• Title/Summary/Keyword: Expansion Method

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ANALYTICAL AND NUMERICAL SOLUTIONS OF A CLASS OF GENERALISED LANE-EMDEN EQUATIONS

  • RICHARD OLU, AWONUSIKA;PETER OLUWAFEMI, OLATUNJI
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.26 no.4
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    • pp.185-223
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    • 2022
  • The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases' molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = hm(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.

Simulation of eccentricity effects on short- and long-normal logging measurements using a Fourier-hp-finite-element method (Self-adaptive hp 유한요소법을 이용한 단.장노말 전기검층에서 손데의 편향 효과 수치모델링)

  • Nam, Myung-Jin;Pardo, David;Torres-Verdin, Carlos;Hwang, Se-Ho;Park, Kwon-Gyu;Lee, Chang-Hyun
    • Geophysics and Geophysical Exploration
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    • v.13 no.1
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    • pp.118-127
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    • 2010
  • Resistivity logging instruments are designed to measure the electrical resistivity of a formation, and this can be directly interpreted to provide a water-saturation profile. However, resistivity logs are sensitive to borehole and shoulder-bed effects, which often result in misinterpretation of the results. These effects are emphasised more in the presence of tool eccentricity. For precise interpretation of short- and long-normal logging measurements in the presence of tool eccentricity, we simulate and analyse eccentricity effects by combining the use of a Fourier series expansion in a new system of coordinates with a 2D goal-oriented high-order self-adaptive hp finite-element refinement strategy, where h denotes the element size and p the polynomial order of approximation within each element. The algorithm automatically performs local mesh refinement to construct an optimal grid for the problem under consideration. In addition, the proper combination of h and p refinements produces highly accurate simulations even in the presence of high electrical resistivity contrasts. Numerical results demonstrate that our algorithm provides highly accurate and reliable simulation results. Eccentricity effects are more noticeable when the borehole is large or resistive, or when the formation is highly conductive.

A Vine-Based Stochastic Loading Technique in Pedestrian Networks Considering Space Syntax Theory (Space Syntax Theory를 반영한 덩굴망기반 확률적 보행네트워크 배정기법)

  • Kim, Jong Hyung;Lee, Mee Young;Nam, Doo Hee
    • The Journal of The Korea Institute of Intelligent Transport Systems
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    • v.15 no.6
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    • pp.71-79
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    • 2016
  • Evaluation of the walkability of the urban pedestrian network requires construction of a pedestrian network model that reflects Space Syntax Theory. Space Syntax Theory deduces an integration value through which materials for evaluation of the pedestrian network's connectivity can be produced; and can aid in illustrating the ease of walkability through the model's calculation of pedestrian indices such as movability, comfort, and safety. But the representation of space syntax theory in the pedestrian network requires that turn delay be added by means of a network-type construction method. While tree-based Dial Algorithm proposed for the logit-based probability walkability distribution model may be effective for link-based pedestrian volume distribution, it requires further network expansion to reflect turn delays. In this research, Vine-based Dial Algorithm is executed in order to obtain a measure reflecting the integration value for Space Syntax Theory. The Vine-based Dial Algorithm of two adjacent links, which forms the minimum unit of the Vine network, has the advantage of encompassing turn delay, and thus eliminates the need for network expansion. Usage of the model to evaluation of complicated pedestrian spheres such as urban roads is left to further research. Especially the progression of the proposed method is deduced through case study.

A Study on Decisions on Investment Factors in the Development of Local Fishing Harbors (지방어항개발의 투자결정요인 분석 - 충청남도 어항 중심으로 -)

