• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.257-273
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• 2010

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

• Bulletin of the Korean Chemical Society
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• v.34 no.11
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• pp.3391-3398
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• 2013

The carboxylated multiwall carbon nanotubes (MWCNT-COOH) and functionalized with isatin derivative (MWCNT-isatin) have been used as efficient adsorbents for the removal of lead (Pb) from aqueous solutions. The influence of variables including pH, concentration of the lead, amount of adsorbents and contact time was investigated by the batch method. The adsorption of the lead ions from aqueous solution by modified MWCNTs was studied kinetically using different kinetic models. The kinetic data were fitted with pseudo-first-order, pseudo-second-order, and intra-particle diffusion models. The sorption process with MWCNT-COOH and MWCNT-isatin was well described by pseudo-second-order and pseudo-first-order kinetics, respectively which it was agreed well with the experimental data. Also, it involved the particle-diffusion mechanism. The values of regression coefficient of various adsorption isotherm models like Langmuir, Freundlich and Tempkin to obtain the characteristic parameters of each model have been carried out. The Langmuir isotherm was found to best represent the measured sorption data for both adsorbent.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.513-523
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• 2015

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2001.11a
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• pp.169-172
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• 2001

There are many people who suffer from simulation sickness when immersing in virtual reality. In this study, we analyzed two photoplethysmogram(PPG) parameters - a second derivative parameter and power spectral density ratios - in order to relate PPG parameters with simulation sickness. 36 young, healthy subjects were participated in the experiment, and each subject was equipped with a PPG electrode during his or her immersion. Simulation sickness section was defined as a 7 - second section which starts from the point where a subject reported simulation sickness, and normal section as a same-length section where no physical stimuli was presented to him or her. We compared the PPG parameters of the simulation sickness sections with the normal sections, - d/a ratio is believed to have lower value during vasodilation and higher value during vasoconstriction, however, we could not find much difference in the parameter between normal and simulation sickness sections. We also compared 1 to 10Hz power spectral density ratios in normal sections with in simulation sickness section, and found that 6 density ratios among them have different value. Therefore, the density ratios might be utilized as parameters to detect simulation sickness of subjects.

• Journal of Advanced Marine Engineering and Technology
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• v.30 no.7
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• pp.791-799
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• 2006

The aim of this paper is to design an adaptive speed control system of a marine diesel engine by fusion of hard computing based proportional integral derivative (PID) control and soft computing based fuzzy control methods. The model of a marine diesel engine is considered as a typical non oscillatory second order system. When its model and the actual marine diesel engine ate not matched, it is hard to control the speed of the marine diesel engine. Therefore, this paper proposes two methods in order to obtain the speed control characteristics of a marine diesel engine. One is an efficient method to determine the PID control parameters of the nominal model of a marine diesel engine. Second is a reference adaptive speed control method that uses a fuzzy controller and derivative operator for tracking the nominal model of the marine diesel engine. It was found that the proposed PID parameters adjustment method is better than the Ziegler & Nichols' method, and that a model reference adaptive control is superior to using only PID controller. The improved control method proposed here, could be applied to other systems when a model of a system does not match the actual system.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.335-350
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• 2016

Based on the notion of $q_k$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

• Journal of Powder Materials
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• v.30 no.1
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• pp.29-34
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• 2023

A fixed-point iteration is proposed to integrate the stress and state variables in the incremental analysis of plastic deformation. The Conventional Newton-Raphson method requires a second-order derivative of the yield function to generate a complicated code, and the convergence cannot be guaranteed beforehand. The proposed fixed-point iteration does not require a second-order derivative of the yield function, and convergence is ensured for a given strain increment. The fixed-point iteration is easier to implement, and the computational time is shortened compared with the Newton-Raphson method. The plane-stress condition is considered for the biaxial loading conditions to confirm the convergence of the fixed-point iteration. 3-dimensional tensile specimen is considered to compare the computational times in the ABAQUS/explicit finite element analysis.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.10
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• pp.974-981
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• 2009

In this paper, a method of auto-tuning of PID (Proportional-Integral-Derivative) and PIDA (Proportional-Integral-Derivative-Acceleration) controllers is proposed that can be applied to a time-delayed second order model. The proposed identification method is based on step responses, but it can be easily automated rising digital controller unlike the existing graphical identification methods. We provide a ways to yield parameter identifications which is independent to initial values of the plants. The tuning rule is based on the pole-placement strategy and is formulated so that it can be implemented using a digital controller with ease.

• Korean Journal of Food Science and Technology
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• v.24 no.5
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• pp.408-413
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• 1992

This study was conducted to determine the effect of the homogenizing grade of sample on absorbance of near infrared reflectance spectrophotometer with which chemical compositions of food were rapidly and effectively analyzed. By the mathematical treatment of absorbance values standard error of prediction was reduced as follows. 1. The absorbance values of various samples ground for the same periods of time were calibrated before or after treatment with first or second derivative in an attempt to accurately predict the components of samples ground for the different periods of time. The standard error of prediction for moisture content were 1.478%, 0.658% and 0.580%, respectively, those for fat content 0.949%, 0.637% and 0.527%, respectively, and those for protein content 0.514%, 0.493% and 0.394%, respectively. Calibration of absorbance values after second derivative treatment showed the highest accuracy in predicting sample components. 2. The absorbance values of various samples ground for the different periods of time were calibrated before or after treatment with first or second derivative in order to accurately predict the components of samples ground for the different periods of time. The standard error of prediction for moisture content were 1.026%, 0.589% and 0.568%, respectively, and those for protein content 0.860%, 0.557% and 0.399%, respectively. The standard error of prediction were lower in the order of calibrations before and after first and second derivative treatments. As a result, calibration of absorbance values after second derivative treatment showed higher accuracy regardless of grinding time of samples.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.165-167
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• 2008

본 논문에서는 기존의 에지 추출 알고리즘을 비교하여 알고리즘이 영상 처리 과정에 미치는 영향을 분석하였다. 기존의 에지 추출 알고리즘인 Sobel, Prewitt, Roberts 등을 비교 분석 한 뒤 1차 미분 조건에 2차 미분의 단점을 보완한 에지 추출 마스크 방식을 제안한다.