• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.547-564
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• 2024

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.195-205
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• 2024

In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a G_δ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in X. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.

• School Mathematics
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• v.14 no.4
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• pp.469-493
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• 2012

The purpose of this study is find the relation between students' concept and types of proof construction. For this, four undergraduate students majored in mathematics education were evaluated to examine how they understand mathematical concepts and apply their concepts to their proving. Investigating students' proof with their concepts would be important to find implications for how students have to understand formal concepts to success in proving. The participants' proof productions were classified into syntactic proof productions and semantic proof productions. By comparing syntactic provers and semantic provers, we could reveal that the approaches to find idea for proof were different for two groups. The syntactic provers utilized procedural knowledges which had been accumulated from their proving experiences. On the other hand, the semantic provers made use of their concept images to understand why the given statements were true and to get a key idea for proof during this process. The distinctions of approaches to proving between two groups were related to students' concepts. Both two types of provers had accurate formal concepts. But the syntactic provers also knew how they applied formal concepts in proving. On the other hand, the semantic provers had concept images which contained the details and meaning of formal concept well. So they were able to use their concept images to get an idea of proving and to express their idea in formal mathematical language. This study leads us to two suggestions for helping students prove. First, undergraduate students should develop their concept images which contain meanings and details of formal concepts in order to produce a meaningful proof. Second, formal concepts with procedural knowledge could be essential to develop informal reasoning into mathematical proof.

• Journal of KIISE
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• v.42 no.2
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• pp.235-241
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• 2015

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.153-163
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• 2010

In this paper a frequency response analysis using Krylov subspace-based model reduction and its design sensitivity analysis with respect to design variables are presented. Since the frequency response and its design sensitivity information are necessary for a gradient-based optimization, problems of high computational cost and resource may occur in the case that frequency response of a large sized finite element model is involved in the optimization iterations. In the suggested method model order reduction of finite element models are used to calculate both frequency response and frequency response sensitivity, therefore one can maximize the speed of numerical computation for the frequency response and its design sensitivity. As numerical examples, a semi-monocoque shell and an array-type $4{\times}4$ MEMS resonator are adopted to show the accuracy and efficiency of the suggested approach in calculating the FRF and its design sensitivity. The frequency response sensitivity through the model reduction shows a great time reduction in numerical computation and a good agreement with that from the initial full finite element model.

• Smart Structures and Systems
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• v.10 no.2
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• pp.131-154
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• 2012

In this paper, it is aimed to determine the seismic behaviour of highway bridges by nondestructive testing using ambient vibration measurements. Eynel Highway Bridge which has arch type structural system with a total length of 216 m and located in the Ayvaclk county of Samsun, Turkey is selected as an application. The bridge connects the villages which are separated with Suat U$\breve{g}$urlu Dam Lake. A three dimensional finite element model is first established for a highway bridge using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three orthogonal directions. The ambient vibration measurements are carried out on the bridge deck under natural excitation such as traffic, human walking and wind loads using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification techniques are employed namely, Enhanced Frequency Domain Decomposition technique in the frequency domain and Stochastic Subspace Identification technique in time domain. Analytical and experimental dynamic characteristic are compared with each other and finite element model of the bridge is updated by changing of boundary conditions to reduce the differences between the results. It is demonstrated that the ambient vibration measurements are enough to identify the most significant modes of highway bridges. After finite element model updating, maximum differences between the natural frequencies are reduced averagely from 23% to 3%. The updated finite element model reflects the dynamic characteristics of the bridge better, and it can be used to predict the dynamic response under complex external forces. It is also helpful for further damage identification and health condition monitoring. Analytical model of the bridge before and after model updating is analyzed using 1992 Erzincan earthquake record to determine the seismic behaviour. It can be seen from the analysis results that displacements increase by the height of bridge columns and along to middle point of the deck and main arches. Bending moments have an increasing trend along to first and last 50 m and have a decreasing trend long to the middle of the main arches.

