• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.41-50
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• 2018

This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras. It is shown that there is an interesting link of the non-triviality for such von Neumann algebras with the determinant of the matrix. A complete characterization of their abelian property is given under a more general setting.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.951-960
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• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• ETRI Journal
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• v.34 no.4
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• pp.503-510
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• 2012

We analyze the relationship between channel coherence bandwidth and two complexity-reduced lattice reduction aided detection (LRAD) algorithms for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems in correlated fading channels. In both the adaptive LR algorithm and the fixed interval LR algorithm, we exploit the inherent feature of unimodular transformation matrix P that remains the same for the adjacent highly correlated subcarriers. Complexity simulations demonstrate that the adaptive LR algorithm could eliminate up to approximately 90 percent of the multiplications and 95 percent of the divisions of the brute-force LR algorithm with large coherence bandwidth. The results also show that the adaptive algorithm with both optimum and globally suboptimum initial interval settings could significantly reduce the LR complexity, compared with the brute-force LR and fixed interval LR algorithms, while maintaining the system performance.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.6
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• pp.105-110
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• 2004

MAC is used for data origin authentication or message integrity protection. In Crypto'03 Cary and Venkatesan introduced new MAC based on unimodular matrix groups. It is to encrypt messages using private keys and to encrypt them again using public keys which are matrices whose determinants are $\pm$1. These matrices have property called k-invertible. This k effects on the collision probability of this new MAC. The smaller k is, the less collisions occur. Cary shows 6-invertible matrices, and 10-invertible matrices whose components are only 1, 0, -1. In this paper we figure out sufficient conditions about choosing 4 matrices among special 22 matrices. Also, we introduce 5-invertible matrices whose components are 1, 0, -1. Those have better efficiency and security.