• Title, Summary, Keyword: function

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ON SOME PROPERTIES OF A SINGLE CYCLE T-FUNCTION AND EXAMPLES

  • Rhee, Min Surp
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.4
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    • pp.885-892
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    • 2010
  • In this paper we study the structures and properties of a single cycle T-finction, whose theory has been lately proposed by Klimov and Shamir. Any cryptographic system based on T-functions may be insecure. Some of the TSC-series stream ciphers have been successfully attacked by some attacks. So it is important to analyze every aspect of a single cycle T-function. We study some properties on a single cycle T-function and we show some examples are single cycle T-functions by these properties, whose proof is easier than existing methods.

An useful Nonlinear Function for RBF Equalizer-and Decision Boundary setting (RBF 등화기용 유용한 비선형 함수와 결정경계의 설정)

  • 박종령;박남천;주창복
    • Proceedings of the Korea Institute of Convergence Signal Processing
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    • pp.1-4
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    • 2000
  • In this paper, A useful nonlinear function for the RBF(Radial Basis Function) equalization is proposed. This proposed function need not calculate an exponential function that is generally used for conventional RBF equalizer and uses the only four rules of arithmetic. Therefore the computational requirement for the RBF equalizer with the proposed function is decreased. As a computer simulation result, the equalizer with the proposed function effectively reduce nonlinear intersymbol interference, caused by nonlinear communication channel.

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A duplication formula for the double gamma function $Gamma_2$

  • Park, Junesang
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.289-294
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    • 1996
  • The double Gamma function had been defined and studied by Barnes [4], [5], [6] and others in about 1900, not appearing in the tables of the most well-known special functions, cited in the exercise by Whittaker and Waston [25, pp. 264]. Recently this function has been revived according to the study of determinants of Laplacians [8], [11], [15], [16], [19], [20], [22] and [24]. Shintani [21] also uses this function to prove the classical Kronecker limit formula. Its p-adic analytic extension appeared in a formula of Casson Nogues [7] for the p-adic L-functions at the point 0.

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Phenomenology of the concept of functions (함수 개념의 현상학)

  • Yoo, Yoon-Jae
    • Journal for History of Mathematics
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    • v.23 no.3
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    • pp.75-90
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    • 2010
  • In this paper function concept is classified in the phenomenological aspect. According to the study, function concept is classified as causality, designation, operation, change, figure, morhism, variables, functional, and operator. This classifications are categorized as pre-level function, basic level function, and upper level function.

APPROXIMATION METHOD FOR SCATTERED DATA FROM SHIFTS OF A RADIAL BASIS FUNCTION

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1087-1095
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    • 2009
  • In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

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Estimating Variance Function with Kernel Machine

  • Kim, Jong-Tae;Hwang, Chang-Ha;Park, Hye-Jung;Shim, Joo-Yong
    • Communications for Statistical Applications and Methods
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    • v.16 no.2
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    • pp.383-388
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    • 2009
  • In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

Bayesian Estimation of the Reliability Function of the Burr Type XII Model under Asymmetric Loss Function

  • Kim, Chan-Soo
    • Communications for Statistical Applications and Methods
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    • v.14 no.2
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    • pp.389-399
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    • 2007
  • In this paper, Bayes estimates for the parameters k, c and reliability function of the Burr type XII model based on a type II censored samples under asymmetric loss functions viz., LINEX and SQUAREX loss functions are obtained. An approximation based on the Laplace approximation method (Tierney and Kadane, 1986) is used for obtaining the Bayes estimators of the parameters and reliability function. In order to compare the Bayes estimators under squared error loss, LINEX and SQUAREX loss functions respectively and the maximum likelihood estimator of the parameters and reliability function, Monte Carlo simulations are used.

The Weight Function in BIRQ Estimator for the AR(1) Model with Additive Outliers

  • Jung Byoung Cheol;Han Sang Moon
    • Proceedings of the Korean Statistical Society Conference
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    • pp.129-134
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    • 2004
  • In this study, we investigate the effects of the weight function in the bounded influence regression quantile (BIRQ) estimator for the AR(1) model with additive outliers. In order to down-weight the outliers of X-axis, the Mallows' (1973) weight function has been commonly used in the BIRQ estimator. However, in our Monte Carlo study, the BIRQ estimator using the Tukey's bisquare weight function shows less MSE and bias than that of using the Mallows' weight function or Huber's weight function.

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A Study on Travel Cost Function of Transit Assignment Model (대중교통 통행배정모형의 통행비용함수 분석)

  • Kim, Kyoung Tae;Lee, Suk Kwon;Kwon, Yong Seok
    • Proceedings of the KSR Conference
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    • pp.1902-1907
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    • 2007
  • This paper suggests improvements in travel cost function of transit assignment model by analysing existing model. Two types of travel cost function are widely used for congested public networks. The one is used for strictly restricting public transport capacity. Another is non-decreasing function such as BPR function. In this paper, we analyse two types of travel cost function in case of intercity rail. The characteristics of intercity rail are different from those of public transit in urban area. Therefore travel cost function must be differently applied in each case.

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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Lee, Dong-Myung;Rathie, Arjun K.;Parmar, Rakesh K.;Kim, Yong-Sup
    • Honam Mathematical Journal
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    • v.33 no.2
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    • pp.187-206
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    • 2011
  • The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.