• Title, Summary, Keyword: symbolic method

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On a Symbolic Method for Fully Inhomogeneous Boundary Value Problems

  • Thota, Srinivasarao
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.13-22
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    • 2019
  • This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

Efficiency of a Symbolic Computation Method for the Real Time Simulation (실시간 시뮬레이션을 위한 기호연산기법의 유용성 검증에 관한 연구)

  • Choe, Dae-Han;Yu, Wan-Seok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.7
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    • pp.1878-1884
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    • 2000
  • In multibody dynamic analysis, one of the most important problems is to reduce computation times for real time simulation. In this paper, a symbolic computation method is implemented and tested for each dynamic analysis step. Applying symbolic formulations to the vehicle dynamics program AutoDyn7, the effectiveness of the symbolic computation method is verified.

A Study on the Effective Symbolic Expression Methods of Uniform Design (유형별 유니폼 디자인의 효과적인 상징표현 방법)

  • Kim, Yun-Hee;Lee, Jae-Jung
    • Journal of the Korean Society of Costume
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    • v.56 no.8
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    • pp.148-159
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    • 2006
  • The objective of this study is to consider the uniform as visual communication, and analyze the expression of symbol shown on the uniform design by the pattern by applying the visual symbol in the communication and operation of the meaning. Also, it is to construct the systematic modeling method of the expression of design symbol by the pattern of uniform in th e various fields. This study is to analyze the symbolic expression method of the uniform design by the pattern by suggesting the symbolic expression method as a frame through the visual symbolic approach of the uniform design and the analysis of semantic symbol according to that. As a result, there arose simplification and emphasis and a method of symbolic expression with the national flag, a conceptual factor characteristically in the sports uniform design. The characteristics of symbolic expression of uniform design were mainly used in the symbolic expression with the customary code and symbol. Also, the uniform in the enterprises were widely used in the expression of uniform with the suggestion and code by the color. As for the characteristics of symbolic expression shown on the event uniform design, the method of symbolic expression by the pattern of uniform was grasped differently asa result of symbolic expression through the image. The method of symbolic expression suggested on this study could be used on a basis of uniform design in the future. Accordingly, this study has a meaning of suggesting the methodology of uniform design that would be a parameter.

On A Symbolic Method for Error Estimation of a Mixed Interpolation

  • Thota, Srinivasarao
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.453-462
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    • 2018
  • In this paper, we present a symbolic formulation of the error obtained due to an approximation of a given function by the mixed-interpolating function. Using the proposed symbolic method, we compute the error evaluation operator as well as the error estimation at any arbitrary point. We also present an algorithm to compute an approximation of a function by the mixed interpolation technique in terms of projector operator. Certain examples are presented to illustrate the proposed algorithm. Maple implementation of the proposed algorithm is discussed with sample computations.

Location Tracking in Indoor Symbolic Space with RFID Sensors (RFID 센서를 이용한 실내 기호공간에서의 위치추적)

  • Kang, Hye-Young;Hwang, Jung-Rae;Li, Ki-Joune
    • Spatial Information Research
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    • v.19 no.3
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    • pp.53-62
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    • 2011
  • Spatial information services in indoor space are an im portant application area of GIS as in outdoor space. Unlike in outdoor space, a position in indoor space is specified by a symbolic code such as room number, rather than coordinate. Therefore tracking in indoor space is no longer a prediction of coordinates but a symbolic estimation on the current position of a moving object. In this paper, we propose a framework for tracking moving objects in indoor symbolic space with RFID sensors. First, we introduce the concepts of indoor symbolic space and tracking in indoor symbolic space, and define the accessibility graph for trackable indoor symbolic space. Second, we propose a deployment method of RFID readers and a construction algorithm of accessibility graph for trackable indoor symbolic space. Third, a tracking method is proposed for moving objects in symbolic indoor space with RFID sensors. Finally, we present an implementation exmaple and the result of experiment with real data to validate the proposed method.

