• 대한수학회지
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• 제41권6호
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• pp.945-955
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• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2015년도 학술발표회
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• pp.218-218
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• 2015

Urbanization and waterworks construction in natural watershed have been causing higher flood risks in lowland areas. Detention basins have become one of the most efficient fundamental instruments for storm water and environmental management at watershed scale. Nowadays, there are many studies coupled numerical methods of flood routing with optimization algorithms to investigate factors that impact on the efficiency of detention basins in flood reduction in a watershed, such as detention basin location, size, and cost and watershed characteristics. Although these couplings have been become more widespread but cumbersome computation and hydraulic data requirement still are their limitations. To tackle the procedure efforts due to numerical integration and data collection, simple approach is proposed to primarily estimate effects of detention basins. The approach basis is the linear system theory applied to the solution of hydrologic flood routing. The paper introduces an analytical method for estimating detention effects deriving by recent studies and innovatively analyses this equation on fractal perspective. Then, an optimization technique is performed by applying harmony search algorithms (HSA) to optimize efficiency of detention basins at watershed scale. The location and size of upstream detention basin are simultaneously obtained. Finally, the proposed methodology, practically applied for a real watershed in Kan river, Iran.

• 과학기술학연구
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• 제3권2호
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• pp.1-27
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• 2003

이 논문은 최근 자연과학 분야에서는 물론이요 사회과학과 더불어 인문예술 영역에 이르는 방대한 학문 영역에서 영향력을 행사하고 있는 복잡계 패러다임의 특성과 전망을 고찰하고자 한 것이다. 흔히 '전체론적 세계관'이라든가 '심층생태학적 관점' 등으로 대변되는 복잡성 패러다임은 개방체계적 사고의 연장선상에 위치한 것으로서, 일차적으로는 개방성, 성장성, 가형성, 否(부)의 엔트로피, 적극적 환류, 자기규제성, 자기목적성, 등종착성과 같은 개방체계적 속성을 함유한다. 그러나 지난 20여 년간 학제적 경계를 초월해 활발히 진전된 복잡계론은 종전의 개방체계론적 논의 수준을 넘어서는 새로운 착상이나 증거를 지속적으로 축적해 온 바, 여기서는 (1) 복잡계 이론이 형성되고 발전되어온 전개과정을 간략히 개관하고, (2) 비평형성, 비선형성, 소산구조 자기조직성, 프랙탈 기하학, 자동생산성 및 공진화와 같은 복잡계의 주요 특성들을 논의하며, (3) 니클라스 루만의 체계이론을 사례로 복잡계 패러다임의 사회과학적 적용을 검토한 후, (4) 복잡계 패러다임의 함의와 전망을 진단해 보고자 한다.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2007년도 추계 종합학술대회 논문집
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• pp.889-893
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• 2007

현재 다양한 연구에서는 유체인 안개의 자연스런 표현을 위해 프랙탈과 카오스 이론을 적용한다. 이러한 연구로 적용할 수 있는 전문 툴들을 사용하는 것은 자연스러운 표현이 가능하기 때문이다. 그러나, 일반인은 이러한 것을 아직 쉽게 표현하기는 매우 어려운데 그것은 고비용과 전문가들을 필요로 하기 때문이다. 따라서 누구나 어렵고 복잡한 고가의 전문툴들과 전문적으로 프로그래밍 제작을 최소로 한 안개의 표현을 쉽게 할수 있도록 하는 것이 일반적인 과제들이다. 본 연구는 이러한 2D 이미지에 대한 유체의 표현연구를 구체화하는 것으로 다양한 이미지 표현이 전문방송에서 개인에 이르는 UCC까지 가능하도록 쉽게 구현하였다. 특히, 이 연구는 3D 공간에서 안개의 유체적인 표현이 가능하기 때문에 한국화를 3D와 같이 표현할 때 배경에 안개의 표현을 쉽게 할 수 있도록 하였다.

• 한국표면공학회지
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• 제53권3호
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• pp.116-123
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• 2020

Ion beam irradiation induces self-organization of nanostructure on the surface of polymer film. We show that the incident angle of Ar ions on polyethylene naphthalate(PEN) film changes self-organized nanostructure. PEN film was irradiated by argon ion beams with the ion incident angle of 0°, 30°, 45°, 60°, and 80°. Nanostructure was altered from dimple to ripple structure as the angle increases. The ripple structure changed to pillar structure after 60°due to that the shallow incident angle increased the ion energy transfer per depth up to 50 eV/Å, which value could induce excessive surface heating and oligomer formation reacting as a physical mask for anisotropic etching. And quantitative analysis of the nanostructures was adapted by using ABC model and fractal dimension theory.

