• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.215-225
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• 2017

In this paper, we study some equivalence relations between continuous frames in a Hilbert space ${\mathcal{H}}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.700-705
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• 2008

In this paper, we propose object classification algorithm for real-time surveillance system. We have approached this problem using silhouette-based template matching. The silhouette of the object is extracted, and then it is compared with representative template models. Template models are previously stored in the database. Our algorithm is similar to previous pixel-based template matching scheme like Hausdorff Distance, but we use 1D image array rather than 2D regions inspired by Hilbert Path. Transformation of images could reduce computational burden to compute similarity between the detected image and the template images. Experimental results show robustness and real-time performance in object classification, even in low resolution images.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.5
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• pp.631-637
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• 2010

In this paper, We propose a method of motion interpretation of pedestrian for active traffic signal control. We detect pedestrian object in a movie of crosswalk area by using the code book method and acquire contour information. To do this stage fast, we use parallel processing based on CUDA (Compute Unified Device Architecture). And we remove shadow which causes shape distortion of objects. Shadow removed object is judged by using the hilbert scan distance whether to human or noise. If the objects are judged as a human, we analyze pedestrian objects' motion, face area feature, waiting time to decide that they have intetion to across a crosswalk for pdestrians. Traffic signal can be controlled after judgement.

• Journal of Ocean Engineering and Technology
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• v.22 no.1
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• pp.30-36
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• 2008

Underwater ambient noise originating from geophysical, biological, and man-made acoustic sources contains information on the source and the ocean environment. Such noise affectsthe performance of sonar equipment. In this paper, three steps are used to identify the ambient noise source, detection, feature extraction, and similarity measurement. First, we use the zero-crossing rate to detect the ambient noisesource from background noise. Then, a set of feature vectors is proposed forthe ambient noise source using the Hilbert-Huang transform and the Karhunen-Loeve transform. Finally, the Euclidean distance is used to measure the similarity between the standard feature vector and the feature vector of the unknown ambient noise source. The developed algorithm is applied to the observed ocean data, and the results are presented and discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1255-1265
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• 1992

Under uniform heat flow, the thermal stress intensity factors for the interfacial crack on a rigid cusp-type inclusion are determined by Hilbert problem expressed with complex variable. The thermal stress intensity factors are expressed in terms of the periodic function of heat flow angle. When the tip of the interfacial crack meets that of the cusp crack, the thermal stress intensity factors have singularities. The thermal stress intensity factors at the interfacial crack tip located in the distance from the cusp crack tip vary with the location of the interfacial crack tip. From the results of the analysis, the complex potential functions and the thermal stress intensity factors for the cusp-type inclusion without the interfacial crack are derived under the cusp surface boundary conditions insulated or fixed to zero relative temperature.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.667-680
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• 2004

We generalize a theorem of W. Benz by proving the following result: Let $H_{\theta}$ be a half space of a real Hilbert space with dimension $\geq$ 3 and let Y be a real normed space which is strictly convex. If a distance $\rho$ > 0 is contractive and another distance N$\rho$ (N $\geq$ 2) is extensive by a mapping f : $H_{\theta}$ \longrightarrow Y, then the restriction f│$_{\theta}$ $H_{+}$$\rho$/2// is an isometry, where $H_{\theta}$＋$\rho$/2/ is also a half space which is a proper subset of $H_{\theta}$. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.

• Proceedings of the KIEE Conference
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• 2007.10a
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• pp.455-456
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• 2007

물체 식별은 감시 시스템에서 중요한 역할을 수행한다. 특히 사람/차 식별은 해당 사물의 존재 유무를 파악하기 위해 다양한 어플리케이션에서 사용된다. 우리는 외곽선 정보를 이용하여 빠르게 물체 식별을 할 수 있는 알고리즘을 제안한다. 감시 영상에서 움직이는 물체를 찾은 후, 외곽선 정보를 추출하여 미리 저장해 둔 사물의 모델과 비교하여 가장 가까운 거리값(유사도)을 찾는 방식이다. 2차원의 영상 처리에는 기본적으로 많은 연산량이 필요하지만, 주변 픽셀 정보를 최대한 유지할 수 있는 할버트 패스(Hilbert Path)를 사용하여 1차원의 배열로 변환한 후 비교하기 때문에 기존 알고리즘보다 빠르게 두 모델간의 유사도를 측정할 수 있다. 제안된 알고리즘은 사람/차 식별에 매우 강인한 성능을 보여주었으며, 기존 템플릿 매칭 기법보다 연산량의 감소로 실시간 감시 시스템에서 사용할 수 있을 것으로 기대된다.

• Geomechanics and Engineering
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• v.11 no.5
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• pp.607-624
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• 2016

Rockburst is becoming more serious in Chinese coal mine. One of the effective methods to control rockburst is blasting. In the paper, we monitored and analyzed the blasting waves at different blast center distances by the Hilbert-Huang transform (HHT) in a coal mine. Results show that with the increase of blast center distance, the main frequency and amplitude of blasting waves show the decreasing trend. The attenuation of blasting waves is slower in the near blast field (10-75 m), compared with the far blast field (75-230 m). Besides, the frequency superposition phenomenon aggravates in the far field. A majority of the blasting waves energy at different blast center distances is concentrated around the IMF components 1-3. The instantaneous energy peak shows attenuation trend with the blast center distance increase, there are two obvious energy peaks in the near blast field (10-75 m), the energy spectrum appears "fat", and the total energy is greater. By contrast, there is only an energy peak in the far blast field, the energy spectrum is "thin", and the total energy is lesser. The HHT three dimensional spectrum shows that the wave energy accumulates in the time and frequency with the increasing of blast center distance.

• Smart Structures and Systems
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• v.18 no.5
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• pp.1063-1085
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• 2016

Taking advantage of the high sensitivity and long-distance detection capability of acoustic emission (AE) technique, this paper focuses on the crack detection in rail head, which is one of the most vulnerable parts of rail track. The AE source location and noise cancellation were studied on the basis of practical rail profile, material and operational noise. In order to simulate the actual AE events of rail head cracks, field tests were carried out to acquire the AE waves induced by pencil lead break (PLB) and operational noise of the railway system. Wavelet transform (WT) was first utilized to investigate the time-frequency characteristics and dispersion phenomena of AE waves. Here, the optimal mother wavelet was selected by minimizing the Shannon entropy of wavelet coefficients. Regarding the obvious dispersion of AE waves propagating along the rail head and the high operational noise, the wavelet transform-based modal analysis location (WTMAL) method was then proposed to locate the AE sources (i.e. simulated cracks) respectively for the PLB-induced AE signals with and without operational noise. For those AE signals inundated with operational noise, the Hilbert transform (HT)-based noise cancellation method was employed to improve the signal-to-noise ratio (SNR). Finally, the experimental results demonstrated that the proposed crack detection strategy could locate PLB-simulated AE sources effectively in the rail head even at high operational noise level, highlighting its potential for field application.