A Symbolic Computation Method for Automatic Generation of a Full Vehicle Model Simulation Code for a Driving Simulator

  • Lee Ji-Young;Lee Woon-Sung
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.395-402
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    • 2005
  • This paper deals with modeling and computer simulation of a full multibody vehicle model for a driving simulator. The multibody vehicle model is based on the recursive formulation and a corresponding simulation code is generated automatically from AUTOCODE, which is a symbolic computation package developed by the authors using MAPLE. The paper describes a procedure for automatically generating a highly efficient simulation code for the full vehicle model, while incorporating realistically modeled components. The following issues have been accounted for in the procedure, including software design for representing a mechanical system in symbolic form as a set of computer data objects, a multibody formulation for systems with various types of connections between bodies, automatic manipulation of symbolic expressions in the multibody formulation, interface design for allowing users to describe unconventional force-and torque-producing components, and a method for accommodating external computer subroutines that may have already been developed. The effectiveness and efficiency of the proposed method have been demonstrated by the simulation code developed and implemented for driving simulation.

Performance Comparison of Symbolic Manipulation Programs using a Validation Method for Numerical Solution (수치해 검증방법을 이용한 기호 연산 프로그램 성능 비교)

  • Yang, Sung-Wook;Lee, Sang-Chul
    • Journal of the Korean Society for Aviation and Aeronautics
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    • v.23 no.2
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    • pp.69-74
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    • 2015
  • We propose a rigorous and practical methodology to evaluate the performance of symbolic manipulation program such as Mathematica, Maple, and Maxima. First, we demonstrate an inverse method to construct the benchmark problems of an initial value problems. The benchmark problems associated with the discrete version of the Chebyshev polynomials provide a rigorous and objective measure to evaluate the performance of symbolic manipulation programs. We compare three symbolic manipulation programs, which are Mathematica, Maple and Maxima, using this methodology. The computation time, the used memory and the perturbation terms are chosen for comparison parameters.

Symbolic computation and differential quadrature method - A boon to engineering analysis

  • Rajasekaran, S.
    • Structural Engineering and Mechanics
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    • v.27 no.6
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    • pp.713-739
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    • 2007
  • Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

Multiplexed Optical Correlation Filter for Optical Parallel Addition Based on Symbolic Substitution with Redundant Binary Number (기호치환을 기초로 한 잉여 이진수 광병렬 가산용 다중 광상관 필터)

  • 노덕수;조웅호;김정우;이하운;김수중
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.33B no.3
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    • pp.109-119
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    • 1996
  • We propsoed a multiplexed optical correlation filter method for an optical parallel addition based on symbolic substitution. In the proposed mthod, we used redundant binary number which was easy to minimize the number of the symbolic substitution rules. We chose MACE filter which had very low sidelobes and good correlation peak compared with SDF filter as the optical correlation recognition filter and encoded input numbers properly to increase the discrimination capability. In order to minimize the number of symbolic substitution rules, sixteen input patterns were divided into six groups of the same addition results and six filters for recognizing the input patterns were used. these filters were multiplexed in two MMACE filter planes and the corresponding substitution method was proposed. Through the computer simulation, we confirmed the proposed method was suitable to implement the optical parallel adder.

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Symbolic Substitution Based on Optical Correlator for Optical Parallel Addition with Redundant Binary Number (잉여 이진수 광병렬 가산을 위한 광상관 기호치환)

  • 노덕수;김정우;조웅호;김수중
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.21 no.1
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    • pp.269-280
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    • 1996
  • We proposed a symbolic substitution method based on an optical correlator for an optical parallel addition. In the proposed symbolic substitution method, we used redundant binary number of the symbolic substitution rules as a number system and chose MAC3E filter which had very low sidelobes and good correlation peak compared with SDF filter as the optical correlation filter. We encoeded input numbers property to increase the discrimination capability and divided inpt patterns into 5 groups of the same addition results to minimize the number of symbolic substitution rules. Through the computer simulation, we confirmed the proposed method was suitable to implement the optical parallel adder.

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