• Honam Mathematical Journal
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• v.29 no.4
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• pp.511-521
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• 2007

Let S($z_1$, $z_2$) be a power series with operator coefficients such that multiplication by 5($z_1$, $z_2$) is a contractive transformation in the Hilbert space $\mathbf{H}_2$($\mathbb{D}^2$, C). In this paper we show that there exists a Hilbert space D($\mathbb{D}$,$\bar{S}$) which is the state space of extended canonical linear system with a transfer fucntion $\bar{S}$(z).

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.801-810
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• 1998

Let A(z), W(z) and C(z) be power series with operator coefficients such that W(z) = A(z)C(z). Let D(A) and D(C) be the state spaces of unitary linear systems whose transfer functions are A(z) and C(z) respectively. Then there exists a Krein space D which is the state space of unitary linear system with transfer function W(z). And the element of D is of the form (f(z) ＋ A(z)h(z), k(z) ＋ C＊(z)g(z)) where (f(z),g(z)) is in D(A) and (h(z),k(z)) is in D(C).

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.481-493
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• 2012

Let $S$ be a upper triangular operator such that $M^L_S:\mathcal{U}_2{\rightarrow}\mathcal{U}_2$ defined by $M^L_S(F)=SF$ is a contraction. Then there exists an unitary linear system whose state space is the extension space $\tilde{D}_L$(S) associated with $\mathcal{H}_L$(S).

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.447-459
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• 1995

A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

• Korean Journal of Optics and Photonics
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• v.5 no.1
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• pp.25-30
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• 1994

We derive a set of formuale which show one-to-one correspondence between the the unitary Jones matrices of transparent anisotropic media and the rotational transformations on the Poincare sphere. By using the formuale one can determine the vectorial representation of the rotational transformation on the Poincare sphere which specifies the direction of the axis and the angle of the rotation in terms of the three parameters specific to the corresponding unitary Jones matrix, and conversely the the three parameters of the uniatry Jones matrix in terms of the vectorial representation of the corresponding rotational transformation on the Poincare sphere. To understand the polarization transmission characteristics of an optical system consisting of transparent linear anisotropic media, start with the Jones calculus to get the unitary Jones matrix for the whole system and then convert it to a rotational transformation on the Poincare sphere, from which we can intuitively understand the effect of the optical system on the polarization state of the light passing through the system.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.12 s.115
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• pp.1224-1230
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• 2006

In this paper, for spatial multiplexing with limited feedback, a precoding scheme is proposed based on the joint use of minimal instantaneous feedback and long-term feedback of a small number of bits, wherein the long-term feedback is used to convey a selected preceding matrix within a precodercodebook consisting of a number of unitary matrices, and the active column vectors of the selected unitary matrix are conveyed to the transmitter using instantaneous feedback. Focusing on the case of dual multi-input multi-output(MIMO) systems, precoder codebook design for maximizing the average throughput of a spatial multiplexing system with a zero-forcing(ZF) receiver is proposed. It is shown that the proposed scheme provides a considerable throughput enhancement over multi-mode antenna selection and multi-mode basis selection only with the additional long-yterm feedback of a small number of bits. For example, the throughput increases by 11.5 % than antenna selection and 5.1% than basis selection, respectively, when SNR=20 dB.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.305-320
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• 2020

This study aims to generalize MINRES-N2 method [1]. It means that we tend to obtain an algorithm to transfer each normal matrix - that its eigenvalues belong to an algebraic curve of low degree k- to its condensed form through using a unitary similarity transformation. Then, we aim to obtain a method to solve a system of linear equations that its coefficient matrix is equal to such a matrix by utilizing it. Finally this method is compared to the well-known GMRES method through using numerical examples. The results obtained through examples show that the given method is more efficient than GMRES.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.5
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• pp.37-43
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• 2012

The closed-loop multiple-input multiple-output (MIMO) system has been adopted by long term evolution (LTE) system. Many techniques are proposed to enhance the transmission of LTE's advanced version to meet the increasing requirement, in which differential codebook gains a lot of interest. Previous researches on designing differential codebooks focused on quasi-diagonal unitary matrix which cannot guarantee the equal gain property. The equal gain property is very important to uplink because the performance of uplink is very sensitive to the peak-to-average power ratio (PAPR). In this paper, we derive the analytical expression of average bit error rate and PAPR for differential precoding MIMO system. Using the analytical results, we investigate the performances of several differential precoding schemes considering non-linear amplifier at the transmitter. Some selected simulation results indicate that the conventional differential precoding schemes have good performances without the consideration of non-linear amplifier. While considering non-linear amplifier, the proposed differential codebook outperforms other differential precoding schemes because it maintains the equal gain per transmit antenna.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.479-487
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• 2009

Let $S(z_1,z_2),\;S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ be power series with operator coefficients such that $S_(z_1,\;z_2)=S_1(z_1,z_2)S_2(z_1,z_2)$. Assume that the multiplications by $S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ are contractive transformations in H($\mathbb{D}^2,\;\mathcal{C}$). Then the factorizations of spaces $\mathcal{D}(\mathbb{D},\;\tilde{S})$ and $\mathcal{D}(\mathbb{D}^2,\mathcal{S})$ are well-behaved.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.21-29
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• 1993

For the study of relaxation processes in complex spin system, a general master equation, which can be used to simulate a vast range of pulse experiments, has been formulated using the Liouville representation of quantum mechanics. The state of a nonequilibrium spin system in magnetic field is described by a density vector in Liouville space and the time evolution of the system is followed by the application of a linear master operator to the density vector in this Liouville space. In this master equation the nuclear spin relaxation due to intramolecular dipolar interaction or randomly fluctuating field interaction is explicitly implemented as a relaxation supermatrix for a strong coupled two-spin (1/2) system. The whole dynamic information inherent in the spin system is thus contained in the density vector and the master operator. The radiofrequency pulses are applied in the same space by corresponding unitary rotational supertransformations of the density vector. If the resulting FID is analytically Fourier transformed, it is possible to represent the final nonstationary spectrum using a frequency dependent spectral vector and intensity determining shape vector. The overall algorithm including relaxation interactions is then translated into an ANSIFORTRAN computer program, which can simulate a variety of two dimensional spectra. Furthermore a new strategy is tested by simulation of multiple quantum signals to differentiate the two relaxation interaction types.