• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.453-474
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• 1998

This study is focused on the possibility if we can use graphic calculators in teaching and learning school mathematics. This study is consisted with four main chapters. In chapter II, the functions of the graphic calculator EL-9600 produced by Sharp Corporation was analyzed focused on the possibilities if the functions could be used in teaching and learning school mathematics. Calculating of real numbers and complex numbers, solving equations and system of linear equations, calculating of matrices, graphing of several functions including polynomial functions, trigonometric functions, exponential and logarithmic functions, calculation of differential and integrals, arranging of statical data, graphing of statistical data, testing of statistical hypotheses, and other more useful functions were founded. In Chapter III, a mathematics textbook developed by Core-Plus Mathematics Project was analyzed focused on how a graphic calculator was used in teaching and learning mathematics, In the textbook, graphic calculator was used as a tool in understanding mathematical concepts and solving problems. Graphic calculator is not just a tool to do complex computations but a tool used in the processes of doing mathematics, In chapter IV, the 7th mathematics curriculum for korean secondary schools was analyzed to find the contents could be taught by using graphic calculators. Most of the domains, except geometric figure, were found that they could be taught by using graphic calculators, In chapter V, a model of a unit using graphic calculator in teaching 7th mathematics curriculum was developed. In this model, graphic calculator was used as a tool in the processes of understanding mathematical concepts and solving problems. This study suggests the possibilities that we can use graphic calculators effectively in teaching and learning mathematical concepts and problem solving for most domains of secondary school mathematics.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.5
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• pp.1123-1131
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• 1996

Several improved quadrature polar separable (QPS) filters have been proposed and applied in texture processing since Knutsson proposed the QPS filter. They include a Knutsson's cosine function or oan exponential attenuation function, as the orientational function, and a Knutsson's exponential function or a finite prolate spheroidal sequence (FPSS) or an asymptotic FPSS, as the radial weighting functions. They represent different properties in terms of the generation of texture images, the orientational estimation, and the segmentation of synthetic texture image. In this paper, we have constructed several kernal functions for the 2-D QPS filter and analyzed their properties. A series of experiments have been carried out in order to estimate the frequency components and orientational angles of a local texture in Fourier domain. finally some problems encountered in applying QPS filters to feature description and segmentation are considered. Experimental results show that the improved Knutsson's filter and the asymptotic FPSS filter are useful in terms of the orientational estimation and the sementation of synthetic texture image.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.475-485
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• 2017

This paper develops a conversion function and method transforming from daily peak load curve used $LOLE_D$ [days/year] to hourly load curve used $LOLE_H$[hours/year]and describes relationship between $LOLE_D$ [days/year] and $LOLE_H$ [hours/year]. The indices can not only be transformed just arithmetically but also have different characteristics physically because of using their different load curves. The conversion function is formulated as variables of capacity and forced outage rate of generator, hourly load daily load factor and daily peak load yearly load factor, etc. Therefore, the conversion function (${\gamma}={\varphi}$(.)) can not be simple. In this study, therefore, the function is formulated as linear times of separated two functions. One is an exponential formed conversion function of daily load factor. Another is formulated with an exponential typed conversion function of daily peak load yearly load factor. Futhermore, this paper presents algorithm and flow chart for transforming from $LOLE_D$[days/year] to $LOLE_H$[hours/year]. The proposed conversion function is applied to sample system and actual KPS(Korea Power System) in 2015. The exponent coefficients of the conversion functions are assessed using proposed method. Finally, assessment errors using conversion function for case studies of sample system and actual system are evaluated to certify the firstly proposed method.

• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.283-302
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• 2007

It is said that the university mathematics education in Korea faces critical situations due to the decreases of both qualities and quantities of students. In this paper we examine college students in order to know their basic ability for understanding about fundamental functions, such as polynomial, trigonometric, logarithm and exponential functions which have learned from highschool mathematics courses. The subject are 354 freshmen of 4 universities located in Daejeon and Chongchung area. The result of this study shows as follows. i ) More than half students are not able to draw graphs of given functions, except polynomial. ii ) More students do not fully understand about function properties such as domain, codomain, range, max and min value, cycle and parallel translation.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.527-542
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• 2005

The main objective of this study is to examine the accuracy of the complete quadratic combination (CQC) rule with the modal responses defined by the ordinates of the uniform hazard spectra (UHS) to evaluate the peak responses of the multi-degree-of-freedom (MDOF) systems subjected to nonstationary seismic excitations. For the probabilistic analysis of the peak responses, it is considered that the seismic excitations can be modeled using evolutionary power spectra density functions with uncertain model parameters. More specifically, a seismological model and the Kanai-Tajimi model with the boxcar or the exponential modulating functions were used to define the evolutionary power spectral density functions in this study. A set of UHS was obtained based on the probabilistic analysis of transient responses of single-degree-of-freedom systems subjected to the seismic excitations. The results of probabilistic analysis of the peak responses of MDOF systems were obtained, and compared with the peak responses calculated by using the CQC rule with the modal responses given by the UHS. The comparison seemed to indicate that the use of the CQC rule with the commonly employed correlation coefficient and the peak modal responses from the UHS could lead to significant under- or over-estimation when contributions from each of the modes are similarly significant.

