• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.593-605
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• 2002

Explicit hounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.295-305
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• 2008

This paper demonstrates how composite-exponential-fitting interpolation rules can be constructed to fit an oscillatory function using not only pointwise values of that function but also of that functions's derivative on a closed and bounded interval of interest. This is done in the framework of exponential-fitting techniques. These rules extend the classical composite cubic Hermite interpolating polynomials in the sense that they become the classical composite polynomials as a parameter tends to zero. Some examples are provided to compare the newly constructed rules with the classical composite cubic Hermite interpolating polynomials (or recently developed interpolation rules).

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.125-131
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• 2005

In this paper, we introduce the concept of derivative of the function f : $\mathbb{Q}p{\to} R$ where $\mathbb{Q}p$ is the field of the p-adic numbers and R is the set of real numbers. And some basic theorems on derivatives are given.

• Korean Journal of Soil Science and Fertilizer
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• v.47 no.5
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• pp.319-323
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• 2014

This study investigates the prediction of soil chemical properties (organic matter (OM), pH, Ca, Mg, K, Na, total acidity, cation exchange capacity (CEC)) on 688 Korean soil samples using the visible-near infrared reflectance (VIS-NIR) spectroscopy. Reflectance from the visible to near-infrared spectrum (350 to 2500 nm) was acquired using the ASD Field Spec Pro. A total of 688 soil samples from 168 soil profiles were collected from 2009 to 2011. The spectra were resampled to 10 nm spacing and converted to the 1st derivative of absorbance (log (1/R)), which was used for predicting soil chemical properties. Principal components analysis (PCA), partial least squares regression (PLSR) and regression rules model (Cubist) were applied to predict soil chemical properties. The regression rules model (Cubist) showed the best results among these, with lower error on the calibration data. For quantitatively determining OM, total acidity, CEC, a VIS-NIR spectroscopy could be used as a routine method if the estimation quality is more improved.

• Korean Journal of Soil Science and Fertilizer
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• v.45 no.4
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• pp.497-502
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• 2012

This study investigates the prediction of soil OM on Korean soils using the Visible-Near Infrared (Vis-NIR) spectroscopy. The ASD Field Spec Pro was used to acquire the reflectance of soil samples to visible to near-infrared radiation (350 to 2500 nm). A total of 503 soil samples from 61 Korean soil series were scanned using the instrument and OM was measured using the Walkley and Black method. For data analysis, the spectra were resampled from 500-2450 nm with 4 nm spacing and converted to the $1^{st}$ derivative of absorbance (log (1/R)). Partial least squares regression (PLSR) and regression rules model (Cubist) were applied to predict soil OM. Regression rules model estimates the target value by building conditional rules, and each rule contains a linear expression predicting OM from selected absorbance values. The regression rules model was shown to give a better prediction compared to PLSR. Although the prediction for Andisols had a larger error, soil order was not found to be useful in stratifying the prediction model. The stratification used by Cubist was mainly based on absorbance at wavelengths of 850 and 2320 nm, which corresponds to the organic absorption bands. These results showed that there could be more information on soil properties useful to classify or group OM data from Korean soils. In conclusion, this study shows it is possible to develop good prediction model of OM from Korean soils and provide data to reexamine the existing prediction models for more accurate prediction.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.185-205
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• 2013

In this study, to begin with, it was discussed to gather vocabularies which are expected to be vocabularies related to four fundamental rules of arithmetic and classify them according to kinds and groups, to demarcate vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics which are associated with addition, subtraction, multiplication, and division directly. Next, the basic vocabularies related to four fundamental rules of arithmetic were discussed. At this time, regarding vocabularies related addition, subtraction, multiplication, and division as coming from the verb add, subtract, multiply, divide respectively, vocabularies that contains the stem of each verb were considered as the basic vocabularies related to four fundamental rules of arithmetics. Following it, vocabularies which assist the operation and indicate the result of the operation were included, then, vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics were demarcated and presented according to the following criteria. First, a newly coined verb or derivative using the noun form of a certain verb as a root should not be used. Second, such vocabularies of which examples do not exist or rarely exist in textbooks/workbooks should not be used, even though they are registered in mathematics glossary book published by ministry of education or Korean dictionary published by the national institute of Korean language. Third, vocabularies which are not replaceable and vocabularies which have some didactical reasons for using them should be used.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.231-242
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• 2023

A novel combinatorial type-2 adaptive neuro-fuzzy inference system (T2-ANFIS) and robust proportional integral derivative (PID) control framework for intelligent vibration mitigation of uncertain structural system is introduced. The fuzzy logic controllers (FLCs), are designed independently of the mathematical model of the system. The type-1 FLCs, have a limited ability to reduce the effect of uncertainty, due to their fuzzy sets with a crisp degree of membership. In real applications, the consequent part of the fuzzy rules is uncertain. The type-2 FLCs, are robust to the fuzzy rules and the process parameters due to the fuzzy degree of membership functions and footprint of uncertainty (FOU). The adaptivity of the proposed method is provided with the optimum tuning of the parameters using the neural network training algorithms. In our approach, the PID control force is obtained using the generalized type-2 neuro-fuzzy in such a way that the stability and robustness of the controller are guaranteed. The robust performance and stability of the presented framework are demonstrated in a numerical study for an eleven-story seismically-excited building structure combined with an active tuned mass damper (ATMD). The results indicate that the introduced type-2 neuro-fuzzy PID control scheme is effective to attenuate plant states in the presence of the structured and unstructured uncertainties, compared to the conventional, type-1 FLC, type-2 FLC, and type-1 neuro-fuzzy PID controllers.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.103-106
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• 1996

This paper presents an iterative fuzzy learning control scheme which is applicable to a broad class of nonlinear systems. The control scheme achieves system stability and boundedness by using the linear feedback plus adaptive fuzzy controller and achieves precise tracking by using the iterative learning rules. The switching mode control unit is added to the adaptive fuzzy controller in order to compensate for the error that has been inevitably introduced from the fuzzy approximation of the nonlinear part. It also obviates any supervisory control action in the adaptive fuzzy controller which normally requires high gain signal. The learning control algorithm obviates any output derivative terms which are vulnerable to noise.

• Journal of Korean Society of Transportation
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• v.8 no.1
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• pp.17-24
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• 1990

The first-best pricing rule which achieves economic efficiency is to equate price with marginal cost. Since public transport demand is derived from some other demand, the user cost as well as the producer cost are considered in its pricing. The optimal price is derived from a derivative of the total social cost with respect to demand. In case of the bus, if there is enough capacity for demand increase, the optimal price is determined by the marginal producer cost resulting from bus sped decrease and by the marginal user cost resulting from journey time increase. Both are caused by boarding and fare collecting time of an additional passenger. Because of the budget constraints, the marginal cost pricing cannot be applied in practice. Then price discrimination as the second-best pricing is introduced. The Ramsey pricing, to charge different prices for different demand elasticities, and nonuniform prices such as travelcards can be applied. However, there is practical difficulty in implementing these prices because of great informational requirements, the costs of administration and the ease to users.