• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.93-111
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• 1993

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.1-14
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• 2002

The paper is analyzed the crisis of mathematics for paradoxes in mathematics, also its process of conquest in the history of mathematics. We have found that various views of the infinity and infinitesimal in the history of mathematics. This study be tried to find out the process development of mathematics on passing through a crisis conquest of mathematics for contradictions in the hi story of mathematics.

• Korean journal of aerospace and environmental medicine
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• v.29 no.2
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• pp.80-82
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• 2019

• Wind and Structures
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• v.12 no.4
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• pp.313-332
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• 2009

This paper numerically and experimentally investigates the control performance of the active mass damper (AMD) systems in a 26-story high-rise building in use. This is the first full-scale application of the AMD system for suppressing the wind-induced vibration of a building structure in Korea. In addition, the AMD system was installed on top of the building already in use, which may be the world's first implementation case. In order to simultaneously mitigate the transverse-torsional coupled vibration of the building, two AMD systems were applied. Moreover, the H-infinity control algorithm has been developed to utilize the maximum capacity of the AMD system. From the results of numerical simulation using the wind load obtained from the wind tunnel tests, it was found that the maximum acceleration responses of the building were reduced significantly. Moreover, the control performance of the installed AMD system was examined by carrying out the free and forced vibration tests. The acceleration responses on top of the building in the controlled case measured under strong wind loads were compared with those in the uncontrolled case numerically simulated by using the wind load deduced from the measured data and a structural model of the building. It is demonstrated that the AMD system shows good control performance in reducing the building accelerations.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.05a
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• pp.199-202
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• 2002

Interfacial properties and electrical sensing for fiber fracture in carbon and SiC fibers/epoxy composites were investigated by the electrical resistance measurement and fragmentation test. As fiber-embedded angle increased, interfacial shear strength (IFSS) of two-type fiber composites decreased, and the elapsed time was long to the infinity in electrical resistivity. The initial slope of electrical resistivity increased rapidly to the infinity at higher angle, whereas electrical resistivity increased gradually at small angle. Furthermore, both fiber composites with small embedded angle showed a fully-developed stress whitening pattern, whereas both composites with higher embedded angle exhibited a less developed stress whitening pattern. As embedded angle decreased, the gap between the fragments increased and the debonded length was wider for both fiber composites. Electro-micromechanical technique can be a feasible nondestructive evaluation to measure interfacial sensing properties depending on the fiber-embedded angle in conductive fiber reinforced composites.

• International Journal of Highway Engineering
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• v.9 no.1 s.31
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• pp.39-46
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• 2007

Different backcalculation results for the same material properties are caused by different structural geometry. In this paper, based on real simulation results for typical pavement systems using 3-dimensional FE models, modified AREA graphs are proposed to graphically backcalculate modulus of elasticity of slab and subgrade based on center deflection and AREA. In modified graph for single infinity slab models, deflection and AREA are increased in deeper depth to bedrock. But, effects of depth to bedrock more than 4.0 meters on backcalculation results are negligible. And, center deflection and AREA generated from multifinite slab models are larger than those of single infinity slab models with same depth to bedrock.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1520-1529
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• 2013

In this paper, we propose and assess the performance of "H infinity filter ($H_{\infty}$, HIF)" and "cost reference particle filter (CRPF)" in the problem of tracking a target based on the measurements of the range and the bearing of the target. HIF and CRPF have the common advantageous feature that we do not need to know the noise statistics of the problem in their applications. The performance of the extended Kalman filter (EKF) is also compared with that of the proposed filters, but the noise information is perfectly known for the applications of the EKF. Simulation results show that CRPF outperforms HIF, and is more robust because the tracking of HIF diverges sometimes, particularly when the target track is highly nonlinear. Interestingly, when the tracking of HIF diverges, the tracking of the EKF also tends to deviate significantly from the true track for the same target track. Therefore, CRPF is very effective and appropriate approach to the problems of highly nonlinear model, especially when the noise statistics are unknown. Nonetheless, HIF also can be applied to the problem of timevarying state estimation as the EKF, particularly for the case when the noise statistcs are unknown. This paper provides a good example of how to apply CRPF and HIF to the estimation of dynamically varying and nonlinearly modeled states with unknown noise statistics.

• Management Science and Financial Engineering
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• v.13 no.2
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• pp.47-77
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• 2007

This paper considers a scheduling problem where a customer orders multiple products(jobs) from a production facility. The objective is to minimize the sum of the order(batch) completion times. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. Although each job has a unique processing time, we consider the case where batch processing times are identical. This simplification allows us to develop heuristics with improved performance bounds. This problem was motivated by a real world problem encountered by foreign electronics manufacturers. We first establish the complexity of the problem. For the two parallel machine case, we introduce two simple but intuitive heuristics, and find their worst case relative error bounds. One bound is tight and the other bound goes to 1 as the number of orders goes to infinity. However, neither heuristic is superior for all instances. We extend one of the heuristics to an arbitrary number of parallel machines. For a fixed number of parallel machines, we find a worst case bound which goes to 1 as the number of orders goes to infinity. Then, a tighter bound is found for the three parallel machine case. Finally, the heuristics are empirically evaluated.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.249-283
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• 2008

The purpose of the study was to investigate the definitions and concept images of Infinity and limits for high school students. In addition, the error patterns of the students were also investigated. The participants were 121 girls highschool students and survey method was used to co11ed data. Only 11 % and 5% of the participants revealed the definitions similar to the standard textbook definitions in limits of infinite sequences and infinite series respectively. The participants showed 6 types of error patterns and had more difficulties in understanding and applying concepts and properties of infinite series than those of infinite sequences.