• 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.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.75-87
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• 2002

The shape derivative for the domain functional will be discussed in the situation of domain inclusion. Hadamard's shape structure is sought by using the material derivative in conjunction with the domain imbedding technique.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.255-265
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• 2016

In this paper, we define and study the delta alpha derivative on time scales. Many basic properties of delta alpha derivative will be obtained.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.33-55
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• 2011

This study explores the characteristics of calculus students' and instructors' discourses on the derivative using a communicational approach to cognition. The data were collected from surveys, classroom observations, and interviews. The results show that the instructors did not explicitly address some aspects of the derivative such as the relationship between the derivative function (f'(x)) and the derivative at a point (f'(a)), and f'(x) as a function, and that students incorrectly described or used these aspects for problem solving. It is also found that both implicitness in the instructors' discourse, and students' incorrect descriptions were closely related to their use of the word, "derivative" without specifying it as "the derivative function" or "the derivative at a point." Comparison between instructors' and students' discourses suggests that explicit discussion about the derivative including exact use of terms will help students see the relationship that f'(a) is a number, a point-specific value of f'(x) that is a function, and overcome their mixed and incorrect notion "the derivative" such as the tangent line at a point.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.343-353
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• 2021

In this paper, we obtain some inequalities concerning the class of generalized derivative and generalized polar derivative which are analogous respectively to the ordinary derivative and polar derivative of polynomials.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.21-29
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• 2006

The method to construct a surface from point data are widely known. But the way to make a surface from derivative data is not usually used since derivative data in engineering appears very often. In this paper, if more than one types of data among three possible data such as point data, first derivative data, second derivative data are given, we can construct a surface. If only first derivative data are given, we add a function value at the one point. If only second derivative data are given, we add a linear function.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.1
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• pp.272-287
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• 2017

This paper proposes new methods, named Derivative Code (DerivativeCode) and Derivative Code Pattern (DCP), for object recognition. The discriminative derivative code is used to capture the local relationship in the input image by concatenating binary results of the mathematical derivative value. Gabor based DerivativeCode is directly used to solve the palmprint recognition problem, which achieves a much better performance than the state-of-art results on the PolyU palmprint database. A new local pattern method, named Derivative Code Pattern (DCP), is further introduced to calculate the local pattern feature based on Dervativecode for object recognition. Similar to local binary pattern (LBP), DCP can be further combined with Gabor features and modeled by spatial histogram. To evaluate the performance of DCP and Gabor-DCP, we test them on the FERET and PolyU infrared face databases, and experimental results show that the proposed method achieves a better result than LBP and some state-of-the-arts.

• The Journal of Korean Medicine
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• v.19 no.1
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• pp.145-164
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• 1998

The purpose of this study is to evaluate the effect of Injinchunggantang-derivative on proliferation of hepatocyte in rats. Cell viability is studied by MTI assay. The gene related to cell replication such as p53, waf1, bcl-2 and $bcl-_{X_L}$ is quantitized by quantitative RT-PCR and the proteins coded by these genes are studied by Western blotting. The results are as follows. 1. The hepatocytes cultured in medium with lnjinchunggantang-derivative showed better viability compared with control grroup in MTI assay, and the hepatocytes cultured in medium with the Injinchunggantang-derivative-and-ethanol-mixed group showed better viability than the hepatocytes cultrued in 10% ethanol culture medium(control group), noting that Injinchunggantang-derivative has protective effect on hepatocyte injury. There was no dose- and time-dependence. 2. In quantitative RT-PCR, i) Bel-2 gene increased significantly both in Injinchunggantang-derivative group and in Injinchunggantang-derivative-and-ethanol-mixed group, while it showed no significant increase or decrease in other group. ii) $Bcl-_{X_L}$ gene increased significantly in Injinchunggantang-derivative group as well as in Injinchunggantang-deri vative-and-ethanol -mixed group. iii) P53 gene showed no significant increase or decrease in hepatocytes cultured in medium with 10% ethanol and in hepatocytes cultured in medium with Injinchunggantang-derivative-and-ethanol-mixed group, suggesting that 10% ethanol induced cell toxicity, thus increased p53 gene expression. iv) Wafl gene showed no significant increase or decrease in hepatocytes cutured in medium with Injinchtrnggantang-derivative, while increased in hepatocytes cultured in medium with 10% ethanol and in hepatocytes cultured in medium with Injinchtrnggantang-derivative-andethanol-mixed group, suggesting that 10% ethanol induced cell toxicity increased wafl gene expression. 3. In the study on protein by western blotting, the band of bcl-2 and $bcl-_{X_L}$ were widened in Injinchtrnggantang-derivative group. Especially the amount of $bcl-_{X_L}$ increased significantly compared with other groups. But in the study on p53 and wafl, there was no significant difference among those groups. Above study shows that Injinchunggantang-derivative has good effect on cell viability and that the genes resistant to cell death such as bcl-2 and $bcl-_{X_L}$ are induced by Injinchunggantang-derivative to resist to cell death by toxic agent And this is reconfirmed in protein study using' western blotting: These results suggest that Injinchunggantang-derivative has inhibitory effect on cell death as well as protective effect on hepatocyte. Therefore this prescription is recommended in various liver diseases such as chronic liver disease and-induced hepatic injury.

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.331-348
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• 2012

With a gradual increase in research on teaching and learning calculus, there have been various studies about students' thinking about the derivative. This paper reviews the results of the existing empirical studies published in Korean and English. These studies mainly have shown that how students think about the derivative is related to their understanding of the related concepts and the representations of the derivative. There are also recent studies that emphasize the importance of how students learn the derivative including different applications of the derivative in different disciplines. However, the current literature rarely addressed how students think about the derivative in terms of the language differences, e.g., in Korean and English. The different terms for the derivative at a point and the derivative of a function, which shows the relation between concepts, may be closely related to students' thinking of the derivative as a function. Future study on this topic may expand our understanding on the role language-specific terms play in students' learning of mathematical concepts.

• The Journal of Korean Medicine
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• v.19 no.2
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• pp.337-372
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• 1998

To evaluate the effects of Injinchunggantang-derivative on cell viability, cell cycle progression, and apoptosis, MTT assay, cell cycle analysis, Cpp32 protease assay, DNA fragnemtation assay, quantitative RT-PCR, and Western blotting were performed. The results were as followes. In MTT assay, etoposide+Injinchunggantang-derivative-treated cells as well as Injinchunggantang-derivative-treated cells showed higher viability than etoposide-treated cells with no time-concentration-dependence, which implied that Injinchunggantang-derivative has hepato-protective effect Cell cycle analysis showed that Injinchunggantang-derivative has no significant effect on the cell cycle. Cpp32 protease assav and DNA fragmentation assay Injinchunggantang-derivative carry inhibitory effects on apoptosis induction. It was suggested that Injinchunggantang-delivative might regulate the cell cycle, in particular $G_1$ checkpoint by blocking p53 and Watl pathway. Injinchunggantang-derivative inhibited the mRNA expressions of Cpp32, Fas, and Bcl-2, which could result in inhibition of apoptosis. These results imply that Injinchunggantang-derivative increases hepatocyte viability, and protects hepatocyte from damage by regulating the expression of genes associated with cell cycle and apoptosis, which explains the mechanism of the clinical effect of Injinchunggantang-derivative on liver diseases.