• Title/Summary/Keyword: exponential functions

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Near-field to far-field transform formula using circular cylindrical scanning based on complex exponential functions (복소 지수함수 기반 원통주사법을 이용한 근역장 - 원역장 변환 공식 -)

  • 류홍균;조용희
    • Proceedings of the Korea Contents Association Conference
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    • 2004.05a
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    • pp.317-322
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    • 2004
  • The improvement of a near-field measurement for an antenna is investigated. We propose the formula of a circular cylindrical scanning based on the Cartesian coordinate. Proposed algorithm for the circular cylindrical scanning is compared with the exact solution for a Hertzian dipole antenna, thus confirming that our approach is useful for most practical measurements.

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STABILITY OF TWO FUNCTIONAL EQUATIONS ARISING FROM DETERMINANT OF MATRICES

  • Choi, Chang-Kwon;Kim, Jongjin;Lee, Bogeun
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.495-505
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    • 2016
  • Let $f:{\mathbb{R}}^3{\rightarrow}{\mathbb{R}}$. In this paper we prove the stability of functional inequalities ${\mid}f(ux+vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$, ${\mid}f(ux-vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$ for all $x,y,z,u,v,w{\in}{\mathbb{R}}$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker [1].

NOTES ON A NON-ASSOCIATIVE ALGEBRAS WITH EXPONENTIAL FUNCTIONS III

  • Choi, Seul-Hee
    • Communications of the Korean Mathematical Society
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    • v.23 no.2
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    • pp.153-159
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    • 2008
  • For $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$, all the derivations of the evaluation algebra $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$ is found in the paper (see [16]). For $M=\{{\partial}_1,\;{\partial}_1^2\},\;Der_{non}(\mathbb{F}[e^{{\pm}x}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ is found in the paper (see [2]). For $M=({\partial}_1^2,\;{\partial}_2^2)$, we find $Der_{non}(\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ in this paper.

Joint Performance of Demodulation and Decoding with Regard to Log-Likelihood Ratio Approximation (대수우도비 근사화에 따른 복조와 복호의 결합 성능)

  • Park, Sung-Joon;Jo, Myung-Suk
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.41 no.12
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    • pp.1736-1738
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    • 2016
  • In modern digital communication systems adapting high-order modulation and high performance channel code, log-likelihood ratios involving the repeated calculations of the logarithm of sum of exponential functions are necessary for demodulation and decoding. In this paper, the approximation methods called Min and MinC are applied to demodulation and decoding together and their complexity and joint performance are analyzed.

Calibration of Glove-Like Hand Input System for Wearable Computer (웨어러블 컴퓨터용 장갑형 손동작 입력 시스템의 보정)

  • 박용수;이상헌;백윤수
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.7
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    • pp.209-216
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    • 2000
  • Recently, Wearable Computers have been applied to medical equipments, inspection system, military and various fields of industries. To support the various application of wearable computer, many researches into the input device for wearable computer have been executed. This paper describes the glove-like hand input system for wearable computer. the characteristics of sensed values, and coupling effects between each sensor. Using these characteristics and coupling effects, the general relation between flexion angles of joints and the values from sensors are proposed as exponential functions. Also, the error range of sensed values is proposed and the glove-like hand input system is calibrated as well by the experiments.

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Lateral Vibration Analysis of a Nonuniform Beam by Ritz's Method (Ritz법에 의한 비균일 단면 외팔보의 횡진동 해석)

  • Park, Sok-Chu
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.10
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    • pp.946-949
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    • 2007
  • This paper discusses the lateral vibration of a beam with boundary condition of one end fixed and the other end free. The uniform beam has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function or mathematical solution could not exist. Even if the solution of Bessel's function exists, as Bessel function is a series function, we must get the solution by numerical method. Author had proposed the solution of the matrix method by Ritz's method and a new mode shape function, and had earned the good results for a wedge beam. Hereby a vibration analysis for the tapered beam with circle cross section was executed, and so good results were showed.

Effect of power law index for vibration of armchair and zigzag single walled carbon nanotubes

  • Khadimallah, Mohamed Amine;Hussain, Muzamal
    • Steel and Composite Structures
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    • v.37 no.5
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    • pp.621-632
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    • 2020
  • This research deals with the study of vibrational behavior of armchair and zigzag single-walled carbon nanotubes invoking extended Love shell theory. The effects of different physical and material parameters on the fundamental frequencies are investigated. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. To discretize the governing equation in eigen-value form, wave propagation approach is developed. Complex exponential functions have been used and the axial model depends on boundary condition that has been described at the edges of carbon nanotubes to calculate the axial modal dependence. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes and current results shows a good stability with comparison of other studies.

A Study on the Forecasing Modeles of Traffic Accident by Region (지역별 교통사고 예측모형에 관한 연구)

  • 박병호
    • Journal of the Korean Regional Science Association
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    • v.11 no.1
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    • pp.21-30
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    • 1995
  • This paper deals with the forecasting models for traffic accident by region. Its objectives are to develop the appropriate model for projecting the accident and to analyze the regional characteristics of the accident model. The main results are as follow. First, the literature review, statistical tests and sensitivity analyses show that the joint model combined both PTM and Exponential functions is appropriate to project the traffic accidents by region. Second, the statistical analyses by region. Second, the statistical analyses on the regional accident models indicate that the levels of significance in terms of t-value, $R^2$ and F-value are very high. Finally, the comparative analyses among regions show that the regional differences on the accident patterns can be explained by the joint models and the accident indices (parameters, $P_{max}$, 1/b, $\eta$ etc.) of each region.

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Reliability Equivalence of a Non-identical Components Parallel System

  • Montaser, M.;Sarhan, Ammar M.
    • International Journal of Reliability and Applications
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    • v.9 no.1
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    • pp.95-112
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    • 2008
  • This paper gives the reliability equivalence factors of a parallel system with n independent and non-identical components. It is assumed here that, the failure rates of the system's components are constants. We used three different methods to improve the system given. Two reliability characteristics (the mean time to failure and the reliability function) are used to perform the system improvement. For this purpose, the reliability functions and the mean times to failures of the original and improved systems are obtained. The results given in this paper generalize the results given in the literatures by setting n = 1, 2. An illustrative numerical example is presented to compare the different reliability factors obtained.

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On a Novel Way of Processing Data that Uses Fuzzy Sets for Later Use in Rule-Based Regression and Pattern Classification

  • Mendel, Jerry M.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.14 no.1
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    • pp.1-7
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    • 2014
  • This paper presents a novel method for simultaneously and automatically choosing the nonlinear structures of regressors or discriminant functions, as well as the number of terms to include in a rule-based regression model or pattern classifier. Variables are first partitioned into subsets each of which has a linguistic term (called a causal condition) associated with it; fuzzy sets are used to model the terms. Candidate interconnections (causal combinations) of either a term or its complement are formed, where the connecting word is AND which is modeled using the minimum operation. The data establishes which of the candidate causal combinations survive. A novel theoretical result leads to an exponential speedup in establishing this.