• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.815-823
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• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.229-241
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• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.701-710
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• 1994

Suppose ${X_n}$ is a Markov process taking values in some arbitrary space $(S, \varphi)$ with n-stemp transition probability $$ P^{(n)}(x, B) = Prob(X_n \in B$\mid$X_0 = x), x \in X, B \in \varphi.$$ We shall call a Markov process with transition probabilities $P{(n)}(x, B)$ $\phi$-irreducible for some non-trivial $\sigma$-finite measure $\phi$ on $\varphi$ if whenever $\phi(B) > 0$, $$ \sum^{\infty}_{n=1}{2^{-n}P^{(n)}}(x, B) > 0, for every x \in S.$$ A non-trivial $\sigma$-finite measure $\pi$ on $\varphi$ is called invariant for ${X_n}$ if $$ \int{P(x, B)\pi(dx) = \pi(B)}, B \in \varphi $$.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.634-636
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• 2005

지능형 로봇 기술이 발전하면서 영상에서 장면을 이해하는 연구가 많은 관심을 받고 있으며, 최근에는 불확실한 환경에서도 좋은 성능을 발휘할 수 있는 확률적 접근 방법이 많이 연구되고 있다. 본 논문에서는 확률적 모델링이 가능한 베이지안 네트워크(BN)를 이용해서 장면 인식 추론 모듈을 설계하고, 실제 환경에서 얻어진 증거 및 베이지안 추론 결과를 결합하여 분류 성능을 향상시키기 위한 방법을 제안한다. 영상 정보는 시간에 대해 연속성을 가지고 있기 때문에, 증거 정보와 베이지안 추론 결과들을 적절히 결합하면 더 좋은 결과를 예상할 수 있으며, 본 논문에서는 확신 요소(Certainty Factor: CF) 분석에 의한 결합 방법을 사용하였다. 성능 평가 실험을 위해서 SET (Scale Invariant Feature Transform) 기법을 이용하여 물체 인식 처리를 수행하고, 여기서 얻어진 데이터를 베이지안 추론의 증거로 사용하였으며, 전문가의 CF 값 정의에 의한 베이지안 네트워크 설계 방법을 이용하였다.

• Journal of Hydrospace Technology
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• v.2 no.2
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• pp.24-35
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• 1996

This paper describes parameter identification techniques formulated for the estimation of maneuvering coefficients of a submerged body. The first part of this paper is concerned with the identifiability of the system parameters. The relationship between a stochastic linear time-invariant system and the equivalent dynamic system is investigated. The second is concerned with the development of the numerically stable identification technique. Two identification techniques are tested; one is the ma7mum likelihood (ML) methods using the Holder & Mead simplex search method and using the modified Newton-Raphson method, and the other is the modified extended Kalman filter (MEKF) method with a square-root algorithm, which can improve the numerical accuracy of the extended Kalman filter. As a results, it is said that the equations of motion for a submerged body have higher probability to generate simultaneous drift phenomenon compared to general state equations and only the ML method using the Holder & Mead simplex search method and the MEKF method with a square-root algorithm gives acceptable results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.121-133
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• 1993

Presented is a study on the establishment of a method of advanced reliability analysis for the realistic analysis and design of reinforced concrete(RC) structures. Considerable variabilities exist in concrete structures due to random nature of concrete materials and member dimensions. The present study analyzes first the uncertainties in concrete, reinforcements and member dimensions and then a method is proposed to determine the probability uncertainties of basic variables. The limit state equations are also proposed for the RC members with axial compression and bending and RC footings. The advanced invariant second-moment method is applied to analyze those structures. The present study provides an important base for realistic reliability analysis of RC structures.

• Journal of Ubiquitous Convergence Technology
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• v.2 no.1
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• pp.18-26
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• 2008

The invariance relation existing in the non-negative matrix factorization (NMF) is used for constructing robust image hashes in this work. The image is first re-scaled to a fixed size. Low-pass filtering is performed on the luminance component of the re-sized image to produce a normalized matrix. Entries in the normalized matrix are pseudo-randomly re-arranged under the control of a secret key to generate a secondary image. Non-negative matrix factorization is then performed on the secondary image. As the relation between most pairs of adjacent entries in the NMF's coefficient matrix is basically invariant to ordinary image processing, a coarse quantization scheme is devised to compress the extracted features contained in the coefficient matrix. The obtained binary elements are used to form the image hash after being scrambled based on another key. Similarity between hashes is measured by the Hamming distance. Experimental results show that the proposed scheme is robust against perceptually acceptable modifications to the image such as Gaussian filtering, moderate noise contamination, JPEG compression, re-scaling, and watermark embedding. Hashes of different images have very low collision probability. Tampering to local image areas can be detected by comparing the Hamming distance with a predetermined threshold, indicating the usefulness of the technique in digital forensics.

• Journal of KIISE
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• v.42 no.7
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• pp.868-877
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• 2015

The barcode area extraction from images has been extensively studied, and existing methods exploit frequency characteristics or depend on the Hough transform (HT). However, the slantedness of the images and noise affects the performance of these approaches. Moreover, it is difficult to deal with the case where an image contains multiple barcodes. We therefore propose a barcode detection algorithm that is robust under such unfavorable conditions. The pre-processing step implements a probabilistic Hough transform to determine the areas that contain barcodes with a high probability, regardless of the slantedness, noise, and the number of instances. Then, a frequency component analysis extracts the barcodes. We successfully implemented the proposed system and performed a series of barcode extraction tests.

• Advances in aircraft and spacecraft science
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• v.9 no.3
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• pp.263-278
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• 2022

The time-varying structural reliability of an aeroelastic launch vehicle subjected to stochastic parameters is investigated. The launch vehicle structure is under the combined action of several stochastic loads that include aerodynamics, thrust as well as internal combustion pressure. The launch vehicle's main body structural flexibility is modeled via the normal mode shapes of a free-free Euler beam, where the aerodynamic loadings on the vehicle are due to force on each incremental section of the vehicle. The rigid and elastic coupled nonlinear equations of motion are derived following the Lagrangian approach that results in a complete aeroelastic simulation for the prediction of the instantaneous launch vehicle rigid-body motion as well as the body elastic deformations. Reliability analysis has been performed based on two distinct limit state functions, defined as the maximum launch vehicle tip elastic deformation and also the maximum allowable stress occurring along the launch vehicle total length. In this fashion, the time-dependent reliability problem can be converted into an equivalent time-invariant reliability problem. Subsequently, the first-order reliability method, as well as the Monte Carlo simulation schemes, are employed to determine and verify the aeroelastic launch vehicle dynamic failure probability for a given flight time.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.4
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• pp.161-166
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• 2018

In this paper, we propose a method for the random selection of pooling operations for the regularization and reduction of cross validation in convolutional neural networks. The pooling operation in convolutional neural networks is used to reduce the size of the feature map and for its shift invariant properties. In the existing pooling method, one pooling operation is applied in each pooling layer. Because this method fixes the convolution network, the network suffers from overfitting, which means that it excessively fits the models to the training samples. In addition, to find the best combination of pooling operations to maximize the performance, cross validation must be performed. To solve these problems, we introduce the probability concept into the pooling layers. The proposed method does not select one pooling operation in each pooling layer. Instead, we randomly select one pooling operation among multiple pooling operations in each pooling region during training, and for testing purposes, we use probabilistic weighting to produce the expected output. The proposed method can be seen as a technique in which many networks are approximately averaged using a different pooling operation in each pooling region. Therefore, this method avoids the overfitting problem, as well as reducing the amount of cross validation. The experimental results show that the proposed method can achieve better generalization performance and reduce the need for cross validation.