• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.13-22
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• 1998

Fractals which represent many of the sets in various scien-tific fields as well as in nature is geometrically too complicate. Then we usually use Hausdorff dimension to estimate their geometrical proper-ties. But to explain the fractals from the hausdorff dimension induced by the Euclidan metric are not too sufficient. For example in digi-tal communication while encoding or decoding the fractal images we must consider not only their geometric sizes but also many other fac-tors such as colours densities and energies etc. So in this paper we define the dimension matrix of the sets by redefining the new metric.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.522-539
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• 2021

In order to solve the problems of the existing audio fingerprint method when extracting audio fingerprints from long speech segments, such as too large fingerprint dimension, poor robustness, and low retrieval accuracy and efficiency, a robust audio fingerprint retrieval method based on feature dimension reduction and feature combination is proposed. Firstly, the Mel-frequency cepstral coefficient (MFCC) and linear prediction cepstrum coefficient (LPCC) of the original speech are extracted respectively, and the MFCC feature matrix and LPCC feature matrix are combined. Secondly, the feature dimension reduction method based on information entropy is used for column dimension reduction, and the feature matrix after dimension reduction is used for row dimension reduction based on energy feature dimension reduction method. Finally, the audio fingerprint is constructed by using the feature combination matrix after dimension reduction. When speech's user retrieval, the normalized Hamming distance algorithm is used for matching retrieval. Experiment results show that the proposed method has smaller audio fingerprint dimension and better robustness for long speech segments, and has higher retrieval efficiency while maintaining a higher recall rate and precision rate.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.1-17
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• 2013

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of $6{\times}6$ by transforming the obtained stiffness matrix. Thus, the dimension, which is $12n{\times}12n$ in classical finite elements, is reduced to the dimension of $6{\times}6$. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.721-733
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• 2022

In this paper we compare parameter estimation by Grassmann manifold optimization and sequential candidate set algorithm in a structured principal fitted component (PFC) model. The structured PFC model extends the form of the covariance matrix of a random error to relieve the limits that occur due to too simple form of the matrix. However, unlike other PFC models, structured PFC model does not have a closed form for parameter estimation in dimension reduction which signals the need of numerical computation. The numerical computation can be done through Grassmann manifold optimization and sequential candidate set algorithm. We conducted numerical studies to compare the two methods by computing the results of sequential dimension testing and trace correlation values where we can compare the performance in determining dimension and estimating the basis. We could conclude that Grassmann manifold optimization outperforms sequential candidate set algorithm in dimension determination, while sequential candidate set algorithm is better in basis estimation when conducting dimension reduction. We also applied the methods in real data which derived the same result.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.759-769
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• 2005

We first discuss jump discontinuity in higher dimension, and then prove a local convergence theorem for wavelet approximations in higher dimension. We also redefine the concept of Gibbs phenomenon in higher dimension and show that wavelet expansion exhibits Gibbs phenomenon.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.9
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• pp.3348-3364
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• 2021

Magic matrix-based data hiding schemes are applied to transmit secret information through open communication channels safely. With the development of various magic matrices, some higher dimensional magic matrices are proposed for improving the security level. However, with the limitation of computing resource and the requirement of real time processing, these higher dimensional magic matrix-based methods are not advantageous. Hence, a kind of data hiding scheme based on a single or a group of multi-dimensional flexible magic matrices is proposed in this paper, whose magic matrix can be expanded to higher dimensional ones with less computing resource. Furthermore, an adaptive mechanism is proposed to reduce the embedding distortion. Adapting to the secret data, the magic matrix with least distortion is chosen to embed the data and a marker bit is exploited to record the choice. Experimental results confirm that the proposed scheme hides data with high security and a better visual quality.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.285-290
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• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.1
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• pp.101-108
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• 2017

As the quantum gate matrix is a $r^{n+1}{\times}r^{n+1}$ dimension when the radix is r, the number of control state vectors is n, and the number of target state vectors is one, the matrix dimension with increasing n is exponentially increasing. If the number of control state vectors is $2^n$, then the number of $2^n-1$ unit matrix operations preserves the output from the input, and only one can be performed the unitary operation to the target state vector. Therefore, this paper proposes a new method of function embedding that can replace $2^n-1$ times of unit matrix operations with deterministic contribution to matrix dimension by arithmetic power switch of the unitary gate. The proposed function embedding method uses a binary literal switch with a multivalued threshold, so that a general purpose hybrid MCU gate can be realized in a $r{\times}r$ unitary matrix.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1483-1494
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• 2021

Let A and B be rings and U be a (B, A)-bimodule. If _BU has finite flat dimension, U_A has finite flat dimension and U ⊗_A C is a cotorsion left B-module for any cotorsion left A-module C, then the Gorenstein flat-cotorsion modules over the formal triangular matrix ring $T=\(\array{A&0\\U&B}\)$ are explicitly described. As an application, it is proven that each Gorenstein flat-cotorsion left T-module is flat-cotorsion if and only if every Gorenstein flat-cotorsion left A-module and B-module is flat-cotorsion. In addition, Gorenstein flat-cotorsion dimensions over the formal triangular matrix ring T are studied.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2023

In this paper, we investigate the dimension and the structure of the centralizer of a square matrix with entries from an arbitrary field.