• 대한수학회지
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• 제41권3호
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• 한국군사과학기술학회지
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• 제24권5호
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• pp.475-481
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• 2021

The on-board processor of satellite Synthetic Aperture Radar(SAR) digitizes the back-scattered echoes and transmits them to the ground. As satellite SAR image of various operating conditions including broadband and high resolution is required, an enormous amount of SAR data is generated. Decimation filter is used for data compression to improve the transmission efficiency of these data. Decimation filter is implemented with the FIR(Finite Impulse Response) filter and here, the decimation ratio and tap length are constrained by resource requirements of FPGA used for implementation. This paper suggests to use a non-integer ratio decimation filter in order to optimize the data transmission efficiency. Also, it proposes a filter design method that remarkably reduces the resource constraints of the FPGA in-use via applying a polyphase filter structure. The required resources for implementing the proposed filter is analysed in this paper.

• 경영과학
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• 제32권4호
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• pp.109-133
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• 2015

This paper considers the allocation and engagement scheduling of air defense missiles by using MIP (mixed integer programming). Specifically, it focuses on developing a realistic MIP model for a real battle situation where multiple enemy missiles are headed toward valuable defended assets and there exist multiple air defense missiles to counteract the threats. In addition to the conventional objective such as the minimization of surviving target value, the maximization of total intercept altitude is introduced as a new objective. The intercept altitude of incoming missiles is important in order to minimize damages from debris of the intercepted missiles and moreover it can be critical if the enemy warhead contains an atomic or chemical bomb. The concept of so called the time window is used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. Lastly, the model is extended to simulate the situation where the guidance radar, which guides a defense missile to its target, has the maximum guidance capacity. The initial mathematical model developed contains several non-linear constraints and a non-linear objective function. Hence, the linearization of those terms is performed before it is solved by a commercially available software. Then to thoroughly examine the MIP model, the model is empirically evaluated with several test problems. Specifically, the models with different objective functions are compared and several battle scenarios are generated to evaluate performance of the models including the extended one. The results indicate that the new model consistently presents better and more realistic results than the compared models.

• 충청수학회지
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• 제28권4호
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• pp.583-590
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• 2015

This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

• 대한수학회지
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• 제56권1호
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• 대한산업공학회지
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• 제38권2호
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• pp.116-124
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• 2012

This paper concerns a joint replenishment problem for a single buyer who sells multiple types of items to end-customers. The buyer periodically replenishes the inventory of each item to a preset order-up-to-level to satisfy the end customers' demands, which may be non-stationary. A joint replenishment policy characterized by variable order-up-to-levels is proposed for the buyer who wishes to minimize the expected cost of operating the retail system. The proposed policy starts each period by calculating the expected cost of ordering and not ordering action based on the information of the current inventory position and forecasted demand for the upcoming period. It then takes advantage of an integer programming model to get a cost effective joint replenishment plan. Computer experiment was performed to test efficiency of the proposed policy. When compared with the most efficient policy currently available, our policy showed a considerable cost savings especially for the problems having non-stationary demands.

• Industrial Engineering and Management Systems
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• 제6권2호
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• pp.136-145
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• 2007

The selection of suppliers and the determination of order quantities to be placed with those suppliers are important decisions in a supply chain. In this research, a non-linear mixed integer programming model is presented to select suppliers and determine the order quantities. The model considers the purchasing cost which takes into account quantity discount, the cost of transportation, the fixed cost for establishing suppliers, the cost for holding inventory, and the cost of receiving poor quality parts. The capacity constraints for suppliers, quality and lead-time requirements for the parts are also taken into account in the model. Since the purchasing cost, which is a decreasing step function of order quantities, introduces discontinuities to the non-linear objective function, it is not easy to employ traditional optimization methods. Thus, a heuristic algorithm, called particle swarm optimization (PSO), is used to find the (near) optimal solution. However, PSO usually generates initial solutions randomly. To improve the PSO solution quality, a heuristic procedure is proposed to find an initial solution based on the average unit cost including transportation, purchasing, inventory, and poor quality part cost. The results show that PSO with the proposed initial solution heuristic provides better solutions than those with PSO algorithm only.

• 대한수학회보
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• 제52권1호
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• pp.239-246
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• 2015

If for every elements x and y of an associative algebraic structure (S, ${\cdot}$) there exists a positive integer r such that $ab=b^ra$, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.

• Industrial Engineering and Management Systems
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• 제11권2호
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• pp.155-164
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• 2012

As the global market becomes more competitive, manufacturing industries face relentless pressure caused by a growing tendency of greater varieties of products, shorter manufacturing cycles and more sophisticated customer requirements. Efficient and effective supplier selection and order allocation decisions are, therefore, important decisions for a manufacturer to ensure stable material flows in a highly competitive supply chain, in particular, when customers are willing to accept products with less desirable product attributes (e.g., color, delivery date) for economic reasons. This paper attempts to solve optimally the challenging problem of supplier selection and order allocation, taking into consideration the customer flexibility for a manufacturer producing multi-products to satisfy the customers' demands in a multi period planning horizon. A new mixed integer programming model is developed to describe the behavior of the supply chain. The objective is to maximize the manufacturer's total profit subject to various operating constraints of the supply chain. Due to the complexity and non-deterministic polynomial-time (NP)-hard nature of the problem, an improved genetic approach is proposed to solve the problem optimally. This approach differs from a canonical genetic algorithm in three aspects: a new selection method to reduce the chance of premature convergence and two problem-specific repair heuristics to guarantee feasibility of the solutions. The results of applying the proposed approach to solve a set of randomly generated test problems clearly demonstrate its excellent performance. When compared with applying the canonical genetic algorithm to locate optimal solutions, the average improvement in the solution quality amounts to as high as ten percent.

• 대한산업공학회지
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• 제25권1호
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• pp.47-55
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• 1999

This paper develops an efficient heuristic algorithm for scheduling workforce level that can accommodate all the requested maintenance jobs. Each job has its own release and due dates as well as man-day requirement, and must be scheduled in a non-interrupted time interval, namely, without preemption. Duration of each job is not fixed, but to be determined within given specific range. The objective is to minimize workforce level to complete all the requested maintenance jobs. We show that the problem can be seen as a variant of the two-dimensional bin-packing problem with some additional constraints. A non-linear mixed integer programming model for the problem is developed, and an efficient heuristic algorithm based on bin-packing algorithms is proposed. In order to evaluate goodness of the solution obtained from the proposed algorithm, a scheme for getting a good lower bound for the optimum solution is presented and analyzed. The computational experiment shows that the proposed algorithm performs quite satisfactorily.