• 한국수학사학회지
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• 제29권2호
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• pp.103-143
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• 2016

We study the topics of the lectures in Analysis in 19th century at Ecole Polytechnique of France through the lists of the contents of the Cours d'Analyse by Cauchy, Sturm and Jordan, respectively and also we show how they stated the definitions of functions, continuity and limits in their Cours d'Analyse. Through this, we see that in 19th century, in France, analysis included differential and integral calculus, differential equations, variations and applications of these to differential geometry, and it was far from today's mathematical analysis.

• East Asian mathematical journal
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• 제36권1호
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권3호
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• pp.217-234
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• 2015

In this tutorial the theoretical background of LQ optimal guidance is reviewed, starting from calculus of variations. LQ optimal control is then introduced and applied to missile guidance to obtain the basic form of LQ optimal guidance laws. Extension of LQ optimal guidance methodology for handling weighted cost function, dynamic lag associated with the missile dynamics and the autopilot, constrained impact angle, and constrained impact time is also described with a brief discussion on the asymptotic properties of the optimal guidance laws. Furthermore, an introduction to polynomial guidance and generalized impactangle-control guidance, which are closed related with LQ optimal guidance, is provided to demonstrate the current status of missile guidance techniques.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2006년도 Proceedings of ISRS 2006 PORSEC Volume II
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• pp.610-614
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• 2006

In this paper the advanced method of geodesic active contours was developed for the task of building detection from aerial and satellite images. Automatic extraction of man-made structures including buildings, building blocks or roads from remote sensing data is useful for land use mapping, scene understanding, robotic navigation, image retrieval, surveillance, emergency management procedures, cadastral etc. A level set method based on a region-driven segmentation model was implemented with which building boundaries were detected, through this curve propagation technique. The essence of this approach is to optimize the position and the geometric form of the curve by measuring information along that curve, and within the regions that compose the image partition. To this end, one can consider uniform intensities inside objects and the background. Thus, given an initial position of the curve, one can determine global, region-driven functions and provide a statistical description of the inside and outside object area. The calculus of variations and a gradient descent method was used to optimize the variational functional by an iterative steady state process. Experimental results demonstrate the potential of the proposed processing scheme.

• Steel and Composite Structures
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• 제20권1호
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• pp.205-225
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• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 추계학술대회 논문집 학회본부
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• pp.361-365
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• 1991

The problem being considered here is the determination of optimal guidance laws for a launch vehicle for scientific missions. The optimal guidance commands are determined in the sense that the least amount of fuel is used. A numerical solution was obtained for the case where the position and velocity state variables satisfy a specified constraint at the time of thrust cutoff. The method used here is based on the Pontryagin's maximum principle. This is the method of solving a problem in the calculus of variations. In particular, it applies to the problem considered here where the magnitude of the control is bounded. Simulations for the optimal guidance algorithm, during the 2nd and the 3rd-stage flight of the Japanese rocket M-3H-3, are carried out. The results show that the guided trajectory that satisfying the terminal constraints is optimal, and the guidance algorithm works well in the presence of some errors during the 1st-stage pre-programmed guidance phase.

• Journal of Oral Medicine and Pain
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• 제47권3호
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• pp.148-151
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• 2022

Obstructive sialadenitis, one of the diseases that most frequently causes swelling and pain in the salivary glands, is mainly caused by structural obstructions. Sialolithiasis is the most frequent cause of the disease, and other causes include calculus formation, duct strictures, foreign bodies, and anatomical variations. Although there is a possibility that facial fillers directly block the salivary ducts, no cases of obstructive sialadenitis associated with them have been reported yet. We report the case of a 34-year-old female patient who complained of recurrent swelling and pain in the left buccal mucosa. She had undergone facial filler injection procedures on her facial area for cosmetic purposes several years before. Based on the findings of magnetic resonance imaging (MRI) and MR sialography, she was diagnosed with obstructive sialadenitis due to facial fillers. Through this case, we should remember to obtain a thorough history including filler treatments in the case of parotid gland swelling. We also suggest proper utilization of advanced imaging such as MRI in evaluating the location of facial fillers.

• Nuclear Engineering and Technology
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• 제16권4호
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• pp.181-194
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• 1984

변분법을 사용하여 원자로의 핵연료 관리문제를 연구하였다. 원자력 발전소에 영향을 미치는 두 함수 즉 이윤함수와 가격함수는 원자로의 연소도방정식과 최대허용출력 밀도에 대한 부등 제약조건이며, 이들은 임계성의 제약조건이 된다. 초기이윤의 변분해는 원자로에 뚜렷한 두 영역이 있음을 보여 주었다. 즉 일정 출력 영역과 최소 재고량 또는 평활 중성자속 영역이 그것이다. 이들 든 영역의 변이점은 전력에 대한 이윤과 연료에 대한 이자 지급에 상당히 중요하다. 그러므로 각 영역에서 동일 농축도의 핵연료를 가질 동일 부피의 세 영역으로 된 원자로를 최적화 하기 위하여 핵연료 주기 가격 함수가 사용 되었다. 최대 허용 출력 밀도에 대한 부등 제약조건들은 이들 부등 제약 조건이 원자로심의 어느 특정 점이나 로심주기를 통하여 항상 동일 제약조건이 되어야 한다. 원자로의 임계성과 출력밀도에 대한 동일 제약조건에 관계된 핵연료의 연소도에 대한 계차 방정식의 해를 구하였으며 최적 농축도의 위치를 구하기-위하여 구배법을 사용하였다. 이들 계산결과는 부동 제약 조건들을 적절히 적용하면 원자로를 최적화하기 위하여 비선형 최적 기술이 사용될 수 있음을 보여 주었다.