• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.4
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• pp.1-10
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• 1982

An experimental investigation on the energy absorption of two staged combined structures is presented, which deals with the plastic collapse test as a series of research on soft bow structure involved in a ship collision. The principle of arithmetic superposition of energy absorption is derived upon experimental analysis and based upon the characteristics of the energy absorptions of component structures. This relationship is related to the further approach toward the design of soft bow.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.3
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• pp.20-25
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• 2009

We propose hardware architecture of floating-point square root and inverse square root arithmetic units using lookup tables. They are used for lighting engines and shader processor for 3D graphic processing. The architecture is based on Taylor series expansion and consists of lookup tables and correction units so that the size of look-up tables are reduced. It can be applied to 32 bit floating point formats of IEEE-754 and reduced 24 bit floating point formats. The square root and inverse square root arithmetic units for 32 bit and 24 bit floating format number are designed as the proposed architecture. They can operation in a single cycle, and satisfy the precision of $10^{-5}$ required by OpenGL 1.x ES. They are designed using Verilog-HDL and the RTL codes are verified using an FPGA.

• Journal of Electrical Engineering and Technology
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• v.10 no.5
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• pp.2062-2069
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• 2015

In the series hybrid active power filter (SHAPF) with magnetic flux compensation (MFC), the system current oscillate in the experimental results when adding the same phase harmonic current command in current control block. This condition endangers the security of the SHAPF. Taking the digit period average arithmetic as example, this paper explains the inter-harmonics current oscillation in the experiment. The conclusion is that the SHAPF is unstable to the inter-harmonics current in theory. Limited by the capacity of the inverter, the system current and the inverter output current do not increase to infinite. At last, some methods are proposed to solve this problem. From the practical viewpoint, the voltage feed-forward control is easy to achieve. It can suppress the current oscillation problems, and also improve the filtering effect. The feasibility of the methods is validated by both the emulation and experiment results.

• Convergence Security Journal
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• v.11 no.3
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• pp.19-24
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• 2011

Software failure time presented in the literature exhibit either constant monotonic increasing or monotonic decreasing, For data analysis of software reliability model, data scale tools of trend analysis are developed. The methods of trend analysis are arithmetic mean test and Laplace trend test. Trend analysis only offer information of outline content. In this paper, we discuss forecasting failure time case of failure time censoring. In this study, time series analys is used in the simple moving average and weighted moving averages, exponential smoothing method for predict the future failure times, Empirical analysis used interval failure time for the prediction of this model. Model selection using the mean square error was presented for effective comparison.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.12
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• pp.2714-2726
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• 1997

In this paper, adaptive symbol changes-based medical image compression method is presented. First, the differenctial image domain is obtained using the differentiation rules or obaptive predictors applied to original mdeical image. Also, the algorithm determines the context associated with the differential image from the domain. Then prediction symbols which are thought tobe the most probable differential image values are maintained at a high value through the adaptive symbol changes procedure based on estimates of the symbols with polarity coincidence between the differential image values to be coded under to context and differential image values in the model template. At the coding step, the differential image values are encoded as "predicted" or "non-predicted" by the binary adaptive arithmetic encoder, where a binary decision tree is employed. The simlation results indicate that the prediction hit ratios of differential image values using the proposed algorithm improve the coding gain by 25% and 23% than arithmetic coder with ISO JPEG lossless predictor and arithmetic coder with differentiation rules or adaptive predictors, respectively. It can be used in compression part of medical PACS because the proposed method allows the encoder be directly applied to the full bit-planes medical image without a decomposition of the full bit-plane into a series of binary bit-planes as well as lower complexity of encoder through using an additions when sub-dividing recursively unit intervals.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• Journal of KIISE:Software and Applications
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• v.27 no.11
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• pp.1073-1081
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• 2000

본 연구에서는 효과적인 시계열 예측을 위하여 구간연산 기능을 갖는 신경망모델을 제안한다. 이는 기존의 FIR 네트워크의 동작특성을 구간연산으로 일반화함으로써 시계열 신호의 동적 특성을 효과적으로 반영할 뿐만 아니라 학습데이타 표현의 유연성을 증대시킨다. 이는 또한 실제 응용에서 신경망 입력 데이타에 내재할 수 있는 측정치 오류의 영향을 보완할 수 있게 하며 데이타 그룹화를 효과적으로 이룰 수 있게 함으로써 입력데이타의 양을 감축시키고 이로부터 학습의 효율을 개선한다. 본 논문에서는 구간연산을 이용하여 네트워크 동작특성, 학습알고리즘을 제시하고 실제 응용시스템에 이를 적용함으로써 제안된 이론의 유용성을 평가한다.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.