Management Science and Financial Engineering
• /
• 제14권2호
• /
• pp.45-66
• /
• 2008

Refuse collection, one of important elements in reverse logistics, is an activity rendering recyclables or wastes and moving them to some points where further treatment is required. Among various decisions in the collection activity, we focus on network design, which is the problem of locating collection points as well as allocating refuses at demand points to collection points while satisfying the capacity restriction at each collection point. Here, the collection point is the place where recyclables or wastes near the point are gathered, and locating the collection points is done by selecting them from a given set of potential sites. The objective is to minimize the sum of fixed costs to open collection points and transportation costs to move refuses from demand points to collection points. An integer programming model is developed to represent the problem mathematically and due to the complexity of the problem, two types of heuristics, one with simultaneous and the others with separate location and allocation, are suggested. Computational experiments were done on test problems up to 500 potential sites, and the results are reported. In particular, some heuristics gave near optimal solutions for small-size test problems, i.e., 2% gaps in average from the optimal solution values.

• 한국정보과학회논문지:시스템및이론
• /
• 제36권1호
• /
• pp.21-25
• /
• 2009

본 논문에서 우리는 평면상에 점들이 주어지는 경우에, 조각적 이차 다항식 곡선으로 맞추는 문제를 다룬다. 곡선은 이차 다항식 선분들로 이루어지고, 하나의 선분은 두 점 사이를 연결한다. 하지만 이 곡선은 점들의 부분집합만을 지나고, 지나지 못하는 점들에 대해서는 $L^{\infty}$거리로 에러를 측정한다. 이 문제에 대해서 우리는 두 가지 최적화 문제를 생각한다. 첫째로 허용 가능한 에러의 범위가 주어지고, 곡선 선분의 개수를 줄이는 문제이고, 둘째로 선분의 개수가 주어지고, 에러를 줄이는 문제이다. 주어진 점들의 개수 n에 대해서, 우리는 첫번째 문제에 대한 $O(n^2)$ 알고리즘과 두번째 문제에 대한 $O(n^3)$ 알고리즘을 제안한다.