• Journal of Advanced Navigation Technology
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• v.18 no.1
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• pp.78-83
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• 2014

In this paper, the solutions of TM (transverse magnetic) scattering problems by perfectly conducting strip grating on two dielectric layers are analyzed by applying the FGMM (Fourier Galerkin moment method) as a numerical method. For the TM scattering problem, the induced surface current density is expected to the very high value at both edges of the strip, then the induced surface current density on the strip is expanded in a series of the multiplication of the functions of appropriate edge boundary condition and the Chebyshev polynomials of the first kind. The numerical results are obtained for the magnitude of induced current density, the normalized reflected power and transmitted power. The numerical results using proposed functions were improved the convergence faster than existing exponential functions, and the numerical results shown the good agreement compared to those of the existing papers.

• Tunnel and Underground Space
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• v.26 no.2
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• pp.100-109
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• 2016

This study suggests three spatial distribution functions of strength parameters, which can be adopted in the derivation of failure conditions for transversely isotropic rocks. All three proposed functions, which are the oblate spheroidal function, the exponential function, and the function based on the directional projection of the strength parameter tensor, consist of two model parameters. With assumption that the cohesion and friction angle can be described by the proposed distribution functions, the transversely isotropic Mohr-Coulomb criterion is formulated and used as a failure condition in the simulation of the conventional triaxial tests. The simulation results confirm that the failure criteria incorporating the proposed distribution functions could reproduce the general trend in the variations of the axial stress at failure and the directions of failure planes with varying inclination of the weankness planes and confining pressure. Among three distribution functions, the function based on the directional projection of the strength parameter tensor yields the highest axial strength, while the axial strength estimated by the oblate spheroidal distribution function is the lowest.

• Journal of The Korean Society of Agricultural Engineers
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• v.63 no.1
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• pp.103-116
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• 2021

Analysis of runoff is substantial for effective water management in the watershed. Runoff occurs by reaction of a watershed to the rainfall and has non-linearity and uncertainty due to the complex relation of weather and watershed factors. ANN (Artificial Neural Network), which learns from the data, is one of the machine learning technique known as a proper model to interpret non-linear data. The performance of ANN is affected by the ANN's structure, the number of hidden layer nodes, learning rate, and activation function. Especially, the activation function has a role to deliver the information entered and decides the way of making output. Therefore, It is important to apply appropriate activation functions according to the problem to solve. In this paper, ANN models were constructed to estimate runoff with different activation functions and each model was compared and evaluated. Sigmoid, Hyperbolic tangent, ReLU (Rectified Linear Unit), ELU (Exponential Linear Unit) functions were applied to the hidden layer, and Identity, ReLU, Softplus functions applied to the output layer. The statistical parameters including coefficient of determination, NSE (Nash and Sutcliffe Efficiency), NSEln (modified NSE), and PBIAS (Percent BIAS) were utilized to evaluate the ANN models. From the result, applications of Hyperbolic tangent function and ELU function to the hidden layer and Identity function to the output layer show competent performance rather than other functions which demonstrated the function selection in the ANN structure can affect the performance of ANN.

• Journal of Life Science
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• v.10 no.1
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• pp.40-44
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• 2000

The SNF2/SW ATPase/helicase family comprises proteins form a variety of species with in vivo functions, such as transcriptional regulation, maintenance of chromosome stability during mitosis, and various types of DNA repair. Here, we reported the characterization of h게2+gene which was iolated by PCR amplification using the conserved domain of SNF2 motifs. Sequence analysis of PCR product showed striking evolutionary conservation among the SNF2 family of proteins. Two transcripts of 6.7 and 3.4 Lb were detected by Northern blot analysis. furthermore, the intensities of these two bands were increased by ultraviolet(UV) irradiation. These results indicate that the hrp2+ is a novel member of the SNF2 family of proteins and is one of the UV-inducible genes in S. pombe. To determine the level of transcripts of hrp2+ gene during cellular growth, Northern blot analysis were performed. This result indicates that the level of hrp2+transcript reached its maximum before cells entered the exponential growth phase. This suggests that hrp2+ gene is experssed mainly at the early stage of cell growth.