• Communications of Mathematical Education
• /
• v.29 no.1
• /
• pp.91-110
• /
• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.167-174
• /
• 2010

In this paper, we investigate the possibility of $2{\pi}$-periodic continuous function approximation by periodic neural networks. Using the Riemann sum and the quadrature formula, we show the capability of a periodic neural network approximation.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.18 no.4
• /
• pp.549-560
• /
• 1993

A simple closed form approximation is developed by a new approach presented in this paper for the microstrip surface dyadic Green's function which arises in the problem of an electric current point source on an infinite planar grounded dielectric substrate. This closed form approximation includes the effects of the space wave, the surface wave and their coupling within the transition region near the source, and remains accurate as near as $0.1{\pi}_1$ from the source point for a substrate thickness as large as $0.04{\pi}_1$, where, ${\pi}_1$, is the free space wavelength, This result can significantly facilitate the rigorous moment method analysis of microstrip antenna arrays on relatively this substrates of practical interest. Numerical results illustrating the accuracy of the closed form approximation are presented and CPU times associated with some mutual impedance calculations are also included.

• Korean Journal of Mathematics
• /
• v.22 no.2
• /
• pp.307-315
• /
• 2014

We investigate an approximation order of a continuous $2{\pi}$-periodic function by periodic neural networks. By using the De La Vall$\acute{e}$e Poussin sum and the modulus of continuity, we obtain a degree of approximation by periodic neural networks.

• Journal of Advanced Marine Engineering and Technology
• /
• v.26 no.2
• /
• pp.219-225
• /
• 2002

Parameter tuning methods by Ziegler-Nichols for PID controllers are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between the methods of Z-N(1) and Z-N(2), or how Z-N(1) can be originated from Z-N(2) by analyzing one loop control system composing of P or PI controller and time delay process. In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into those composing of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.1
• /
• pp.251-268
• /
• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• Journal of the Korean Chemical Society
• /
• v.16 no.3
• /
• pp.119-134
• /
• 1972

Various MO methods with differing degrees of sophistication are shown to yield qualitatively consistent results for methyl isoalloxazins. However, with crude methods such as the HMO and ${\omega}$-technique, the choice of Coulomb and resonance integralsis critical, in contrast with simpler molecular systems. The empirical value of ${\omega}$=0.5 appears to be more reasonable than 1.4. Methyl groups in these flaving are best treated by the group orbital approximation. The pseudo-heteroatom approximation overestimates methyl hyperconfiguration with the Pariser-Parrpole SCR MO method. siglet ${\pi}{\rightarrow}{\pi}^*$ transition energies are calculated by the P-P-P method and agree reasonably with the experimental values. 2- and 4-Thioisoalloxazine analogs are also treated. Reactivity indices of the flavin molecule are presented, includeing superdelocalizability. frontier orbital and radical densities. Various aspects of the applications of these indices of the methyl groups on dipolemoments, inozation potentialsm elctron affinities, and spectra are decribed in detail.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.4
• /
• pp.831-841
• /
• 2017

The irrational number ${\pi}$ is defined as the ratio of circumference of a circle to its radius and always becomes constant. This article does Monte Carlo approximation of its value using the famous Buffon's needle experiment and shows that its convergence is not always proportional to the sample size. We also do Monte Carlo simulations to see the convergence of the computed ${\pi}$ values from the random walk series with independent normal increment. Finally we apply the theoretical derivation to various financial time series data such as KOSPI, stock prices of Korean big firms, global stock indices and major foreign exchange rates. The historical data shows that log transformed data random walk process but most of their first lagged data don't follow a normal distribution. More importantly the computed value from the ratio of the regression coefficient ${\pi}$ tend to converge a constant, unfortunately not ${\pi}$. Using this result we could doubt on the efficient market hypothesis, and relate the degree of the hypothesis with the amount of deviation of the estimated ${\pi}$ values.

• Journal of the Korean Chemical Society
• /
• v.63 no.2
• /
• pp.73-77
• /
• 2019

We compared methodologies based on the density functional theory (DFT), e.g., time-dependent DFT (TD-DFT), TD-DFT within Tamm-Dancoff approximation (TDA-DFT), and spin-unrestricted DFT (UDFT), that are usually employed to optimize the geometries of ${\pi}$-conjugated molecules in their lowest lying triplet excited ($T_1$) state. As a model system for ${\pi}$-conjugated molecules, we employed 1,2,3,4,5-pentacyano-6-phenyl-benzene. In conjunction with 6-31G(d) basis sets, we made use of gap-tuned range-separated ${\omega}B97X$ functional which is often employed recently in the calculations of molecular excited states. Near the equilibrium geometries, we found that the important difference between the geometries derived at UDFT level and those at TD-DFT or TDA-DFT methods: more stable ground-state energies but higher triplet excitation energies for UDFT derived geometries. In the studies, we discuss such differences in more detail.

• Journal of Educational Research in Mathematics
• /
• v.27 no.4
• /
• pp.811-831
• /
• 2017

The purpose of this study is to analyze the contents of pi of Chosun-sanhak and organize the teaching and learning activities to help to understand the concept of pi deeply using the analysis results. The results of this study are as follows. First, Chosun-sanhak used various approximate values of pi and those were represented as the form to reveal the meaning of the ratio of radius and circumference. Second, There were the freedom of selection of the approximate values of pi suitably. Lastly, the enriched leaning about pi need to draw a distinction pi from approximate values of pi, choose the suitable approximate values of pi and compare the method of calculation of circumference and the area of circle of Chosun-sanhak and today's mathematics. In conclusion, I proposed several issues which is worth exploring further in relation to pi and Chosun-Sanhak.