• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.221-226
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• 2015

The natural projection of a parameter lower (upper) distribution set for a self-similar measure on a self-similar set satisfying the open set condition is the cylindrical lower or upper local dimension set for the Legendre self-similarmeasure which is derived from the self-similar measure and the self-similar set.

• Korean Management Science Review
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• v.22 no.1
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• pp.167-178
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• 2005

The 2DBPP(Two-Dimensional Bin Packing Problem) is a problem of packing each item into a bin so that no two items overlap and the number of required bins is minimized under the set of rectangular items which may not be rotated and an unlimited number of identical .rectangular bins. The 2DBPP is strongly NP-hard and finds many practical applications in industry. In this paper we discuss a tabu search approach which includes tabu list, intensifying and diversification Strategies. The HNFDH(Hybrid Next Fit Decreasing Height) algorithm is used as an internal algorithm. We find that use of the proper parameter and function such as maximum number of tabu list and space utilization function yields a good solution in a reduced time. We present a tabu search algorithm and its performance through extensive computational experiments.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.1-5
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• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Design & Manufacturing
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• v.14 no.1
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• pp.1-7
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• 2020

In this study, the variation of the shrinkage in the thickness direction of the molded parts according to the gate size of the polymer core fabricated through the 3D printer using the SLS method was studied. The polymer cores are laser sintered and the powder material is nylon base PA2200. The polymer cores have lower heat transfer rate and rigidity than the metal core due to the characteristics of the material. Therefore, the injection molding test conditions are set to minimize the deformation of the core during the injection process. The resin used in the injection molding test is a PP material. The packing condition was set to 80, 90 and 100% of the maximum injection pressure for each gate size. The runner diameter used was ∅3mm, and the gates were fabricated in semicircle shapes with cross sections 1, 2, and 3 ㎟, respectively. Thickness measurement was performed for 10 points at 2.5 mm intervals from the point 2.5 mm away from the gate, and the shrinkage to thickness was measured for each point. The shrinkage rate according to the gate size tends to decrease as the cross-sectional area decreases as the maximum injection pressure increases. The average thickness shrinkage rate was close to 0% when the packing pressure was 90% for the gate area of 1mm2. When the holding pressure was set to 100%, the shrinkage was found to decrease by 3% from the standard dimension due to the over-packing phenomenon. Therefore, the smaller the gate, the more closely the molded dimensions can be molded due to the high pressure generation. It was confirmed that precise packing process control is necessary because over-packing phenomenon may occur.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.245-250
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• 2009

We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a bi-Lipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.271-283
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• 2018

In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 118, (2008), pp. 273-279.). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.733-738
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• 2008

Using an information of dimensions of divergence points, we give full information of dimensions of the completely decomposed class of the lower(upper) distribution sets of a self-similar Cantor set. Further using a relationship between the distribution sets and the subsets generated by the lower(upper) local dimensions of a self-similar measure, we give full information of dimensions of the subsets by the local dimensions.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.503-510
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• 2005

Let $\left{K_{\alpha}\right}_{{\alpha}{\in}{\mathbb{R}}}$ be the multifractal spectrums of a perturbed Cantor set K. We find the set of values ${\alpha}$ of nonempty set $K_{\alpha}$ by using the Birkhoff ergodic theorem. And we also show that such $K_{\alpha}$ is a fractal set in the sense of Taylor [12].

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.402-408
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• 2002

Multicast technology allows the transmission of data from one source node to a selected group of destination nodes. Multicast routes typically use trees, called multicast routing trees, to minimize resource usage such as cost and bandwidth by sharing links. Moreover, the quality of service (QoS) is satisfied by distributing data along a path haying no more than a given number of arcs between the root node of a session and a terminal node of it in the routing tree. Thus, a multicast routing tree for a session can be represented as a hop constrained Steiner tree. In this paper, we consider the hop-constrained multicast route packing problem with bandwidth reservation. Given a set of multicast sessions, each of which has a hop limit constraint and a required bandwidth, the problem is to determine a set of multicast routing trees in an arc-capacitated network to minimize cost. We propose an integer programming formulation of the problem and an algorithm to solve it. An efficient column generation technique to solve the linear programming relaxation is proposed, and a modified cover inequality is used to strengthen the integer programming formulation.

• Design & Manufacturing
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• v.14 no.3
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• pp.8-16
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• 2020

In this study, the vibration signal of the mold was measured and analyzed to monitoring the process time and characteristics during injection molding. A 5 inch light guide plate mold was used to injection molding and the vibration signal was measured by MPU6050 acceleration sensor module attached the surface of fixed mold base. Conditions except for injection speed and packing pressure were set to the same value and the change of the vibration signal of the mold according to injection speed and packing pressure was analyzed. As a result, the vibration signal had a large change at three points: "Injection start", "V/P switchover", and "Packing end". The time difference between "injection start" and "V/P switchover" means the injection time in the injection molding process, and the time difference between "V/P switchover" and "Packing end" means the packing time. When the injection time and packing time obtained from the vibration signal of the mold are compared with the time recorded in the injection molding machine, the error of the injection time was 2.19±0.69% and the error of the packing time was 1.39±0.83%, which was the same level as the actual value. Additionally, the amplitude at the time of "injection start" increased as the injection speed increased. In "V/P switchover", the amplitude tended to be proportional to the pressure difference between the maximum injection pressure and the packing pressure and the amplitude at the "packing end" tended to the pressure difference between the packing pressure and the back pressure. Therefore, based on the result of this study, the injection time and packing time of each cycle can be monitored by measuring the vibration signal of the mold. Also, it was confirmed that the level and trend of process variables such as the injection speed, maximum injection pressure, and packing pressure can be evaluated as the change of the mold vibration during injection molding.