• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.63-68
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• 1990

In this paper, we give the Radon-Nikodym derivative of a measure taking values in a dual Banach space.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.65-74
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• 2015

In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.503-520
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• 2022

We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.559-567
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• 2015

This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.

• YAKHAK HOEJI
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• v.30 no.2
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• pp.100-103
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• 1986

The second derivative absorption spectra of acetaminophen in commercial tablet forms were measured without prior separation from other pharmaceutical adjuvants. The second derivative spectra of acetaminophen were found to have no influence on the characteristic absorbance band of it. A plot of 25 sets of the ordinate (Z) values with various acetaminophen concentrations mixed in other additives gave a straight line (correlation coefficient, 0.9999) and the slope was 2.901${\times}10^{-2}Z$ value/($\mu\textrm{g}$/ml). The procedures were sufficiently sensitive, precise and economical for the assay of tablets of acetaminophen.

• Journal of IKEEE
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• v.23 no.3
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• pp.817-825
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• 2019

Difference equation is useful for control algorithm in the microprocessor. To approximate a derivative values from sampled data, it is used the methods of forward, backward and central differences. The key of computing discrete derivative values is the finite difference coefficient. The focus of this paper is a new approach method of finite difference formula. And we apply the proposed method to the recursive least squares(RLS) algorithm.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1389-1410
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• 2016

This paper proposes a hybrid of topological derivative-based level set method (LSM) and isogeometric analysis (IGA) for structural topology optimization. In topology optimization a significant drawback of the conventional LSM is that it cannot create new holes in the design domain. In this study, the topological derivative approach is used to create new holes in appropriate places of the design domain, and alleviate the strong dependency of the optimal topology on the initial design. Furthermore, the values of the gradient vector in Hamilton-Jacobi equation in the conventional LSM are replaced with a Delta function. In the topology optimization procedure IGA based on Non-Uniform Rational B-Spline (NURBS) functions is utilized to overcome the drawbacks in the conventional finite element method (FEM) based topology optimization approaches. Several numerical examples are provided to confirm the computational efficiency and robustness of the proposed method in comparison with derivative-based LSM and FEM.

• Geomechanics and Engineering
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• v.37 no.6
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• pp.591-597
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• 2024

The purpose of this paper is to depict the effect of gravity on a nonlocal thermoelastic medium with initial stress. The Lord-Shulman and Green-Lindsay theories with fractional derivative order serve as the foundation for the formulation of the fundamental equations for the problem. To address the problem and acquire the exact expressions of physical fields, appropriate non-dimensional variables and normal mode analysis are used. MATLAB software is used for numerical calculations. The projected outcomes in the presence and absence of the gravitational field, along with a nonlocal parameter, are compared. Additional comparisons are made for various fractional derivative order values. It is evident that the variation of physical variables is significantly influenced by the fractional derivative order, nonlocal parameter and gravity field.

• Journal of the Korean Society of Food Culture
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• v.24 no.2
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• pp.212-218
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• 2009

This study was carried out to determine the quality characteristics of Jeju mandarin orange jellies containing sugar (control) and sugar derivative sweeteners (erythritol, isomaltooligosaccharide, sorbitol, and xylitol) to be consumed by the elderly. The gelling agents were carrageenan and gellan gum at the concentration of 0.27%, respectively. The average age of the subjects for the acceptance test was 78. The lightness (L), redness (a), and yellowness (b) values of the carrageenan gel were higher than those of the gellan gum gel using the same sugars. The L, a, and b values of the carrageenan gel made with sugar derivative sweeteners were higher than those of the respective gel made with sugar. Whereas there were almost no differences between the color values of the gellan gum gels made with sugar and sugar derivative sweeteners, respectively. The gelling and melting temperatures of the carrageenan gel with erythritol were highest and those of the respective gel with xylitol were lowest among the sugar derivative sweeteners. The gelling and melting temperatures of the gellan gum gels with erythritol and isomaltooligosaccharide, respectively, were lower, and those of the respective gel made with xylitol were higher compared to that with sugar. There was no break down in the gellan gum gel. The break down rate of the carrageenan gel made with isomaltooligosaccharide was highest and that of the respective gel with xylitol was lowest among the sugar derivative sweeteners. The hardness, adhesiveness, springiness, and chewiness of the gellan gum gel were greater compared to the carrageenan gel. The adhesiveness levels of the carrageenan gels made with sugar derivative sweeteners were lower, and their springiness was higher than the respective gel with sugar. All the TPA characteristics of the gellan gum gels made with erythritol and xylitol, respectively, were higher than the respective gel with sugar. The rupture properties of the gels were the same as their TPA characteristics. The sensory acceptance of the carrageenan and gellan gum gels made with sugar were highest among all the sweeteners. There were no significant differences in the sensory acceptance scores of the carrageenan gels made with xylitol, erythritol, and sugar, respectively, and there were also no significant differences in the sensory acceptance scores of the gellan gum gels made with xylitol, sorbitol, and sugar, respectively. Xylitol was preferred in both the carrageenan and gellan gum gels. Thus, xylitol appears to be an appropriate alternative sweetener to sugar in Jeju mandarin orange jelly for consumption by the elderly, with regard to the acceptability and stability of the gel.

• Journal of the Korean Chemical Society
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• v.37 no.1
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• pp.112-118
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• 1993

A water-soluble chromogenic reagent, N,N'-oxalylbis(2-pyridyl-3'-sulphobenzoylhydrazone) has been synthesized. Spectrophotometric and first-and second-derivative spectrophotometric methods for the determination of copper with the reagent have been developed. Determination has been performed by measuring the absorbance and the first-and second-derivative values of the copper complexes in aqueous solutions (pH 1.89) at 379, 395, 363 and 421 nm, respectively. The method allows the determination of 0.12-1.20 ${\mu}g$ /ml of copper and has been applied to the analysis of aluminium alloy samples. The best results have been obtained from the measurements of the second-derivative values at 421 nm.