• Title/Summary/Keyword: polynomial root

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An Algebraic Function Control on the Optimal Spaced Grounding Conductor (최적 접지도체간격에 관한 대수함수제어)

  • Song, Young-Joo;Choi, Hong-Kyoo
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.20 no.5
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    • pp.116-124
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    • 2006
  • No matter how the equally spaced grounding grid is designed there are many problem. The best-fitted design for unequally spaced grounding grid is a part that must be considered. This paper Suggest a new way of calculation for grounding grid space of ground conductor by an algebraic function control(The first-order function, Root function, Polynomial function etc.) and on the optimal spaced grounding conductor that make the under 2[%] between maximum potential and minimum potential.

A Study of Conjugate Laminar Film Condensation on a Flat Plate (수평평판에서 복합 층류 막응축에 대한 연구)

  • Lee Euk-Soo
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.17 no.4
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    • pp.303-311
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    • 2005
  • The problem of conjugate laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A simple and efficient numerical method is proposed for its solution. The interfacial temperature is obtained as a root of 3rd order polynomial for laminar film condensation, and it is presented as a function of the conjugate parameter. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Jacob number, $Ja^{\ast}$, defined by an overall temperature difference, a property ratio R and the conjugate parameter ${\zeta}$. The approximate solutions thus obtained reveal the effects of the conjugate parameter.

A study on derivation of root's formulas of cubic and quartic equation by method analogy (방법유추를 통한 3차와 4차 방정식의 근의 공식 유도)

  • Lyou, Ik-Seung;Shin, Hyun-Yong;Han, In-Ki
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.505-514
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    • 2008
  • In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

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Stock-Index Prediction using Fuzzy System and Knowledge Information (퍼지시스템과 지식정보를 이용한 주가지수 예측)

  • Kim, Hae-Gyun;Kim, Sung-Shin
    • Proceedings of the KIEE Conference
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    • 2001.07d
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    • pp.2030-2032
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    • 2001
  • In recent years, many attempts have been made to predict the behavior of bonds, currencies, stock, or other economic markets. Most previous experiments used multilayer perceptrons(MLP) for stock market forecasting. The Kospi 200 Index is modeled using different neural networks and fuzzy system predictions. In this paper, a multilayer perceptron architecture, a dynamic polynomial neural network(DPNN) and a fuzzy system are used to predict the Kospi 200 index. The results of prediction is compared with the root mean squared error(RMSE) and the scatter plot. Results show that both networks can be trained to predict the index. And the fuzzy system is performing slightly better than DPNN and MLP.

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Estimation Method of the Best-Approximated Form Factor Using the Profile Measurement of the Aspherical Ophthalmic Lens (단면 형상 측정을 이용한 비구면 안경 렌즈의 최적 근사화된 설계 계수의 추정 방법)

  • Lee Hocheol
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.5 s.170
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    • pp.55-62
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    • 2005
  • This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

The Analysis of Munsell Value Function by Cubic Spline Method (Cubic Spline Method에 의한 Munsell Value Function의 해석)

  • Jeong, Hong-Soo;Kim, Gong-Ju;Im, Jin-Mo;Park, Pyong-Ki;Rhee, John M.
    • Textile Coloration and Finishing
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    • v.2 no.2
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    • pp.20-32
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    • 1990
  • In this paper, a new method by Cubic Spline to analyze Munsell Value Function is proposed. The values calculated by this method are compared with ones by Judd's Polynomial and Cube Root Functions, etc. For performing these computation algorithms have been developed.

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Short-Distance Gate Subtree Algorithm for Capacitated Minimum Spanning Tree Problem (능력한정 최소신장트리 문제의 근거리 게이트 서브트리 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.21 no.6
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    • pp.33-41
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    • 2021
  • This paper proposes heuristic greedy algorithm that can be find the solution within polynomial time with solution finding rule for the capacitated minimum spanning tree(CMST) problem, known as NP-hard. The CMST problem can be solved by computer-aided meta-heuristic because of the Esau-Williams heuristic polynomial time algorithm has a poor performance. Nevertheless the meta-heuristic methods has a limit performance that can't find optimal solution. This paper suggests visual by handed solution-finding rule for CMST. The proposed algorithm firstly construct MST, and initial feasible solution of CMST from MST, then optimizes the CMST with the subtree gates more adjacent to root node. As a result of total 30 cases of OR-LIB 10 data, Q=3,5,10, the proposed algorithm gets the best performance.

