• Journal of applied mathematics & informatics
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• v.24 no.1_2
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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 $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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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 the Korean Statistical Society
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• v.35 no.2
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.179-202
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• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.753-762
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• 2014

A three-step sextic simple-root finder is constructed with the use of weighting functions of derivative-to-derivative ratios. Their convergence and computational properties are investigated along with concrete numerical examples to verify the theoretical analysis.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.77-82
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• 1980

There are many definitions of the fractional derivative. It is purpose of this paper to show some results which were got for fractional partial derivative of functions of two variables and to give an application of the fractional partial derivative.

• The Journal of Korean Medicine
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• v.23 no.1
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• pp.133-144
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• 2002

Objectives : Korean traditional medicinal herbs have been used to improve the function of the hematopoietic system. The purpose of this study is to examine the hematopoietic effects of Juakium-derivative on aplastic anemia. Methods : In vitro, after bone marrow cells of mice with aplastic anemia induced by benzene were cultured with Juakium-derivative, we measured the gene expressions of hematopoietic cytokines, the intracellular TPO and SCF expression and the colony number of CFU-GEMM and BFU-E. Results : The results are summarized as follows : 1. The gene expressions of hematopoietic cytokines (TPO, c-mpl, SCF, c-kit, IL-3, EPO, EpoR, GM-CSF) and the TPO and SCF expression of the group treated with Juakium-derivative increased significantly more than those of the control group. 2. The colony number of CFU-GEMM and BFU-E in the rEPO plus rIL-3 plus Juakium-derivative group increased significantly compared with the only rEPO plus rIL-3 group. Conclusion : It was acknowledged that Juakium-derivative has hemato-potentiating effects on aplastic anemia induced by benzene and it is expected that Juakium-derivative can be used clinically for the patient with hematopoietic system disorder. This study could also be used further as important research data for Korean oriental medicine about hemato-potentiating. The exact mechanism explaining our study would need to be studied further.

• Journal of the Korean Statistical Society
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• v.30 no.3
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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.

• Tribology and Lubricants
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• v.26 no.5
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• pp.272-276
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• 2010

Aminated oilve oil derivative as the new organic disperse phases of the water soluble metal working fluid has been synthesized and tribological properties of the aqueous solutions composed of aminated olive oil derivative investigated using Four Ball Wear Tester and Falex EP Tester. The formulated aqueous solutions showed higher antiwear and extreme pressure properties and also lower friction coefficient. On the basis of the the results, water soluble aminated oilve oil derivative showed excellent tribological properties due to the polarizability of oleic acid derivative composed of majority part in oilve oil.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1621-1630
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• 2015

In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.