• Structural Engineering and Mechanics
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• 제83권3호
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• pp.341-351
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• 2022

During bolted flange assembly, the contact stiffness of some areas of the joint surface may be low due to the elastic interaction. In order to improve the contact stiffness at the lowest position of bolted flange, the correlation model between the initial bolt pre-tightening force and the contact stiffness of bolted flange is established in this paper. According to the stress distribution model of a single bolt, an assumption of uniform local contact stiffness of bolted flange is made. Moreover, the joint surface is divided into the compressive stress region and the elastic interaction region. Based on the fractal contact theory, the relationship model of contact stiffness and contact force of the joint surface is proposed. Considering the elastic interaction coefficient method, the correlation model of the initial bolt pre-tightening force and the contact stiffness of bolted flange is established. This model can be employed to reverse determine the tightening strategy of the bolt group according to working conditions. As a result, this provides a new idea for the digital design of tightening strategy of bolt group for contact stiffness of bolted flange. The tightening strategy of the bolted flange is optimized by using the correlation model of initial bolt pre-tightening force and the contact stiffness of bolted flange. After optimization, the average contact stiffness of the joint surface increased by 5%, and the minimum contact stiffness increased by 6%.

• Geomechanics and Engineering
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• 제30권5호
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• pp.401-411
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• 2022

To obtain the dynamic mechanical properties, fracture modes, energy and brittleness characteristics of Furong Baijiao coal rock, the dynamic impact compression tests under 0, 4, 8 and 12 MPa confining pressure were carried out using the split Hopkinson pressure bar. The results show that failure mode of coal rock in uniaxial state is axial splitting failure, while it is mainly compression-shear failure with tensile failure in triaxial state. With strain rate and confining pressure increasing, compressive strength and peak strain increase, average fragmentation increases and fractal dimension decreases. Based on energy dissipation theory, the dissipated energy density of coal rock increases gradually with growing confining pressure, but it has little correlation with strain rate. Considering progressive destruction process of coal rock, damage variable was defined as the ratio of dissipated energy density to total absorbed energy density. The maximum damage rate was obtained by deriving damage variable to reflect its maximum failure severity, then a brittleness index BD was established based on the maximum damage rate. BD value declined gradually as confining pressure and strain rate increase, indicating the decrease of brittleness and destruction degree. When confining pressure rises to 12 MPa, brittleness index and average fragmentation gradually stabilize, which shows confining pressure growing cannot cause continuous damage. Finally, integrating dynamic deformation and destruction process of coal rock and according to its final failure characteristics under different confining pressures, BD value is used to classify the brittleness into four grades.

• 한국데이타베이스학회:학술대회논문집
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• 한국데이타베이스학회 1999년도 춘계공동학술대회: 지식경영과 지식공학
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• pp.175-186
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• 1999

Detecting the features of significant patterns from their own historical data is so much crucial to good performance specially in time-series forecasting. Recently, a new data filtering method (or multi-scale decomposition) such as wavelet analysis is considered more useful for handling the time-series that contain strong quasi-cyclical components than other methods. The reason is that wavelet analysis theoretically makes much better local information according to different time intervals from the filtered data. Wavelets can process information effectively at different scales. This implies inherent support fer multiresolution analysis, which correlates with time series that exhibit self-similar behavior across different time scales. The specific local properties of wavelets can for example be particularly useful to describe signals with sharp spiky, discontinuous or fractal structure in financial markets based on chaos theory and also allows the removal of noise-dependent high frequencies, while conserving the signal bearing high frequency terms of the signal. To date, the existing studies related to wavelet analysis are increasingly being applied to many different fields. In this study, we focus on several wavelet thresholding criteria or techniques to support multi-signal decomposition methods for financial time series forecasting and apply to forecast Korean Won / U.S. Dollar currency market as a case study. One of the most important problems that has to be solved with the application of the filtering is the correct choice of the filter types and the filter parameters. If the threshold is too small or too large then the wavelet shrinkage estimator will tend to overfit or underfit the data. It is often selected arbitrarily or by adopting a certain theoretical or statistical criteria. Recently, new and versatile techniques have been introduced related to that problem. Our study is to analyze thresholding or filtering methods based on wavelet analysis that use multi-signal decomposition algorithms within the neural network architectures specially in complex financial markets. Secondly, through the comparison with different filtering techniques' results we introduce the present different filtering criteria of wavelet analysis to support the neural network learning optimization and analyze the critical issues related to the optimal filter design problems in wavelet analysis. That is, those issues include finding the optimal filter parameter to extract significant input features for the forecasting model. Finally, from existing theory or experimental viewpoint concerning the criteria of wavelets thresholding parameters we propose the design of the optimal wavelet for representing a given signal useful in forecasting models, specially a well known neural network models.