Predictive model for the shear strength of concrete beams reinforced with longitudinal FRP bars

  • Alzabeebee, Saif;Dhahir, Moahmmed K.;Keawsawasvong, Suraparb
    • Structural Engineering and Mechanics
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    • v.84 no.2
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    • pp.143-154
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    • 2022
  • Corrosion of steel reinforcement is considered as the main cause of concrete structures deterioration, especially those under humid environmental conditions. Hence, fiber reinforced polymer (FRP) bars are being increasingly used as a replacement for conventional steel owing to their non-corrodible characteristics. However, predicting the shear strength of beams reinforced with FRP bars still challenging due to the lack of robust shear theory. Thus, this paper aims to develop an explicit data driven based model to predict the shear strength of FRP reinforced beams using multi-objective evolutionary polynomial regression analysis (MOGA-EPR) as data driven models learn the behavior from the input data without the need to employee a theory that aid the derivation, and thus they have an enhanced accuracy. This study also evaluates the accuracy of predictive models of shear strength of FRP reinforced concrete beams employed by different design codes by calculating and comparing the values of the mean absolute error (MAE), root mean square error (RMSE), mean (𝜇), standard deviation of the mean (𝜎), coefficient of determination (R2), and percentage of prediction within error range of ±20% (a20-index). Experimental database has been developed and employed in the model learning, validation, and accuracy examination. The statistical analysis illustrated the robustness of the developed model with MAE, RMSE, 𝜇, 𝜎, R2, and a20-index of 14.6, 20.8, 1.05, 0.27, 0.85, and 0.61, respectively for training data and 10.4, 14.1, 0.98, 0.25, 0.94, and 0.60, respectively for validation data. Furthermore, the developed model achieved much better predictions than the standard predictive models as it scored lower MAE, RMSE, and 𝜎, and higher R2 and a20-index. The new model can be used in future with confidence in optimized designs as its accuracy is higher than standard predictive models.

A Study on the Improvement of Geometric Quality of KOMPSAT-3/3A Imagery Using Planetscope Imagery (Planetscope 영상을 이용한 KOMPSAT-3/3A 영상의 기하품질 향상 방안 연구)

  • Jung, Minyoung;Kang, Wonbin;Song, Ahram;Kim, Yongil
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.38 no.4
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    • pp.327-343
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    • 2020
  • This study proposes a method to improve the geometric quality of KOMPSAT (Korea Multi-Purpose Satellite)-3/3A Level 1R imagery, particularly for efficient disaster damage analysis. The proposed method applies a novel grid-based SIFT (Scale Invariant Feature Transform) method to the Planetscope ortho-imagery, which solves the inherent limitations in acquiring appropriate optical satellite imagery over disaster areas, and the KOMPSAT-3/3A imagery to extract GCPs (Ground Control Points) required for the RPC (Rational Polynomial Coefficient) bias compensation. In order to validate its effectiveness, the proposed method was applied to the KOMPSAT-3 multispectral image of Gangnueng which includes the April 2019 wildfire, and the KOMPSAT-3A image of Daejeon, which was additionally selected in consideration of the diverse land cover types. The proposed method improved the geometric quality of KOMPSAT-3/3A images by reducing the positioning errors(RMSE: Root Mean Square Error) of the two images from 6.62 pixels to 1.25 pixels for KOMPSAT-3, and from 7.03 pixels to 1.66 pixels for KOMPSAT-3A. Through a visual comparison of the post-disaster KOMPSAT-3 ortho-image of Gangneung and the pre-disaster Planetscope ortho-image, the result showed appropriate geometric quality for wildfire damage analysis. This paper demonstrated the possibility of using Planetscope ortho-images as an alternative to obtain the GCPs for geometric calibration. Furthermore, the proposed method can be applied to various KOMPSAT-3/3A research studies where Planetscope ortho-images can be provided.

Automatic Geometric Calibration of KOMPSAT-2 Stereo Pair Data (KOMPSAT-2 입체영상의 자동 기하 보정)

  • Oh, Kwan-Young;Jung, Hyung-Sup
    • Korean Journal of Remote Sensing
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    • v.28 no.2
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    • pp.191-202
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    • 2012
  • A high resolution satellite imagery such as KOMPSAT-2 includes a material containing rational polynomial coefficient (RPC) for three-dimensional geopositioning. However, image geometries which are calculated from the RPC must have inevitable systematic errors. Thus, it is necessary to correct systematic errors of the RPC using several ground control points (GCPs). In this paper, we propose an efficient method for automatic correction of image geometries using tie points of a stereo pair and the Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) without GCPs. This method includes four steps: 1) tie points extraction, 2) determination of the ground coordinates of the tie points, 3) refinement of the ground coordinates using SRTM DEM, and 4) RPC adjustment model parameter estimation. We validates the performance of the proposed method using KOMPSAT-2 stereo pair. The root mean square errors (RMSE) achieved from check points (CPs) were about 3.55 m, 9.70 m and 3.58 m in X, Y;and Z directions. This means that we can automatically correct the systematic error of RPC using SRTM DEM.