• Journal for History of Mathematics
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• v.21 no.3
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• pp.67-96
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• 2008

In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.7
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• pp.1289-1294
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• 2010

In this paper, a new discrete integral static output feedback variable structure controller based on the a new integral dynamic-type sliding surface and output feedback discrete version of the disturbance observer is suggested for the control of uncertain linear systems. The reaching phase is completely removed by introducing a new proposed integral dynamic-type sliding surface. The output feedback discrete version of disturbance observer is presented for effective compensation of uncertainties and disturbance. A corresponding control with disturbance compensation is selected to guarantee the quasi sliding mode on the predetermined integral dynamic-type sliding surface for guaranteeing the designed output in the integral dynamic-type sliding surface from any initial condition for all the parameter variations and disturbances. Using discrete Lyapunov function, the closed loop stability and the existence condition of the quasi sliding mode is proved. Finally, an illustrative example is presented to show the effectiveness of the algorithm.

• Nuclear Engineering and Technology
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• v.53 no.8
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• pp.2556-2563
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• 2021

Metaheuristic algorithms can work well in solving or optimizing problems, especially those that require approximation or do not have a good analytical solution. Particle swarm optimization (PSO) is one of these algorithms. The response quality of these algorithms depends on the objective function and its regulated parameters. The nonlinear nature of the pressurized light-water nuclear reactor (PWR) dynamics is a significant target for PSO. The two-point kinetics model of this type of reactor is used because of fission products properties. The proportional-integral-derivative (PID) controller is intended to control the power level of the PWR at a short-time transient. The absolute error (IAE), integral of square error (ISE), integral of time-absolute error (ITAE), and integral of time-square error (ITSE) objective functions have been used as performance indexes to tune the PID gains with PSO. The optimization results with each of them are evaluated with the number of function evaluations (NFE). All performance indexes achieve good results with differences in the rate of over/under-shoot or convergence rate of the cost function, in the desired time domain.

• Journal of Oral Medicine and Pain
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• v.25 no.1
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• pp.87-97
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• 2000

This study was performed to investigate the effects of repetitive mandibular opening movement and change of head posture on the vibration of temporomandibular(TM) joint. For this study, 23 patients with internal derangement of TM joint were selected. All they had clinically noticeable TM joint sound. Observation of the joint vibration were performed in four head postures, namely, natural head posture (NHP), forward head posture(FHP), upward head posture(UHP), and downward head posture(DHP). For recording of joint sound vibration, Sonopak of Biopak system(Bioresearch Inc., Milwaukee, USA) was used, The author could take results related to integral higher than 300Hz, integral lower than 300Hz, ratio of integral higher than 300Hz to integral lower than 300Hz, total integral which was sum of higher and lower integral, peak amplitude, and peak frequency in each opening movement, which was carried out three times in each head posture. Integral means amount of vibration. The data obtained were analysed by SPSS windows program and the results of this study were as follows : 1. In NHP, total integral in right TM joint was 5O.3Hz in the first opening, 67.9Hz in the second opening, and 74.0Hz in the third opening movement, bur there was no significant increase of total integral with repetitive opening movement. This finding was similar in left TM joint. Integral lower than 300Hz were higher than integral higher than 300Hz in almost every opening movement. 2. There was no significant difference of total integral between right and left side of TM joint, but there was a tendency of higher total integral in right TM joint than that in left TM joint except for results in DHP. 3. Peak amplitude in NHP ranged from 2.0 to 4.7, and peak frequency in NHP were 101.4-170.0Hz. And there was no consistent findings related to increase or decrease of these value according to repetitive opening in each head posture. 4. Change of head posture did not result any difference in integral, peak amplitude, and peak frequency. In conclusion, change of head posture and repetitive mandibular opening movement did not make any significant effect on the vibration of temporo-mandibular joint, especially, on total integral, peak amplitude, and peak frequency.

• School Mathematics
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• v.10 no.3
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• pp.375-399
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• 2008

Infinitesimal did not play an explicit role concerning definite integral in the textbook nowadays. But studies which investigate understanding of students on definite integral show that many students comprehend definite integral with infinitesimal. Formally infinitesimal is not taught at mathematics classroom, but many students identify definite integral as infinite sum of infinitesimals. This means that definite integral itself contains some structural elements that allow infinitesimal interpretation. In this study we investigate the role of infinitesimal In the historical development of partition-sum in definite integral, extract didactical issues concerning understanding of definite integral, and analyse Korean mathematics textbooks. Finally we propose some suggestions on the teaching of definite integral which contains the process of refinement intuition.

