• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.345-370
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• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1435-1438
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• 2005

In hands-free telephone systems, the received speech signal is fed back to the microphone and constitutes the so-called echo. To cancel the effect of this time-varying echo path, it is necessary to device an adaptive filter between the receiving and the transmitting ends. For a typical FIR realization, the length of the fullband adaptive filter results in high computational complexity and low convergence rate. Consequently, subband adaptive filtering schemes have been proposed to improve the performance. In this work, we use deterministic approach to analyze the relationship between fullband and subband adaptive filtering structures. With block adaptive filtering structure as an intermediate stage, the analysis is divided into two parts. First, to avoid aliasing, it is found that the matrix of block adaptive filters is in the form of pseudocirculant, and the elements of this matrix are the polyphase components of the fullband adaptive filter. Second, to transmit the near-end voice signal faithfully, the analysis and the synthesis filter banks in the subband adaptive filtering structure must form a perfect reconstruction pair. Using polyphase representation, the relationship between the block and the subband adaptive filters is derived.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.6
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• pp.78-89
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• 1996

Every mechanical component is fabricated with the variations in its size and shape, and the allowable range of the variation is specified by the tolerance in the design stage. Geometric tolerances specify the size or the thickness of each shape entity itself or its relative position and orientation with respect to datums. Since the range of shape variation can be represented by the variation of the coordinate system attached to the shape, the transformation matrix of the coordinate system would mathematically express the range of shape variation if the interval numbers are inserted for the elements of the transformation matrix. For the shape entity specified by the geometric tolerance with reference to datums, its range of variation can be also derived by propagating the transformation matrices composed of interval numbers. The propagation depends upon the order of precedence of datums.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.4-6
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• 2003

A holistic representation, such as sparse ceding or independent component analysis (ICA), was successfully applied to explain early auditory processing and sound classification. In contrast, Part-based representation is an alternative way of understanding object recognition in brain. In this paper. we employ the non-negative matrix factorization (NMF)［1］which learns parts-based representation for sound classification. Feature extraction methods from spectrogram using NMF are explained. Experimental results show that NMF-based features improve the performance of sound classification over ICA-based features.

• MALSORI
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• no.29_30
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• pp.43-60
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• 1995

Standard generative phonologists assumed that there were no orders or hierarchies among distinctive features. This means that the distinctive features which make up a segment are independent and unordered. The unordered linear matrix cannot explain phonological phenomena such as complex segments as hierarchical representation does neatly. The hierarchical feature representation theory which embodies the concept of multi-tiered phonological representation organizes distinctive features in the appearance of hierarchical dominance. This paper aims to show how we can solve some problems of the linear feature representation. As regard underlying representation the theory of underspecification is discussed. I propose a feature hierarchy similar to that of Sagey(1986) but slightly different. I show English consonantal assimilation in feature hierarchical model compared with that of feature changing theory of linear representation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.1
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• pp.254-276
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• 2019

Since the amount of information on the internet is growing rapidly, it is not easy for a user to find relevant information for his/her query. To tackle this issue, the researchers are paying much attention to Document Summarization. The key point in any successful document summarizer is a good document representation. The traditional approaches based on word overlapping mostly fail to produce that kind of representation. Word embedding has shown good performance allowing words to match on a semantic level. Naively concatenating word embeddings makes common words dominant which in turn diminish the representation quality. In this paper, we employ word embeddings to improve the weighting schemes for calculating the Latent Semantic Analysis input matrix. Two embedding-based weighting schemes are proposed and then combined to calculate the values of this matrix. They are modified versions of the augment weight and the entropy frequency that combine the strength of traditional weighting schemes and word embedding. The proposed approach is evaluated on three English datasets, DUC 2002, DUC 2004 and Multilingual 2015 Single-document Summarization. Experimental results on the three datasets show that the proposed model achieved competitive performance compared to the state-of-the-art leading to a conclusion that it provides a better document representation and a better document summary as a result.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.511-519
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• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.95-106
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• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.663-675
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• 2007

We investigate the representation of the solution of discrete linear Volterra difference systems by means of the resolvent matrix and fundamental matrix, respectively, and then study the boundedness of the solutions of discrete Volterra systems by improving the assumptions and the proofs of Medina#s results in [6].

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.641-653
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• 2020

To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: $${\max}\{X:X=X^*,\;\(\array{A&V&X\\V&B&W\\X&W&C}\){\geq}0\}$$. We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.