  • Lee, Kwang-Nam;Jung, Jin-Ho;Choi, Jae-Wook
    • Ocean and Polar Research
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    • v.33 no.4
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    • pp.473-483
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    • 2011
  • In the recent WTO/DDA negotiations, discussions are progressing to forbid fishery subsidies which have negative effect on the natural environment and the fishery resources and to lower or to eliminate the tariff/non-tariff barriers that distort trade liberalization. As a result, linking to the weak structural environment of Korea's fishing villages; such a scheme has jeopardized the livelihood of fishermen who settle down in local fishing harbors. Against this backdrop, the government is attempting to positively respond to changes in the fishing environment in a number of different ways: promotion of fishing tourism, fishing harbor reinforcement in function, developing fishing villages, and harbors. With respect to investment by priority in fishing harbor development, it is very important to appropriately select investment targets based on objective criteria. A small number of harbors are chosen and investment plans by harbor are systematically devised, economic feasibility and the effects of investment are analyzed and reviewed in relation to each target harbor. This paper is designed to review and assess objective evaluation methods and the degree of importance for the designation of target harbors, dealing with local harbors in Chung Nam Do as a model. Each local government has tried to reorganize existing harbors and develop new harbors, considering a fall in the number of fishing vessels and the expansion of maritime leisure activities. In order to overcome the limit of existing harbors in function, to raise the income of fishermen, and to activate tourism, they have shifted their focus from simple functions such as vessel evacuation and anchoring to harbor beautification, which can work as a basis for fishing tourism. This paper points out that the AHP analysis method for prioritizing local harbors in Chung Nam Do should help to be chosen target harbors in other cities and provinces. Each local government has attempted to reorganize existing harbors and to develop new harbors, taking into consideration the decline in the number of fishing vessels and the expansion of maritime leisure activities. In order to overcome the limited number of functional harbors, to raise the income of fishermen, and to boost tourism, they have shifted their focus from simple functions, such as vessel evacuation and anchoring, to harbor beautification, which can work as a basis for fishing tourism. This paper shows that the AHP analysis method for prioritizing local harbors in Chungcheongnam-do could aid in the effective selection of target harbors in other cities and provinces.

Development of a n-path algorithm for providing travel information in general road network (일반가로망에서 교통정보제공을 위한 n-path 알고리듬의 개발)

  • Lim, Yong-Taek
    • Journal of Korean Society of Transportation
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    • v.22 no.4 s.75
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    • pp.135-146
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    • 2004
  • For improving the effectiveness of travel information, some rational paths are needed to provide them to users driving in real road network. To meet it, k-shortest path algorithms have been used in general. Although the k-shortest path algorithm can provide several alternative paths, it has inherent limit of heavy overlapping among derived paths, which nay lead to incorrect travel information to the users. In case of considering the network consisting of several turn prohibitions popularly adopted in real world network, it makes difficult for the traditional network optimization technique to deal with. Banned and penalized turns are not described appropriately for in the standard node/link method of network definition with intersections represented by nodes only. Such problem could be solved by expansion technique adding extra links and nodes to the network for describing turn penalties, but this method could not apply to large networks as well as dynamic case due to its overwhelming additional works. This paper proposes a link-based shortest path algorithm for the travel information in real road network where exists turn prohibitions. It enables to provide efficient alternative paths under consideration of overlaps among paths. The algorithm builds each path based on the degree of overlapping between each path and stops building new path when the degree of overlapping ratio exceeds its criterion. Because proposed algorithm builds the shortest path based on the link-end cost instead or node cost and constructs path between origin and destination by link connection, the network expansion does not require. Thus it is possible to save the time or network modification and of computer running. Some numerical examples are used for test of the model proposed in the paper.

An On-chip Cache and Main Memory Compression System Optimized by Considering the Compression rate Distribution of Compressed Blocks (압축블록의 압축률 분포를 고려해 설계한 내장캐시 및 주 메모리 압축시스템)

  • Yim, Keun-Soo;Lee, Jang-Soo;Hong, In-Pyo;Kim, Ji-Hong;Kim, Shin-Dug;Lee, Yong-Surk;Koh, Kern
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.1_2
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    • pp.125-134
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    • 2004
  • Recently, an on-chip compressed cache system was presented to alleviate the processor-memory Performance gap by reducing on-chip cache miss rate and expanding memory bandwidth. This research Presents an extended on-chip compressed cache system which also significantly expands main memory capacity. Several techniques are attempted to expand main memory capacity, on-chip cache capacity, and memory bandwidth as well as reduce decompression time and metadata size. To evaluate the performance of our proposed system over existing systems, we use execution-driven simulation method by modifying a superscalar microprocessor simulator. Our experimental methodology has higher accuracy than previous trace-driven simulation method. The simulation results show that our proposed system reduces execution time by 4-23% compared with conventional memory system without considering the benefits obtained from main memory expansion. The expansion rates of data and code areas of main memory are 57-120% and 27-36%, respectively.

A Study on the Promotion Method of Domestic Video Security Industry (국내 영상보안산업 활성화 방안 연구)

  • Yoo, Soonduck;Ryu, Daehyun
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.17 no.3
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    • pp.9-21
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    • 2017
  • The purpose of this study is to identify the current situation and actual condition of the video security industry, The research method was based on interviews with twelve specialists, and examined the market trends, the problems of the video security industry, the improvement plan and the government promotion strategy. The problem with the domestic video security industry is that there are the decline in overseas exports and the slowdown in exports to China, insufficient measures to overcome certification barriers due to the strengthening of national certification system, domestic demand growth slowed, expansion of domestic market share of Chinese products, lack of high-tech development of domestic products, lack of expertise in technology development and operation and inadequate legislation for revitalizing the video security industry. The improvement plan is as follows. Need to implement export expansion support policy, need to build tailored response system for each country, need improvement of security related demand creation system, take measures such as domestic industrial protection policy, certification barriers and tariff barriers, induce future core technology to create high added value. The government also needs to actively support human resources development, and induce stabilization of relevant laws and institutions. This study will contribute to the development of related industries by suggesting the development direction of the video security industry.

