• East Asian mathematical journal
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• v.15 no.1
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• pp.81-90
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• 1999

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.55-64
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• 2023

In this paper, we propose a two-level overlapping domain decomposition preconditioner for three dimensional vector field problems posed in H(div). We introduce a new coarse component, which reduces the computational complexity, associated with the coarse vertices. Numerical experiments are also presented.

• Journal of Power Electronics
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• v.16 no.4
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• pp.1336-1345
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• 2016

A modified space vector pulse width modulation (SVPWM) strategy based on vector space decomposition and its equivalent carrier-based PWM realization are proposed in this paper, which is suitable for six-phase asymmetrical dual stator induction machines (DSIMs). A DSIM is composed of two sets of symmetrical three-phase stator windings spatially shifted by 30 electrical degrees and a squirrel-cage type rotor. The proposed SVPWM technique can reduce torque ripples and suppress the harmonic currents flowing in the stator windings. Above all, the equivalent relationship between the proposed SVPWM technique and the carrier-based PWM technique has been demonstrated, which allows for easy implementation by a digital signal processor (DSP). Simulation and experimental results, carried out separately on a simulation system and a 3.0 kW DSIM prototype test bench, are presented and discussed.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.245-253
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• 2009

A new hard problem called the vector decomposition problem (VDP) was recently proposed by Yoshida et al., and it was asserted that the VDP is at least as hard as the computational Diffie-Hellman problem (CDHP) under certain conditions. Kwon and Lee showed that the VDP can be solved in polynomial time in the length of the input for a certain basis even if it satisfies Yoshida's conditions. Extending our previous result, we provide the general condition of the weak instance for the VDP in this paper. However, when the VDP is practically used in cryptographic protocols, a basis of the vector space ${\nu}$ is randomly chosen and publicly known assuming that the VDP with respect to the given basis is hard for a random vector. Thus we suggest the type of strong bases on which the VDP can serve as an intractable problem in cryptographic protocols, and prove that the VDP with respect to such bases is difficult for any random vector in ${\nu}$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.3
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• pp.27-33
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• 2007

Recently, a new hard problem on a two dimensional vector space called vector decomposition problem (VDP) was proposed by M. Yoshida et al. and proved that it is at least as hard as the computational Diffe-Hellman problem (CDHP) on a one dimensional subspace under certain conditions. However, in this paper we present the VDP relative to a specific basis can be solved in polynomial time although the conditions proposed by M. Yoshida on the vector space are satisfied. We also suggest strong instances based on a certain type basis which make the VDP difficult for any random vector relative to the basis. Therefore, we need to choose the basis carefully so that the VDP can serve as the underlying intractable problem in the cryptographic protocols.

• Journal of Power Electronics
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• v.17 no.6
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• pp.1500-1511
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• 2017

The purpose of this paper is to study a high-performance control scheme for neutral-point-clamping three-level (NPC-3L) inverter fed dual three-phase permanent magnet synchronous motor (PMSM) drives by considering some asymmetric factors such as the non-identical parameters in phase windings. To implement this, the system model is analyzed for dual three-phase PMSM drives with asymmetric factors based on the vector space decomposition (VSD) principle. Based on the equivalent circuits, PI controllers with feedforward compensation are used in the d-q subspace for regulating torque, where the cut-off frequency of the PI controllers are set at the twice the fundamental frequency for compensating both the additional DC component and the second order component caused by asymmetry. Meanwhile, proportional resonant (PR) controllers are proposed in the x-y subspace for suppressing the possible unbalanced currents in the phase windings. A dual three-phase space vector modulation (DT-SVM) is designed for the drive, and the balancing factor is designed based on the numerical fitting surface for balancing the DC link capacitor voltages. Experimental results are given to demonstrate the validity of the theoretical analysis and the proposed control scheme.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.99-107
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• 1993

A vector space K with scalar product <.,.> is called a Krein space if it can be decomposed as a northogonal sum of a Hilbert space and an anti-space of a Hilbert space. The space K induces a Hilbert space $K_{J}$ in the inner product <.,.> $K_{J}$=<.,.>K, where $J^{2}$=I. the eigenspaces of J are denoted by $K^{+}$$_{J}$, which is a Hilbert space and $K^{-}$$_{J}$, which is an anti-space of a Hilbert space. Then the Krein space K is the orthogonal sum of $K^{+}$$_{J}$ and $K^{-}$$_{J}$. Such a decomposition of K is called a fundamental decomposition. In general, fundamental decompositions are not unique. The norm of the Hilbert space depends on the choice of a fundamental decomposion, but such norms are equivalent. The topology generated by these norms is called the strong or Mackey topology of K. It is used to define all topological notions on the Krein space K with respect to this topology. The Pontryagin index of a Krein space is the dimension of the antispace of a Hilbert space in any such decomposition. the dimension does not depend on the choice of orthogonal decomposition. A Krein space is called a Pontryagin space if it has finite Pontryagin index.dex.yagin index.dex.

• Korean Journal of Cognitive Science
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• v.23 no.3
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• pp.295-322
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• 2012

In this paper, we cluster similar word senses applying vector space model and HAL (Hyperspace Analog to Language). HAL measures corelation among words through a certain size of context (Lund and Burgess 1996). The similarity measurement between a word pair is cosine similarity based on the vector space model, which reduces distortion of space between high frequency words and low frequency words (Salton et al. 1975, Widdows 2004). We use PCA (Principal Component Analysis) and SVD (Singular Value Decomposition) to reduce a large amount of dimensions caused by similarity matrix. For sense similarity clustering, we adopt supervised and non-supervised learning methods. For non-supervised method, we use clustering. For supervised method, we use SVM (Support Vector Machine), Naive Bayes Classifier, and Maximum Entropy Method.

• Journal of Power Electronics
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• v.16 no.3
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• pp.936-945
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• 2016

Large magnitude common-mode voltage (CMV) and its variation dv/dt have an adverse effect on motor drives that leads to early winding failure and bearing deterioration. For matrix converters, the switch states that connect each output line to a different input phase result in the lowest CMV among all of the valid switch states. To reduce the output CMV for matrix converters, this paper presents a new space vector modulation (SVM) strategy by utilizing these switch states. By this mean, the peak value and the root mean square of the CMV are dramatically decreased. In comparison with the conventional SVM methods this strategy has a similar computation overhead. Experiment results are shown to validate the effectiveness of the proposed modulation method.

• Journal of international Conference on Electrical Machines and Systems
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• v.2 no.3
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• pp.330-335
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• 2013

This paper performs two kinds of Field-Oriented Control (FOC) for dual three phase permanent magnet synchronous motor (DTP-PMSM).The first is based on vector space decomposition to study the effect of current harmonics on electromechanical energy conversion. And the second presents the coupling relations between two sets of windings using two d-q transformation. And then this paper has deeply studied the differences between these two strategies, the different effect on the control of harmonic current and the reason for these differences. MATLAB-based Simulation studies of a 3KW DTP-PMSM are carried out to verify the analysis of differences between the two FOC strategies.