• 충청수학회지
• /
• 제3권1호
• /
• pp.63-68
• /
• 1990

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

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권1호
• /
• pp.65-74
• /
• 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.

• 대한수학회논문집
• /
• 제37권2호
• /
• pp.503-520
• /
• 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.

• 호남수학학술지
• /
• 제37권4호
• /
• pp.559-567
• /
• 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.

• 약학회지
• /
• 제30권2호
• /
• pp.100-103
• /
• 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.

• 전기전자학회논문지
• /
• 제23권3호
• /
• pp.817-825
• /
• 2019

마이크로프로세서를 이용한 제어알고리즘 구현에서 차분방정식이 매우 유용하게 사용된다. 샘플링 데이터로부터 미분 값을 추정하기 위해 전향, 후향 및 중심 차분 방식이 사용되어왔다. 차분 값을 계산하기 위해서는 차분계수가 매우 중요하다. 본 논문에서는 유한 차분 계수를 계산하기 위한 새로운 방식을 제시하고자 한다. 제안된 방식의 유효성을 입증하기 위해 RLS 알고리즘을 적용한 파라미터 추정에 대하여 적용하였다.

• Steel and Composite Structures
• /
• 제21권6호
• /
• pp.1389-1410
• /
• 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
• /
• 제37권6호
• /
• pp.591-597
• /
• 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.

• 한국식생활문화학회지
• /
• 제24권2호
• /
• pp.212-218
• /
• 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.

• 대한화학회지
• /
• 제37권1호
• /
• pp.112-118
• /
• 1993

수용성 발색시약인 N,N'-oxalylbis(2-pyridyl-3'-sulphobenzoylhydrazone)을 합성하여 분광광도법 및 1, 2차 미분 분광광도법에 의한 구리의 정량법을 개발하였다. 정량은 구리착물 수용액(pH 1.89)의 흡광도 및 1,2차 미분값을 379, 395, 363 그리고 421nm의 파장에서 각각 측정함으로써 수행되었다. 정량 가능한 구리의 농도 범위는 0.12~1.20${\mu}g$ /ml 였으며 이 방법을 알루미늄 합금시료의 분석에 적용하였다. 2차 미분 분광광도법으로 421nm에서 측정했을 때가 가장 좋은 결과를 나타내었다.