• Journal of the Korean Statistical Society
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• 제35권2호
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• pp.213-224
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• 2006

We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations using the influence function and the derivative influence measures. The influence function for regression coefficients is derived and its sample versions are used for influence analysis. The derivative influence measures under certain perturbation schemes are derived. It can be seen that the influence function method and the derivative influence measures yield the same influence information. An illustrative example in longitudinal data analysis is given and we compare the results provided by the influence function method and the derivative influence measures.

• 대한수학회논문집
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• 제34권2호
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• pp.507-522
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• 2019

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.499-509
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• 2001

We investigate the influence of observations on a test of additional information about discrimination using the influence function and the derivative influence measures. the influence function for the test statistic is derived and this sample versions are used for influence analysis. The derivative influence measures for the test statistic under a perturbation scheme are derived. It will be seen that the influence function method and the derivative influence measures yield the same result. Furthermore, we will derive the relationships between the influence function and the derivative influence measures when the sample size is large. an illustrative example is given and we will compare the results provided by the influence function method and the derivative influence measures.

• The Journal of the Acoustical Society of Korea
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• 제18권2E호
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• pp.31-38
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• 1999

This paper focuses on extracting formants from transfer function, derived from linear prediction analysis of speech signal. The second derivative of the log magnitude spectrum of the transfer function, the first and third derivatives of the phase spectrum of the transfer function in the z-plane are discussed. Their resolutions of detecting formants are analyzed and some comparisons are given. Theoretical analyses and experimental results show that the third derivative of the phase spectrum decays more rapidly around the formant locations than the first derivative of the phase spectrum and the second derivative of the log magnitude spectrum. Compared with the second derivative of the log spectrum and the first derivative of the phase spectrum, the third derivative of the phase spectrum has higher resolution in frequency domain and provides more accurate formant extraction.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• 대한수학교육학회지:수학교육학연구
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• 제21권1호
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• pp.33-55
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• 2011

미적분학 강사와 학생의 미분에 관한 담화의 특징을 인식에 관한 의사소통적 접근을 통해 조사하였다. 이 연구의 자료는 설문, 수업 관찰, 그리고 인터뷰를 통해 수집되었다. 연구의 결과는 강사들이 도함수와 미분계수의 관계, 함수로써 의 도함수 등 미분의 성질들을 명백히 서술함 없이 사용한다는 것과 학생들의 문제 풀이에 있어 이런 성질들을 부정확하게 서술하고 사용한다는 것을 보여준다. 미분에 관한 교사들의 암묵적인 담화와 학생들의 부정확한 설명은 그들이 용어, "미분"을 "미분계수" 혹은 "도함수"로 구분하지 않고 사용한다는 사실과 밀접한 관련이 있는 것으로 밝혀졌다. 강사와 학생의 담화 비교는 분명한 용어 사용을 포함한 미분의 수학적인 성질에 대한 명백히 설명이 학생들이 도함수의 한 값으로의 미분계수를 이해하는 것과 접선과 같은 도함수의 부정확한 개념을 극복하는 데 도움을 줄 수 있음을 암시한다.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.335-344
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• 2015

In the paper we discuss the value distribution of the product of the derivative of a transcendental meromorphic function and a power of the function.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• 대한수학회논문집
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• 제33권2호
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.