• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• Journal of Information Science Theory and Practice
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• v.1 no.3
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• pp.6-11
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• 2013

A new explanation, using exponential functions, is given for the S-shaped functional relation between the mean citation score and the proportion of top 10% (and other percentages) publications for the 500 Leiden Ranking universities. With this new model we again obtain an explanation for the concave or convex relation between the proportion of top $100{\theta}%$ publications, for different fractions of ${\theta}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• Korean Journal of Heritage: History & Science
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• v.39
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• pp.281-314
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• 2006

Several explanations exist about the usage of disk-shaped bronze implements in the ancient society. Some argue that they were used as mirrors, others suggest percussion instruments, and still others bronze ornaments. Differences between disk-shaped bronze implements and mirrors with multiple knobs are that the former have no visible design, only one handle, and a sharp curvature unlike the latter with smooth curvature. The question is whether disk-shaped bronze implements excavated from Korean peninsula have any light reflecting function. To answer this question, I carefully studied the concave surfaces of disk-shaped bronze implements excavated from Goejeong-dong, Tongso-ri and Hapsong-ri sites. The main findings are as follows: (1) The concave sides of the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites were highly polished, and they were as reflective as bronze mirrors. (2) The concave side of the disk-shaped bronze implement from Hapsong-ri site was unpolished, and it was different from bronze mirrors. (3) As for the convex sides of the disk-shaped bronze implements, they did not appear to have been polished with care. Considering the above findings, the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites belong to the stage where they could act as both mirrors and instruments. On the contrary, the disk-shaped bronze implement from Hapsong-ri site can belong to the stage where it lost the function of being a mirror as the result of maintaining only its function as an instrument. Even though disk-shaped implements had two functions, it can be considered that the light reflecting function expanded the role of a mirror with multiple knobs and the sound function helped the engraved round bronze implement to be converted into an eight-armed bronze rattle. Since it has been reported that shamans used bronze mirrors as percussion instruments in their performances in Korean peninsula and Siberia, I propose a reconsideration of the usage of mirrors in the ancient East Asia. Although the essential function of a mirror is to reflect light, other possible usages involving important functions need to be further investigated.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.113-120
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• 2006

This paper proposed the control algorithm fur aspheric surface grinding and was verified by the experiment. The functions of the algorithm were simultaneous control of the position and interpolation of the aspheric curve. The non-linear formula of the tool position was derived from the aspheric equations and the shape of the tool. The function was partitioned by an certain interval and the control parameters were calculated at each control section. The movement in a session was interpolated with acceleration and velocity. The position error was feed-backed by rotary encorder. The concept of feedback algorithm was correcting position error by increasing or decreasing the speed. In the experiment, two-axis machine was controlled to track the aspheric surface by the proposed algorithm. The effect of the control and process parameters was monitored. The result showed that the maximum tracking error was under sub-micro level for the concave and convex surfaces.

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.259-264
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• 2000

The functions of the plug valve are the control of flow rate as well closing and opening pipe lines. Analyses on the flow characteristics in plug valve port are required to improve the performance and safety at severe operating conditions such as high-pressure and high-temperature. In this study, numerical analyses are carried out with varying the opening rate (fraction of the full open to close) of the valve and the shapes of valve Uk: straight, convex, concave and mixed shapes. The parameters influencing the flow characteristics in the valve are the discharge coefficient( $C_v$) and the resistance coefficient( K). Therefore, the distributions of static pressure, velocity vector and stream lines are investigated, and $C_v$ and K are calculated in each opening rate and shape. In case of full open, the static pressure passed through the valve port has almost been recovered. However, in case of other opening rates, the pressure does not permanently regained due to pressure drop leading to loss. This phenomenon in each shape of the valve shows the different behaviors. Calculation results show that the mixed shape has the best flow attribute.

• Earthquakes and Structures
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• v.14 no.6
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• pp.589-598
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• 2018

An attempt is conducted to explore the relationship between the macroscopic global damage and the local damage of shear-type RC frames. A story damage index, which can be expressed as multi-variate functions of modal parameters, is deduced based on the tridiagonal matrix of the shear-type frame. The global damage model is also originated from structural modal parameters. Due to the connection of modal damage indexes, the relationship between the macroscopic global damage and the local story damage is reasonably established. In order to validate the derivation, a case study is carried out via an 8-story shear-type frame. The sensitivities of modal damage indexes to the location and severity of local story damages are studied. The evolution of the global damage is investigated as well. Results show that the global damage is sensitive to the degree of story damage, but it's not sensitive to its location. As the number of the damaged stories increases, more and more modes will be involved. Meanwhile, the global damage evolution curve changes from the concave shape to the S-type and then finally transforms into the convex shape. Through the proposed story damage, modal damage and global damage model, a multi-level damage assessment method is established.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.4
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• pp.199-204
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• 2021

In this study, an isogoemetric analysis (IGA) method that uses NURBS (Non-Uniform Rational B-Spline) basis functions in computer-aided design (CAD) systems is employed to account for the geometric exactness of curved electrodes constituting an electro-adhesive pad in electrostatic problems. The IGA is advantageous for obtaining precise normal vectors when computing the electro-adhesive forces on curved surfaces. By performing parametric studies using numerical examples, we demonstrate the superior performance of the curved electrodes, which is attributed to the increase in the normal component of the electro-adhesive forces. In addition, concave curved electrodes exhibit better performance than their convex counterparts.