• 대한수학회보
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• 제51권1호
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제26권3호
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• pp.253-270
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• 2023

This study aims to investigate the extent to which Korean high school textbooks incorporate opportunities for students to engage in the mathematical modeling process through tasks related to exponential and logarithmic functions. The tasks in three textbooks were analyzed based on the actions required for each stage in the mathematical modeling process, which includes identifying essential variables, formulating models, performing operations, interpreting results, and validating the outcomes. The study identified 324 units across the three textbooks, and the reliability coefficient was 0.869, indicating a high level of agreement in the coding process. The analysis revealed that the distribution of tasks requiring engagement in each of the five stages was similar in all three textbooks, reflecting the 2015 revised curriculum and national curriculum system. Among the 324 analyzed tasks, the highest proportion of the units required performing operations found in the mathematical modeling process. The findings suggest a need to include high-quality tasks that allow students to experience the entire process of mathematical modeling and to acknowledge the limitations of textbooks in providing appropriate opportunities for mathematical modeling with a heavy emphasis on performing operations. These results provide implications for the development of mathematical modeling activities and the reconstruction of textbook tasks in school mathematics, emphasizing the need to enhance opportunities for students to engage in mathematical modeling tasks and for teachers to provide support for students in the tasks.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• 한국정보통신학회논문지
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• 제26권2호
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• pp.325-328
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• 2022

A convolutional neural network(CNN) is widely used in the computer vision tasks, but its computing power requirement needs a design of a special circuit. Most of the computations in a CNN can be implemented efficiently in a digital circuit, but the SoftMax layer has operations unsuitable for circuit implementation, which are exponential and logarithmic functions. This paper proposes a new method to integrate the exponential and logarithmic tables of the conventional circuits into a single table. The proposed structure accesses a look-up table (LUT) only with a few maximum values, and the LUT has the result value directly. Our proposed method significantly reduces the space complexity of the SoftMax layer circuit implementation. But our resulting circuit is comparable to the original baseline with small degradation in precision.

• 대한수학회보
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• 제49권1호
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제7권3호
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• pp.191-209
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• 2003

In this paper, we present a new environment of learning and teaching of trigonometric, exponential and logarithmic functions, the most difficult parts for students to learn among functions, through sound and music, students like the most. First, by using sound and music, we try to arouse student's interest. Second, we let students see and hear properties of transcendental functions so that students can understand and remember them easily. Finally we encourage students to compose their favorite song using transcendental functions so that they can experience the practicality of transcendental functions.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.95-111
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• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• Structural Engineering and Mechanics
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• 제86권5호
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• pp.621-633
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• 2023

Stability analysis and support system estimation of the Beheshtabad water transmission tunnel is investigated in this research. A combination approach based on the rock mass rating (RMR) and rock mass quality index (Q) is used for this purpose. In the first step, 40 datasets related to the petrological, structural, hydrological, physical, and mechanical properties of tunnel host rocks are measured in the field and laboratory. Then, RMR, Q, and height of influenced zone above the tunnel roof are computed and sorted into five general groups to analyze the tunnel stability and determine its support system. Accordingly, tunnel stand-up time, rock load, and required support system are estimated for five sorted rock groups. In addition, various empirical relations between RMR and Q i.e., linear, exponential, logarithmic, and power functions are developed using the analysis of variance (ANOVA). Based on the significance level (sig.), determination coefficient (R²) and Fisher-test (F) indices, power and logarithmic equations are proposed as the optimum relations between RMR and Q. To validate the proposed relations, their results are compared with the results of previous similar equations by using the variance account for (VAF), root mean square error (RMSE), mean absolute percentage error (MAPE) and mean absolute error (MAE) indices. Comparison results showed that the accuracy of proposed RMR-Q relations is better than the previous similar relations and their outputs are more consistent with actual data. Therefore, they can be practically utilized in designing the tunneling projects with an acceptable level of accuracy and reliability.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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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.

• Structural Engineering and Mechanics
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• 제89권1호
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• pp.1-11
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• 2024

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.