• Land and Housing Review
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• v.12 no.3
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• pp.97-108
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• 2021

In bridge abutment structures, lateral squeeze due to lateral stress of embankment placement and thermal movement of the bridge structure leads to failure of approach slabs, girders, and bridge bearings. Recently, GRS (Geosynthetic-Reinforced Soil) integral bridge has been proposed as a new countermeasure. The GRS integral bridge is a combining structure of a GRS retaining wall and an integral abutment bridge. In this study, numerical analyses which considered construction sequences and earthquake loading conditions are performed to compare the behaviors of conventional PSC (Pre-Stressed Concrete) girder bridge, traditional GRS integral bridge structure and GRS integral bridge with bracket structures (newly developed LH-type GRS integral bridge). The analysis results show that the GRS integral bridge with bracket structures is most stable compared with the others in an aspect of stress concentration and deformation on foundation ground including differential settlements between abutment and backfill. Furthermore, the GRS integral bridge with/without bracket structures was found to show the best performance in terms of seismic stability.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1781-1791
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• 1991

For the cracked plate under transient temperature distribution, J-integral is expressed in the form of line integral by using convolution integral. The J$_{1}$ integral is calculated for a through line center cracked steel plate under thermal and mechanical loading conditions and the calculated values are in good agreement with previous results. The effect of inertia term on the J$_{1}$ integral is not negligible for a glass but for a steel. For the glass plate, the rates of J$_{1}$ integral value to time increase if the values of material properties such as specific heat, thermal conductivity, thermal diffusivity and Young`s modulus as well as crack length and temperature difference in cracked edge increase.

• Proceedings of the KWS Conference
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• 2004.05a
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• pp.264-266
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• 2004

for the kぉ mechanics analysis of a crack in a weld of dissimilar steels, residual stress analysis and fracture analysis must be performed simultaneously. The standard definition of the J-integral leads to a path dependent value in the presence of a residual stress field. And unlike cracks in homogeneous materials, a bimaterial interface crack always induces both opening and shearing modes of stress in the vicinity of the crack tip. Therefore, it is necessary to develope a path independent J-integral definition for a crack in a residual stress field generated by welding of dissimilar steels. This paper addresses the modification of the Rice-J-integral to produce a path independent J-integral when residual stresses due to welding of dissimilar steels and external forces are present. The residual stress problem is heated as an initial stain problem and the J-integral proposed for this class of problems is used And a program which can evaluate the 1-integral for a crack in a weld of dissimialr steels is developed using proposed J-integral definition.

• Journal of Korean Society on Water Environment
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• v.21 no.4
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• pp.410-415
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• 2005

The main purpose of this study is to evaluate the characteristics of three sets of traditional control methods (proportional, integral, and proportional - integral controls) through lab-scale biological reactor experiments. An increase in proportional gain ($K_c$) resulted in reduced dissolved oxygen (DO) offset under proportional control. An increase in integral time ($T_i$) resulted in a slower response in DO concentration with less oscillation, but took longer to get to the set point. P-I control showed more stable and efficient control of DO and airflow rates compared to either proportional control or integral control. Developed P-I control system was successfully applied to lab-scale Sequencing Batch Reactor (SBR) for treating industrial wastewater with high organic strength.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.99-106
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• 2002

This paper presents an analytical investigation on the behavior of simple span integral abutment bridge. An integral abutment bridge is a simple span or multiple span continuous deck type bridge having the deck integral with the abutment wall. Although the temperature variation and earth pressure are the major attributor to the total stress in integral abutment bridge, the superstructure has been designed by modeling it as a simple or continuous beam In order to investigate the effect of temperature change and earth pressure on the superstructure of integral bridge, the simple span integral bridge is modeled as a plane frame element. Performing frame analysis, the variations of bending moment and axial force of superstructure due to the various loading combination are investigated with respect to the flexural rigidity of piles, and the bending moment and axial force obtained by frame analysis are compared with the maximum bending moment obtained by conventional design method and initial prestressing force respectively.