• Journal of Internet Computing and Services
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• v.19 no.1
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• pp.67-76
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• 2018

This paper addresses the problem of efficient processing of region monitoring queries. The centralized methods used for existing region monitoring query processing assumes that the mobile object periodically sends location-updates to the server and the server continues to update the query results. However, a large amount of location updates seriously degrade the system performance. Recently, some distributed methods have been proposed for region monitoring query processing. In the distributed methods, the server allocates to all objects i) a resident domain that is a subspace of the workspace, and ii) a number of nearby query regions. All moving objects send location updates to the server only when they leave the resident domain or cross the boundary of the query region. In order to allocate the resident domain to the moving object along with the nearby query region, we use a query index structure that is constructed by splitting the workspace recursively into equal halves. However, However, the above index structure causes unnecessary division, resulting in deterioration of system performance. In this paper, we propose an adaptive split method to reduce unnecessary splitting. The workspace splitting is dynamically allocated i) considering the spatial relationship between the query region and the resultant subspace, and ii) the distribution of the query region. We proposed an enhanced QR-tree with a new splitting method. Through a set of simulations, we verify the efficiency of the proposed split methods.

• The Journal of the Acoustical Society of Korea
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• v.24 no.4
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• pp.230-237
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• 2005

The angle-tracking of maneuvering targets is required to the state estimation and classification of targets in underwater acoustic systems. The Problem of angle-tracking multiple closed and crossing targets has been studied by various authors. Sword et al. Proposed a multiple target an91e-tracking algorithm using angular innovations of the targets during a sampling Period are estimated in the least square sense using the most recent estimate of the sensor output covariance matrix. This algorithm has attractive features of simple structure and avoidance of data association problem. Ryu et al. recently Proposed an effective multiple target angle-tracking algorithm which can obtain the angular innovations of the targets from a signal subspace instead of the sensor output covariance matrix. Hwang et al. improved the computational performance of a multiple target angle-tracking algorithm based on the fact that the steering vector and the noise subspace are orthogonal. These algorithms. however. are ineffective when a subset of the incident sources are coherent. In this Paper, we proposed a new multiple target angle-tracking algorithm for coherent and incoherent sources. The proposed algorithm uses the relationship between source steering vectors and the signal eigenvectors which are multiplied noise covariance matrix. The computer simulation results demonstrate the improved Performance of the Proposed algorithm.

• Journal of Digital Convergence
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• v.17 no.2
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• pp.163-170
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• 2019

Over the past decade, the development of the Web explosively increased the data. Feature selection step is an important step in extracting valuable data from a large amount of data. This study proposes a novel opinion mining model based on combining feature selection (FS) methods with Word embedding to vector (Word2vec) and BOW (Bag-of-words). FS methods adopted for this study are CFS (Correlation based FS) and IG (Information Gain). To select an optimal FS method, a number of classifiers ranging from LR (logistic regression), NN (neural network), NBN (naive Bayesian network) to RF (random forest), RS (random subspace), ST (stacking). Empirical results with electronics and kitchen datasets showed that LR and ST classifiers combined with IG applied to BOW features yield best performance in opinion mining. Results with laptop and restaurant datasets revealed that the RF classifier using IG applied to Word2vec features represents best performance in opinion mining.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.4
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• pp.221-232
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• 2023

This paper presents a novel convolutional neural network (CNN)-based approach for predicting bolt clamping force in the early bolt loosening state of bolted structures. The approach entails tightening eight bolts with different clamping forces and generating frequency responses, which are then used to create a similarity map. This map quantifies the magnitude and shape similarity between the frequency responses and the initial model in a fully fastened state. Krylov subspace-based model order reduction is employed to efficiently handle the large amount of frequency response data. The CNN model incorporates a regression output layer to predict the clamping forces of the bolts. Its performance is evaluated by training the network by using various amounts of training data and convolutional layers. The input data for the model are derived from the magnitude and shape similarity map obtained from the frequency responses. The results demonstrate the diagnostic potential and effectiveness of the proposed approach in detecting early bolt loosening. Accurate bolt clamping force predictions in the early loosening state can thus be achieved by utilizing the frequency response data and CNN model. The findings afford valuable insights into the application of CNNs for assessing the integrity of bolted structures.