• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.385-390
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• 1996

Let X be a smooth projective threefold whose anticanonical division $-K_X$ is ample, i.e., Fano threefold. In this paper, we studied the linear system $$\mid$-nK_X$\mid$$ for a positive integer n. In Theorem 4, we studied the cases that $\-nK_X$\mid$$ has no base-points and the cases that $$\mid$-nK_X$\mid$$ generate the birational map. In Proposition 5, we studied the possible exceptional cases given in Theorem 4. Some results in this paper are already known, but we have gave brief proofs for those results.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.865-872
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• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1597-1617
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• 2017

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely many non-similar integer Sharygin triangles.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.189-199
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• 1994

This paper considers the covering network design problem (CNDP). In the CNDP, an undirected graph is given where nodes correspond to potential facility sites and arcs to potential links connecting facilities. The objective of the CNDP is to identify the least cost connected subgraph whose nodes cover the given demand points. The problem difines a demand point to be covered if some node in the selected graph is present within an appropriate distance from the demand point. We present an integer programming formulation for the problem and develop a dual-based solution procedure. The computational results for randomly generated test problems are also shown.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.227-236
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• 2020

A set {a₁, a₂,_…, a_m} of positive integers is called 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 torsion group of elliptic curve E_k constructed by Diophantine triple, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.28B no.5
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• pp.382-393
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• 1991

In this paper, we propose a method for recognizing printed Korean characters using the Preceding Layer Driven multi-layer perceptron. The new learning algorithm which assigns the weight values to an integer and makes use of the transfer function as the step function was presented to design the hardware. We obtained 522 Korean character-image as an experimental object through scanner with 600DPI resolution. The preprocessing for feature extraction of Korean character is the separation of individual character, noise elimination smoothing, thinnig, edge point extraction, branch point extraction, and stroke segmentation. The used feature data are the number of edge points and their shapes, the number of branch points, and the number of strokes with 8 directions.

• Journal of Korean Institute of Industrial Engineers
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• v.1 no.2
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• pp.39-49
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• 1975

The problem treated is that of locating distribution centers(depot) in a network, so as to minimize the total cost which is the sum of transportation cost, (from factory to centers and from centers to demand points), construction cost, inventory cost and traffic increasing cost. This problem is mathematically an integer program and a non-linear model. This study avoids various inefficient aspects, which many studies have shown, by introducing a matrix notation, node and link function. An algorithm, for determining the optimal location of distribution center which has zone in which demand points are located at some node of a network, is presented. Finally this paper describes a numerical example and discusses its results.

• Journal of Korea Multimedia Society
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• v.22 no.2
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• pp.210-224
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• 2019

Given a positive integer k as input, a spatial preference query finds the k best data objects based on the scores (e.g., qualities) of feature objects in their spatial neighborhoods. Several solutions have been proposed for spatial preference queries in Euclidean space. A few algorithms study spatial preference queries in undirected spatial networks where each edge is undirected and the distance between two points is the length of the shortest path connecting them. However, spatial preference queries have not been thoroughly investigated in directed spatial networks where each edge has a particular orientation that makes the distance between two points noncommutative. Therefore, in this study, we present a new method called ALPS+ for processing spatial preference queries in directed spatial networks. We conduct extensive experiments with different setups to demonstrate the superiority of ALPS+ over conventional solutions.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.2
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• pp.709-730
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• 2017

To address the challenge of unprecedented growth in mobile data traffic, ultra-dense network deployment is a cost efficient solution to offload the traffic over some small cells. The overlapped coverage areas of small cells create more than one candidate access points for one mobile user. Signal strength based user association in IEEE 802.11 results in a significantly unbalanced load distribution among access points. However, the effective bandwidth demand of each user actually differs vastly due to their different preferences for mobile applications. In this paper, we formulate a set of non-linear integer programming models for joint user association control and user demand guarantee problem. In this model, we are trying to maximize the system capacity and guarantee the effective bandwidth demand for each user by soft-association control with a software defined network controller. With the fact of NP-hard complexity of non-linear integer programming solver, we propose a Kernighan Lin Algorithm based graph-partitioning method for a large-scale network. Finally, we evaluated the performance of the proposed algorithm for the edge users with heterogeneous bandwidth demands and mobility scenarios. Simulation results show that the proposed adaptive soft-association control can achieve a better performance than the other two and improves the individual quality of user experience with a little price on system throughput.