• Title, Summary, Keyword: exponential function

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AN EXACT LOGARITHMIC-EXPONENTIAL MULTIPLIER PENALTY FUNCTION

  • Lian, Shu-jun
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1477-1487
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    • 2010
  • In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the local optimizers of a nonlinear problem are precisely the local optimizers of the logarithmic-exponential multiplier penalty problem.

Reliability estimation and ratio distribution in a general exponential distribution

  • Lee, Chang-Soo;Moon, Yeung-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.3
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    • pp.623-632
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    • 2014
  • We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P(X < Y ) and the skewness trends of the density function of the ratio X=(X+Y) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.

Generation and Characteristics of Exponential Pulse Shaping Functions using Chebychev Identity Equation and Bessel Coefficients (Chebychev 항등식과 Bessel 계수를 이용한 지수펄스모형함수 생성 및 특성)

  • Lee, Jeong-Jae;Park, Sun-Kwang
    • Journal of the Institute of Convergence Signal Processing
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    • v.10 no.1
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    • pp.60-65
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    • 2009
  • In this paper, we propose a new exponential pulse shaping function based on Chebychev identity equation and Bessel coefficients. The proposed pulse shaping function can produce various pulses with the different characteristics in the time and frequency domain by changing its two parameters. By differentiating the exponential pulse shaping function, we obtain new different pulse functions, in which the even order derivatives of the exponential pulse shaping function are orthogonal to its odd order derivatives. To find the efficiency of the proposed exponential pulse shaping function we analyze its essential characteristics and compare them with those of the conventional Gaussian pulses. We can choose the most suitable exponential pulse waveform according to the design criteria of communication systems.

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COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS

  • Qi, Feng;Zhang, Xiao-Jing
    • The Pure and Applied Mathematics
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    • v.21 no.2
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    • pp.141-145
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    • 2014
  • In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).

ON THE EXPONENTIAL FUZZY PROBABILITY

  • Yun Yong-Sik;Song Jae-Choong;Ryu Sang-Uk
    • Communications of the Korean Mathematical Society
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    • v.21 no.2
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    • pp.385-395
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    • 2006
  • We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

Modeling of Time Delay Systems using Exponential Analysis Method

  • Iwai, Zenta;Mizumoto, Ikuro;Kumon, Makoto;Torigoe, Ippei
    • 제어로봇시스템학회:학술대회논문집
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    • pp.2298-2303
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    • 2003
  • In this paper, very simple methods based on the exponential analysis are presented by which transfer function models for processes can easily be obtained. These methods employ step responses or impulse responses of the processes. These can also give a more precise transfer function model compared to the well-known graphical methods. Transfer functions are determined based on Prony method, which is one of the oldest and the most representative methods in the exponential analysis. Here, the method is reformed and applied to obtain the so-called low-order transfer function with pure time delay from the data of the step response. The effectiveness of the proposed method is examined through several numerical examples and experiments of the 2-tank level control process.

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Mechanical degradation kinetics of poly(ethylene oxide) in a turbulent flow

  • Sung, Jun-Hee;Lim, Sung-Taek;Kim, Chul-Am;Heejeong Chung;Park, Hyoung-Jin
    • Korea-Australia Rheology Journal
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    • v.16 no.2
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    • pp.57-62
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    • 2004
  • Turbulent drag reduction (DR) efficiency of water soluble poly(ethylene oxide) (PEO) with two different molecular weights was studied as a function of polymer concentration and temperature in a turbulent flow produced via a rotating disk system. Its mechanical degradation behavior as a function of time in a turbulent flow was also analyzed using both a simple exponential decay function and a fractional exponential decay equation. The fractional exponential decay equation was found to fit the experimental data better than the simple exponential decay function. Its thermal degradation further exhibited that the susceptibility of PEO to degradation increases dramatically with increasing temperature.

FRF Distortion Caused by Exponential Window Function on Impact Hammer Testing and Its Solution (지수창함수를 사용한 임팩트햄머 실험에서 주파수응답함수의 왜곡과 개선책)

  • 안세진;정의봉
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.5
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    • pp.334-340
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    • 2003
  • Exponential window function Is widely used In impact hammer testing to reduce leakage error as well as to get a good S/N ratio. The larger its decaying rate is, the more effectively the leakage errors are reduced. But if the decay rate of the exponential window is too large, the FRF is distorted. And the modal parameters of the system can not be exactly identified by modal analysis technique. Therefore, it is a difficult problem to determine proper decay rate in impact hammer testing. In this paper, amount of the FRF distortion caused by exponential window is theoretically uncovered. A new circle fitting method is also proposed so that the modal parameters are directly extracted from impulse response spectrum distorted by the exponential-windowed impulse response data. The results by the conventional and proposed circle fitting method are compared through a numerical example.

On simple estimation technique for the reliability of exponential lifetime model

  • Al-Hemyari, Z.A.;Al-Saidy, Obaid M.;Al-Ali, A.R.
    • International Journal of Reliability and Applications
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    • v.14 no.2
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    • pp.79-96
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    • 2013
  • Exponential distribution plays a key role in engineering reliability and its applications. The exponential failure model has been studied for years. This article introduces two new preliminary test estimators for the reliability function (R(t)) in complete and censored samples from the exponential model with the use of a prior estimation (${\theta}_0$) of the mean (${\theta}$). The proposed preliminary test estimators are studied and compared numerically with the existing estimators. Computer-intensive calculations for bias and relative efficiency show that for, different values of levels of significance and for varying constants involved in the proposed estimators, the proposed estimators are far better than classical and existing estimators.

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