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self-similar Cantor 집합의 spectrum 곡선에 관한 고찰
백인수 부산 외국어 대학교 2002 外大論叢 Vol.25-2 No.-
We survey the recent results about multi-fractal of a self-similar Cantor set. We also survey our recent results about multi-fractal spectra of self-similar Cantor set induced by self-similar probability measures and its distribution sets and study their set-theoreti4 relationship. We use some spectrum curve to study them. As a comparison of our results with those of Olsen and Falconer, we show our method to compute a subset composing a multi-fractal is much easier than those of Olsen and Falconer. Finally we give some conjecture related to a generalization of our result for a self-similar set.
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POWER INEQUALITY ON THE SIMPLEX
백인수 충청수학회 2012 충청수학회지 Vol.25 No.2
The power inequality QN k=1 xxk k QN k=1 pxk k holds for the points (x1; :::; xN),(p1; :::; pN) of the simplex. We show this using the analytic method combining Frostman's density theorem with the strong law of large numbers.
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백인수,Luc Mongeau,James E. Braun 대한기계학회 2010 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.24 No.9
The performance of a working prototype, operated with and without water flow through the heat exchangers, was measured and found to be in reasonably close agreement to predictions from a simulation code, DELTAE, based on linear thermoacoustic theory. Further analysis and DELTAE simulations showed that the coefficient of performance may be significantly reduced when the stack temperature profile becomes non-linear, i.e. when the system is operated for a temperature span smaller than the optimal value for a given stack length. Guidelines to avoid this condition are provided.
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Topological Magnitude of a Special Subset in a Self-similar Cantor Set
백인수 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.1
We study the topological magnitude of a special subset from the distri-bution subsets in a self-similar Cantor set. The special subset whose very elementhas no acumulation point of a frequency sequence as ome num ber elated to thesimilarity dimension of the self-similar Cantor set is of the rst category in theself-similar Cantor set.
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백인수 釜山 外國語 大學校 1999 外大論叢 Vol.19 No.4
Many teachers are dubious about their abilities to teach the students well even though they had good achievements in their grades when they were students in their university. There is a gap between their knowledge that they learned in the university and the contents which they should teach in the middle school. In this note, we will give some bridge between them. This bridge can help the teachers understand the real numbers well and find the insight in the contents of real number-related topics in mathematics in the middle school. We introduce why the comprehension of real number is necessary to teach the contents of real number-related topics in mathermatics in the middle school. First we explain the real number system using line. We also study the fundamental axioms in the real number system. Secondarily, we give an approach to construct the set of real numbers. We start it from the construction of the set of natural numbers using the Peano axioms. At last, we give some points of which teachers should take care when they teach the real number-related fields.
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백인수 부산 외국어 대학교 2003 外大論叢 Vol.27 No.-
We construct diagrams to explain relations between the subset in the distribution class and the subset in the spectra classes on a self-similar Cantor set. Using these diagrams, we easily understand the relationships among the subsets in the spectral classes determined by a self-similar measure on a self-similar Cantor set and its lower or upper local dimensions. Finally we add some useful results of relationships among them in the diagrams.
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백인수,Paek, In-Su 한국음향학회 2009 韓國音響學會誌 Vol.28 No.1
정재파 열음향 냉각기의 스텍에서의 온도 구배와 냉각기 효율의 관계에 대한 연구를 수행하였다. 스택에서의 로트식 (Rott Equation) 을 이용하여, 스택을 통과하는 엔탈피 플럭스의 크기가 크게 되면, 스택에서의 온도구배가 비선형의 특성을 나타내는 것을 밝혀내었다. 또한 이런 비선형의 스택 온도구배가 열음향 냉각기의 냉각 효율을 저하시키는 것을 확인하였다. 1/4 파장의 정재파 열음향 냉각기를 이용한 시뮬레이션을 통해, 특정길이의 스택에 대해 냉각 용량이 커질수록, 또한 특정냉각 용량에 대해, 스택의 길이가 길어질수록 비선형의 스택 온도구배가 크게 일어남을 알아낼 수 있었다. Investigations of the relation between the stack temperature profile of a standing wave thermoacoustic cooler and the cooling efficiency were performed. Based on the mathematical derivations using the Rott Equation, it was found that the temperature profile along the stack becomes nonlinear as the enthalpy flux passing through the stack increases. It was also found that such nonlinear temperature profiles lower the cooling efficiency. Simulations using a thermoacoustic simulation program called DELTAE showed that the nonlinear temperature profile occurs with a long stack and large cooling load.
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백인수 부산외국어대학교 교육대학원 1999 敎育論叢 Vol.- No.-
Many teachers are dubious about their abilities to teach the students well even though they had good achievements in their grades when they were students in their university. There is a gap between their knowledge that they learned in the university and the contents which they should teach in the middle school. In this note, we will give some bridge between them. This bridge can help the teachers understand the equations well and find the insight in the contents of equation-related topics in mathematics in the middle school. We introduce why the comprehension of equations is necessary to teach the contents of equation-related topics in mathematics in the middle school. First we explain the equations using the unknown letters in the expression of equality with some purpose. Secondarily, we study a well-known method to solve simultaneous equations. The method uses necessary conditions to obtain the solutions of the simultaneous equations. We compare the set of solutions with the set generated by the necessary conditions. At last, we suggest some teaching method which the teacher should consider when they teach the equation-related fields.
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