• 한국지능정보시스템학회:학술대회논문집
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• 한국지능정보시스템학회 1999년도 춘계공동학술대회-지식경영과 지식공학
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• pp.175-186
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• 1999

Detecting the features of significant patterns from their own historical data is so much crucial to good performance specially in time-series forecasting. Recently, a new data filtering method (or multi-scale decomposition) such as wavelet analysis is considered more useful for handling the time-series that contain strong quasi-cyclical components than other methods. The reason is that wavelet analysis theoretically makes much better local information according to different time intervals from the filtered data. Wavelets can process information effectively at different scales. This implies inherent support for multiresolution analysis, which correlates with time series that exhibit self-similar behavior across different time scales. The specific local properties of wavelets can for example be particularly useful to describe signals with sharp spiky, discontinuous or fractal structure in financial markets based on chaos theory and also allows the removal of noise-dependent high frequencies, while conserving the signal bearing high frequency terms of the signal. To data, the existing studies related to wavelet analysis are increasingly being applied to many different fields. In this study, we focus on several wavelet thresholding criteria or techniques to support multi-signal decomposition methods for financial time series forecasting and apply to forecast Korean Won / U.S. Dollar currency market as a case study. One of the most important problems that has to be solved with the application of the filtering is the correct choice of the filter types and the filter parameters. If the threshold is too small or too large then the wavelet shrinkage estimator will tend to overfit or underfit the data. It is often selected arbitrarily or by adopting a certain theoretical or statistical criteria. Recently, new and versatile techniques have been introduced related to that problem. Our study is to analyze thresholding or filtering methods based on wavelet analysis that use multi-signal decomposition algorithms within the neural network architectures specially in complex financial markets. Secondly, through the comparison with different filtering techniques results we introduce the present different filtering criteria of wavelet analysis to support the neural network learning optimization and analyze the critical issues related to the optimal filter design problems in wavelet analysis. That is, those issues include finding the optimal filter parameter to extract significant input features for the forecasting model. Finally, from existing theory or experimental viewpoint concerning the criteria of wavelets thresholding parameters we propose the design of the optimal wavelet for representing a given signal useful in forecasting models, specially a well known neural network models.

• 자원환경지질
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• 제27권6호
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• pp.557-561
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• 1994

Quality factor Q 값은 처음 도착(倒着)한 P파(波)의 주기당(週期當) 에너지 손실(損失)을 주파수(周波數)의 함수(函數)로 직접(直接) 측정(測定)할 수 있다. 이때 관심(關心)의 대상(對象)이 되는 주파수대(周波數帶)(주로 1-100 Hz)내(內)에서 고유(固有) Q는 주파수(周波數)와 무관(無關)하고, 산란(散亂) Q는 주파수(周波數)와 밀접(密接)한 관계(關係)가 있다는 가정하(假定下)에 고유(固有) Q값과 산란(散亂) Q값의 전체(全體) Q값에 대(對)한 상대적(相對的)인 비솔(比率)을 계산(計算)할 수 있다. 이에 대(對)한 검증(檢證)은 탄성파(彈性波)가 점탄성(粘彈性)이고 부균질(不均質)한 매질(媒質)을 통과(通過)할 때의 합성탄성파(合成彈性波) 기록지(記錄紙)를 만들고 고유(固有) Q에 대(對)해서는 완화기구(緩和機具)(relaxation mechanism)가, 산란(散亂) Q에 대(對)해서는 산란(散亂)(satter)에 대(對)한 fractal 분포(分布)가 포함(包含)되는 pseudospectral 해(解)를 이용(利用)하여 실시(實施)될 수 있다. 대체로 S파(波)의 전체(全體) Q값이 P파(波)의 전체(全體) Q값보다 더 작다는 것이 정설(定說)로 되어있다. 역(逆)으로, 전체(全體) Q값은 합성탄성파(合成彈性波) 기록지(記錄紙)로 부터 최소자승법(最小自乘法)을 이용(利用)하여 구(求)할 수 있다. 이때 가정(假定)된 Q값의 절대값이 충분(充分)히 작아야만 P파(波)와 S파(波)의 고유(固有) Q값($Q_p$와 $Q_s$)의 가정(假定)은 신빙성(信憑性)이 높고 또한 유일(唯一)한 값을 가질 수 있다. 산란(散亂) Q값으로 부터 결정(決定)할 수 있는 매질(媒質)의 속도(速度)와 산란(散亂)의 크기에 대(對)한 표준편차(標准偏差)는 Blair의 수식(數式)에서 예측(豫測)할 수 있듯이 서로 상호보완관계(相互補完關係)에 있기 때문에 여러가지의 값을 가질 수 있다. 본(本) 연구결과에 의(依)하면, P파(波)에 있어서는 고유(固有) Q와 산란(散亂) Q가 모두 중요(重要)한 요소(要素)로 작용(作用)하며, S파(波)에 있어서는 고유(固有) Q가 산란(散亂) Q보다 더 중요(重要)한 요소(要素)로 작용(作用)한다.