• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.10
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• pp.1940-1946
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• 2015

An optical coherent system is considered for the next-generation optical access networks in enhancing the data rate and transmission distance. In this system, however, I/Q amplitude imbalance may occur at several parts of the system, leading to serious performance degradation. Asymmetric structure of a coherent receiver at the location of subscriber is one of the sources of I/Q imbalance. Therefore, this imbalance parameters must be removed or compensated to secure the transmission performance. In this paper, the source of I/Q amplitude imbalance is analyzed, and then the way to compensate for the imbalance at the receiver side is suggested. Performance after the compensation is estimated using simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.9C
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• pp.810-819
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• 2007

The I/Q unbalance which is generated by non-ideal components such as a $90^{\circ}$ phase shifter and I/Q filters is an inevitable physical phenomenon and leads to performance degradation when we implement a coherent two-dimensional (2-D) modulation/demodulation system. This paper provides an exact and general expression for the SEP(symbol error probability) of DVB-S2 system with I/Q phase and amplitude unbalance over AWGN channel. Coordinate rotation and shift techniques used to redefine a received signal are key mathematical tools. In conclusion, the derived result is expressed as a linear combination of the 2-D Gaussian Q-functions.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.399-412
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• 2001

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.

• Korean Journal of Soil Science and Fertilizer
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• v.37 no.4
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• pp.220-227
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• 2004

Phosphorus desorption study is essential to understanding P behavior in agricultural and environmental soils because phosphorus is considered as two different aspects, a plant nutrient versus an environmental contaminant. This study was conducted to determine soil P buffering power related to P desorption quantity intensity (Q/I) parameters, $Q_{max}$(an index of P release capacity) and $l_0$(an index of the intensity factor), and to investigate the characteristics of relationship between the P desorption Q/I parameters and the soil properties. Soil samples were prepared with treatments of 0 and $100mg\;P\;kg^{-1}$ applied as $KH_2PO_4$ solution. The P desorption Q/I curves were obtained by a procedure using anion exchange resin beads and described by an empirical equation ($Q=aI^{-1}+bln(I+1)+c$). The P desorption Q/I curves for the high available P (${\g}20mg\;kg^{-1}$ of Olsen P) soils were characteristic concave trends with or without soil P enrichment, whereas for the low available P (${\lt}20mg\;kg^{-1}$ of Olsen P) soils, the anticipated Q/I concave curves could not be obtained without a proper amount of P addition. When the soils were enriched in phosphates, the values of desorbed solid phase labile P and solution P, such as $Q_{max}$ and $I_0$ respectively, were increased, but the ratio of $Q_{max}$ versus $I_0$ was decreased. Thus, the slope of desorption Q/I curve represented as phosphorus buffering power, $|BP_0|$, is decreased. The $|BP_0|$ values of the high available P soils ranged between 48 and $61L\;kg^{-1}$ in the P untreated samples and between 18 and $44L\;kg^{-1}$ in the P enriched samples. Overall $|BP_0|$ values of both low and high available P soils treated with $l00mg\;P\;kg^{-1}$ ranged between 14 and $79L\;kg^{-1}$. The $Q_{max}$, values ranged between 71.4 and $173.1mg\;P\;kg^{-1}$, and the lo values ranged between 0.98 and $3.82mg\;P\;L^{-1}$ in the P enriched soils. The $Q_{max}$ and $I_0$ values that control the P buffering power may be not specifically related to a specific soil property, but those values were complicatedly related to soil pH, clay content, soil organic matter content, and lime. Also, phosphorus release activity, however, markedly depended on the desorbability of the applied P as well as the native labile P.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.3C
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• pp.237-244
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• 2006

I/Q phase unbalance caused by non-ideal circuit components is inevitable physical phenomenons and leads to performance degradation when we implement a practical coherent M-ary phase shift keying(M-PSK) demodulator. In this paper, we present an exact and general expression involving two-dimensional Gaussian Q-functions for the bit error rate(BER) of uniform M-PSK with I/Q phase unbalance over an additive white Gaussian noise(AWGN) channel. First we derive a BER expression for the k-th bit of 8, 16-PSK signal constellations when Gray code bit mapping is employed. Then, from the derived k-th bit BER expression, we present the exact and general average BER expression for M-PSK with I/Q phase unbalance. This result can readily be applied to numerical evaluation for various cases of practical interest in an I/Q unbalanced M-PSK system, because the one- and two-dimensional Gaussian Q-functions can be easily and directly computed using commonly available mathematical software tools.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.2
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• pp.18-26
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• 2015

In this paper, we studied the method for analyzing and estimating the parameters that induce I/Q imbalance in the repeater using direct conversion RF. In repeater, amplitude, phase, and filter mismatch are generated in the receiving-end which converts RF signal to baseband signal. And amplitude and phase mismatch are generated in the transmitting-end which converts baseband signal to RF signal. Accordingly, we modeled the parameters that cause I/Q imbalance in the structure of the repeater in order, and proposed a feedback test structure from the transmitting-end to the receiving-end for estimating the corresponding parameters. By comparing the test transmitting signal and received signal, it is possible to estimate the I/Q imbalance parameters which occurred from mixed components of real and imaginary part. And it was confirmed that I/Q imbalance phenomenon has been properly compensated with estimated parameters at the direct conversion RF repeater.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.129-130
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• 2007

I/Q demodulator is designed using RC-CR quadrature divider with two balanced mixer for WLAN applications. The I/Q demodulator has low power dissipation, good I/Q mismatch, a good isolation and conversion loss. The measured results shows close agreement with the predicted performance.