• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.349-353
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.47-56
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• 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.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.745-757
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.155-160
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• 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.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.383-384
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• 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
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• v.15 no.1
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• pp.160-176
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• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9B
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• pp.1697-1703
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• 1999

In this paper, we propose the fast block matching algorithm with half pel accuracy using the lower bound of mean absolute difference (MAD) at search point of half pel accuracy motion estimation. The proposed method uses the lower bound of MAD at search point of half pel accuracy which calculated from MAD's at search points of integer pel accuracy. We can reduce the computational complexity by executing the block matching operation only at the necessary search point. The points are selected when the lower bound of MAD at that point is smaller than reference MAD of integer pel motion estimation. Experimental results show that the proposed method can reduce the computational complexity considerably and keeping the same performance with conventional method.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.25-36
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• 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
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• v.14 no.2
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• pp.45-66
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• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.21-25
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• 2009

In this paper, we study the problem to fit a piecewise-quadratic polynomial curve to points in the plane. The curve consists of quadratic polynomial segments and two points are connected by a segment. But it passes through a subset of points, and for the points not to be passed, the error between the curve and the points is estimated in $L^{\infty}$ metric. We consider two optimization problems for the above problem. One is to reduce the number of segments of the curve, given the allowed error, and the other is to reduce the error between the curve and the points, while the curve has the number of segments less than or equal to the given integer. For the number n of given points, we propose $O(n^2)$ algorithm for the former problem and $O(n^3)$ algorithm for the latter.