Water wave reflection over shear currents and dredged multi-arrayed trenches (외부 흐름과 준설된 다열 함몰지형에 의한 파랑의 반사)

  • Cho, Yong-Sik;Lee, Kwang-Jun;Lee, Jun-Whan
    • Journal of Korea Water Resources Association
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    • v.53 no.10
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    • pp.871-876
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    • 2020
  • Understanding the wave characteristics near the outlet of coastal power plants for cooling water in the vicinity of the dredged areas is critically important for the construction and operation of the plants. By Employing the eigenfunction expansion method, in this study, we analyzed the reflection of monochromatic water waves over (1) shear currents near the outlet and (2) multi-arrayed trenches representing dredged areas. We firstly optimized the number of grids expressing shear currents and the number of evanescent modes based on a convergence test. We then analyzed the sensitivity of the reflection coefficients depending on (1) magnitude of shear currents, (2) width of shear currents, (3) a distance between adjacent trenches, and (4) a number of trenches. The results showed that the reflection coefficient was more sensitive to the number of trenches and the distance between trenches than the velocity of shear currents and the width of shear currents. We also found that even the effect of shear currents is relatively small, the effect is not negligible in a relative water depth from shallow to near shallow water waves (0.01 < kh ≦ 0.70).

Effect of Some Additives for Yukwa (Popped Rice Snack) Quality Improvement and Process Modification Trials (유과 품질향상을 위한 첨가물의 효과와 공정 단순화 시도)

  • Shin, Dong-Hwa;Kim, Myung-Kon;Chung, Tae-Kyu;Lee, Hyun-Yu
    • Korean Journal of Food Science and Technology
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    • v.22 no.3
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    • pp.272-277
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    • 1990
  • Some additives were applied to improve Yukwa(Popped rice snack) quality and process modifications were tested for cutting down soaking time and application of rice flour. Addition of soaked soybean (3%, w/w) to dough showed higher expansion rate and better physical properties with more acceptable quality by sensory evaluation of Yukwa. Baking powder, modified starch and alcoholic liquor, Mackeali(rice wine, turbid). Soju(distilled liquor) and Yakju(rice wine, clear), were no positive effect on quality of Yukwa but alcoholic liquor gave more fine texture than others. High temprature soaking $(60^{\circ}C)$ of rice for 3 hours which is near gelatinization temperature of rice starch. gave same quality of Yukwa comparing with long time soaking (12 hours) at room temperature. Extention of high temperature soaking (12 hours) did not improve the quality of Yukwa. The 100 mesh of rice flour by dry milling method was better in expansion rate and hardness than 40 and 80mesh but it was worse than ordinary wet milling. It was notified that milling method and milling mechines for Yukwa preparation should be studied in more detail.

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Measurement of Thermal Expansion Coefficient of Package Material Using Strain Gages (스트레인 게이지를 이용한 패키지 재료의 열팽창계수 측정)

  • Yang, Hee-Gul;Joo, Jin-Won
    • Journal of the Microelectronics and Packaging Society
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    • v.20 no.3
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    • pp.37-44
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    • 2013
  • It is well known that thermal deformation of electronic packages with Pb-Sn solder and with lead-free solder is significantly affected by material properties consisting the package, as well as those of the solder itself. In this paper, the method for determining coefficient of thermal expansion(CTE) of new material is established by using temperature characteristic of strain gages, and the CTE of molding compound are obtained experimentally. The temperature-dependent CTE of molding compound for Pb-Sn solder and that for lead-free solder are obtained by using strain measurements with well known steel specimen and aluminium specimen as reference specimens, and the CTE's are also measured non-contactly by using moire interferometry. Those results are compared, and the agreement between the two types of strain gage experiment and the moire experiment show the strain gage method used in this paper to be reliable. In the case of the molding compound for Pb-Sn solder, the CTE is measured as approximately $15.8ppm/^{\circ}C$ regardless of the temperature. In the case for the lead-free solder, the CTE is measured as of approximately $9.9ppm/^{\circ}C$ below the temperature of $100^{\circ}C$, and then the CTE is increased sharply depending on the temperature, and reaches to $15.0ppm/^{\circ}C$ at $130^{\circ}C$.