• Journal of the Korean Society for Aviation and Aeronautics
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• v.31 no.2
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• pp.55-65
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• 2023

Due to extreme urbanization, ground transportation in the city center is saturated, and problems such as the lack of expansion infrastructure and traffic congestion increase social costs. To solve this problem, a 3D mobility platform, Urban Air Mobility (UAM), has emerged as a new alternative. A vertiport is a physical space that conducts a similar role to an airport terminal. Vertiport consists of take-off and landing facilities (TLOF, Touchdown and Lift-Off area), space for boarding and disembarking from UAM aircraft (gates), taxiways, and passenger terminals. The type of vertiport (structure, number of facilities) and concept of operations are key variables that determine the number of UAM aircraft that can be accommodated per hour. In this study, a capacity calculation method was presented using an optimization technique (Deterministic Integer Linear Programming). The absolute capacity of the vertiport was calculated using an optimization technique, and a sensitivity analysis was also performed.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.751-763
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• 2015

Let ${\alpha}$ be a positive integer, and let $p_1$, $p_2$ be two distinct prime numbers with $p_1$ < $p_2$. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form $2^{\alpha}p_1p_2$ and $2^{\alpha}p_1^2p_2$, and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture's prime number pair. Another kind has the form $p_1=2^{{\alpha}+1}-1$ and $p_2={\frac{p^2_1+p_1+1}{3}}$, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.

• IE interfaces
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• v.22 no.1
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• pp.38-43
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• 2009

This paper deals with two most important problems, from both practical and theoretical standpoints, arising when building the ships in N different docks. Such docks have become core components of modern ship construction. One problem is to minimize the number of building docks in the shipyard, while the other is to keep the usage rate of resources fed into docks as constant as possible. In this paper the combined problem is formulated as a single-integer programming model. The LP-relaxation of this model is solved by column-generation techniques. Practical applications of this formulation are also discussed.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.89-96
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• 2009

In this article, we show a generalization of Clement's theorem on the pair of primes. For any integers n and k, integers n and n + 2k are a pair of primes if and only if 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) whenever (n, (2k)!) = (n + 2k, (2k)!) = 1. Especially, n or n + 2k is a composite number, a pair (n, n + 2k), for which 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) is called a pair of pseudoprimes for any positive integer k. We have pairs of pseudorimes (n, n + 2k) with $n{\leq}5{\times}10^4$ for each positive integer $k(4{\leq}k{\leq}10)$.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.5 no.1
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• pp.37-42
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• 2006

A reversible audio watermarking algorithm is presented in this paper. This algorithm transforms the audio signal with the integer wavelet transform first in order to enhance the correlation between neighbor audio samples. Audio signal has low correlation between neighbor samples, which makes it difficult to apply difference expansion scheme. Second, a novel difference expansion scheme is used to embed more data by reducing the size of location map. Therefore, the difference expansion scheme used in this paper theoretically secures high embedding capacity under low perceptual distortion. Experiments show that this scheme can hide large number of information bits and keeps high perceptual quality.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.3
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• pp.17-33
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• 2000

We consider the Steiner tree packing problem. For a given undirected graph G =(V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets(nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. The model contains exponential number of variables, but the problem can be solved using a polynomial time column generation procedure. We test the algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.5
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• pp.205-210
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• 2007

The integration method of binary and real encoding in genetic algorithm is proposed to deal with design variables of various types in gear drive design. The method is applied to optimum design of multi-stage gear drive. Integer and Discrete type design variables represent the number of teeth and module, and continuous type design variables represent face width, helix angle and addendum modification factor etc. The proposed genetic algorithm is applied for the gear ratio optimization and the volume optimization(minimization) of multi-stage geared motor which is used in field. In result, the proposed design optimization method shows an effectiveness in optimum design process and the new design has a better results compared with the existing design.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.2
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• pp.74-81
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• 2006

In this paper, we deal with the separation of data by concurrently determined, piecewise nonlinear discriminant functions. Toward the end, we develop a new $l_1$-distance norm error metric and cast the problem as a mixed 0-1 integer and linear programming (MILP) model. Given a finite number of discriminant functions as an input, the proposed model considers the synergy as well as the individual role of the functions involved and implements a simplest nonlinear decision surface that best separates the data on hand. Hence, exploiting powerful MILP solvers, the model efficiently analyzes any given data set for its piecewise nonlinear separability. The classification of four sets of artificial data demonstrates the aforementioned strength of the proposed model. Classification results on five machine learning benchmark databases prove that the data separation via the proposed MILP model is an effective supervised learning methodology that compares quite favorably to well-established learning methodologies.

• Management Science and Financial Engineering
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• v.11 no.1
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• pp.63-78
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• 2005

Disassembly scheduling is the problem of determining the ordering and disassembly schedules of used or end-of-life products while satisfying the demand of their parts or components over a certain planning horizon. This paper considers the case of the assembly product structure for the cost-based objective of minimizing the sum of purchase, setup, inventory holding, and disassembly operation costs. To represent and solve the problem optimally, this paper presents an integer programming model, which is a reversed form of the multi-level lot sizing formulation. Computational experiments on an example derived from the literature and a number of randomly generated test problems are done and the results are reported.