• East Asian mathematical journal
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• v.26 no.5
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• pp.649-654
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• 2010

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.3
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• pp.545-551
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• 2012

In this paper, we propose a new cryptosystem based on the IQC depended on the complexity of class number and intractibility of factoring integer, and introduce two algorithm which reduce encryption and decryption times. To recognize the security of the cryptosystem, we take a simple example to analyze the complexities of public key and secret key and then introduce the operating process of the cryptosystem.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1249-1268
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• 2011

For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.147-155
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• 2014

Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.559-578
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• 2019

We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.

• ETRI Journal
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• v.42 no.4
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• pp.562-574
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• 2020

Quadrature spatial modulation (QSM) utilizes the in-phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.

• International Journal of Internet, Broadcasting and Communication
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• v.11 no.3
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• pp.27-33
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• 2019

Quadrature spatial modulation (QSM) utilizes the in-phase and quadrature spatial dimensions to transmit the real and imaginary parts, respectively, of a single signal symbol. Improved QSM (IQSM) builds upon QSM to increase the spectral efficiency by transmitting the real and imaginary parts of two signal symbols using antenna combinations of size of two. In this paper, we propose a double QSM (DQSM) scheme that transmits the real and imaginary parts of two signal symbols independently through any of the transmit antennas. The two signal symbols are drawn from two different constellations of the same size with the first symbol drawn from any of the conventional modulation sets while the second is drawn from an optimally rotated version of the first constellation. The optimum rotation angle is obtained through extensive Monte Carlo simulations to minimize the bit error rate (BER) of the system. Simulation results show that for a given spectral efficiency, DQSM performsrelatively close to IQSM while requiring a smaller number of transmit antennas, and outperformsIQSM by up to 2 dB when the same number of antennas are used.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.7
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• pp.196-202
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• 2000

In the precision point synthesis of mechanisms, it is usually required to solve a system of polynomial equations. With the aid of efficient algorithms such as elimination, it is possible to obtain all the solutions of the equations in the complex domain. But among these solutions only real values can be used fur real mechanisms, while imaginary ones are liable to be discarded. In this article, a method is presented, which leads the imaginary solutions to real domain permitting slight alteration of prescribed positions and eventually increases the number of feasible mechanisms satisfying the desired motion approximately. Two synthesis problems of planar 4-bar path generation and spatial 7-bar motion generation are given to verify the proposed method.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.2
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• pp.106-114
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• 2015

In the fabrication of offshore oil and gas facilities, the significance of dimension control is growing continuously. But, it is difficult to determine the deformation of the structure during fabrication by simple lab tests due to the large size and the complicated shape. Strain-boundary method (a kind of shrinkage method) based on the shell element was proposed to predict the welding distortion of a structure effectively. Modeling of weld geometry in shell element is still a difficult task. In this paper, a concept of imaginary temperature pair is introduced to handle the effect of geometric factors such as groove shape, plate thickness and pass number, etc. Single pass imaginary temperature pair formula is derived from the relation between the groove area and the FE mesh size. By considering the contribution of each weld layer to the whole weldment, multi-pass imaginary temperature is also derived. Since the temperature difference represents the distortion increment, cumulative distortion curve can be drawn by integrating the temperature difference. This curve will be a useful solution when engineers meet some problems occurred in the shipyard. A typical example is shown about utilization of this curve. Several verifications are conducted to examine the validity of the proposed methodology. The applicability of the model is also demonstrated by applying it to the fabrication process of the heavy ship block. It is expected that the imaginary temperature model can effectively solve the modeling problem in shell element. It is also expected that the cumulative distortion curve derived from the imaginary temperature can offer useful qualitative information about angular distortion without FE analysis.

• Geotechnical Engineering
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• v.6 no.4
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• pp.43-52
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• 1990

To investigate the effects of soil properties of the soft zone around a pile subjected 1,o the horizontal harmonic vibration, the parametric study is perfomed. The determination of the soil reaction or stiffness of the Winkler springs representing the soil around a pile is performed by dividing the soil profile into a number of homogeneous obtained from this study are as follows : 1) The real and imaginary parts of the stiffness show clear variations for the different shear modulus ratios, poisson's ratios, and distance retios to outer boundary as the dimensionless frequency increases. The differences are more pronounced for the imaginary part of the stiffness. 2) The stiffness of soil shows clear decrease. The real parts of the stiffness show larger as the frequency increases. On the other hand, the imaginary parts of the stiffness show smaller.