• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.449-472
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• 2015

Let X be a nonempty set and $\mathcal{F}$(X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics ${\tau}:\mathcal{F}(X){\rightarrow}\mathbb{R}$ recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets A with ${\mid}A{\mid}{\leqslant}n$ make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters $diam_{{\tau}^n}$ and find conditions under which $B{\mapsto}diam_{{\tau}^n}B$ is a Balk's metric. We prove the necessary and sufficient conditions under which the restriction ${\tau}$ to the set of $A{\in}\mathcal{F}(X)$ with ${\mid}A{\mid}{\leqslant}3$ is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed.

• 공학교육연구
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• 제16권2호
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• pp.24-30
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• 2013

This paper deals with the measurement theory and technique of linear expansion coefficient for solid material using Michelson interferometer. The Michelson interferometer produces interference fringes by splitting a beam of monochromatic light so that one beam strikes a fixed mirror and the other a movable mirror. When the reflected beams are brought back together, an interference pattern results. Precise distance measurements until a quarter of wave length can be made with the Michelson interferometer by moving the mirror and counting the interference fringes which move by a photo diode. This paper represents the application of Michelson interferometer for measuring infinitesimal length system and shows the measurement method of linear expansion coefficients for various materials like copper, aluminum and iron. the results are good agreement with theoretical value within margin of error for each materials.

• 한국수학사학회지
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• 제29권3호
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• pp.157-172
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• 2016

Sophus Lie's research is regarded as one of the most important mathematical advancements in the $19^{th}$ century. His pioneering research in the field of differential equations resulted in an invaluable consolidation of calculus and group theory. Lie's group theory has been investigated and constantly modified by various mathematicians which resulted in a beautifully abstract yet concrete theory. However Lie's early intentions and ideas are lost in the mists of modern transfiguration. In this paper we explore Lie's early academic years and his object of studies which clarify the ground breaking ideas behind his theory.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 학술대회 논문집 전문대학교육위원
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• pp.20-23
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• 2001

This paper presents a novel design approach composed of two sequential processes for 3D magnetic shielding problems, which results in the global optimum solution in a shorter time. The feature of the proposed approach is the adoption of the specific boundary element with permeability of infinity. Assuming the permeability of infinity enables us to regard the thickness of ferromagnetic shields as infinitesimal, and thus to simplify the investigated model adequately in numerical analysis. This reduces the number of unknown variables and saves us a large amount of CPU-time for grasping the broad characteristics of the model. Some numerical results that demonstrate the validity of the proposed approach are also presented.

• 설비공학논문집
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• 제14권6호
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• pp.512-518
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• 2002

The real chip and similarity model were used to investigate the thermal behavior and velocity distribution of air from the heat source with the location and the amount of heat experimentally and numerically, and compared. The heat generated in the block is not cooled by convection and show the high temperature by the stagnation of heat flow. After maintaining the high temperature of block by the natural convection, the sudden drop of temperature with the air flow was shown in the channel but the decreasing rate was small with the time. The inward block was effected by infinitesimal air flow generated between block and channel and outward block was effected by the entry condition.

• 동력기계공학회지
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• 제14권5호
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• pp.71-75
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• 2010

Leak detection technology is a challenging research until nowadays, because it has wide and various applications in industry. Furthermore pneumatic component reliability test based on ISO requires air leakage measurement. The conventional measurement methods need a complex operation and the calibration of leak detector. Tracing the history of our study, we proposed a new method for measurement of leak flow rate using isothermal chamber. In this study, propose a simulation model of isothermal chamber by infinitesimal flow -rate, such as a leak flow-rate. The effectiveness of the proposed simulation model is proved by simulation and experimental results. Base on the comparison results, proposed simulation model is good agreement with experimental results.

• 충청수학회지
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• 제14권1호
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• pp.21-28
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• 2001

In this paper we show that the following results remain valid for arbitrary Jordan derivations as well: Let d be a derivation of a complex Banach algebra A. If $d^2(x){\in}rad(A)$ for all $x{\in}A$, then we have $d(A){\subseteq}rad(A)$ ([5, p. 243]), and in a case when A is unital, $d(A){\subseteq}rad(A)$ if and only if sup{$r(z^{-1}d(z)){\mid}z{\in}A$ invertible} < ${\infty}$([3]), where rad(A) stands for the Jacobson radical of A, and r(${\cdot}$) for the spectral radius.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2006년도 하계종합학술대회
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• pp.183-184
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• 2006

The simulation on the mechanism of terahertz NSOM(near-field scanning optical microscopy) have been investigated. Based on experimental results, we have demonstrated the antenna effects on the coupling between a metal tip and substrate for an emission-type terahertz NSOM. It has been found that the lateral resolution can be estimated by a simplified model using an infinitesimal dipole in the substrate.

• 한국통신학회논문지
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• 제21권10호
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• pp.2703-2709
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• 1996

This paper proposes an exact numerical method for analyzing a dipole antenna attached on a dielectric slab. A Green's function for an infinitesimal current filament on a dielectric slab is derived and a field integral equation is formulated using a boundary condition. The moment Method is used to solve the field integral equation to otain current distribution on the antenna. Since an asymptotic function is used to compute the impedance matrix elements, the computataion time is significantly reduced. Using the computed current distributions, the input impedances, the resonance lengths and the resonant resistances of the antennas for various values of the thichnessandthe dielectric constant of the slab are obtained. It was found that the resonant length and the resonant resistance are decrease monotonically as the dielectric constant increases, however, those are changed up-and-down as the substrate thickness increases.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 추계학술발표대회 논문집
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• pp.128-133
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• 2000

The objective of this research is to develop real-time failure detection techniques for damage assessment of composite materials using optical fiber sensors. Signals from matrix cracking or fiber fracture in composite laminates are treated by signal processing unit in real-time. This paper describes the implementation of time-frequency analysis such as the Short Time Fourier Transform(STFT) to determine the time of occurrence of failure. In order to verify the performance of the optical fiber sensor for stress wave detection, we performed pencil break test with EFPI sensor and compared it with that of PZT. The EFPI sensor was embedded in composite beam to sense the failure signals and a tensile test was performed. The signals of the fiber optic sensor when damage occurred were characterized using STFT and wavelet transform. Failure detection system detected the moment of failure accurately and showed good sensitivity with the infinitesimal failure signal.