• 한국수학교육학회지시리즈A:수학교육
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• 제51권3호
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• pp.211-221
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• 2012

We discovered that definition of a Geometrical Progression(Sequence) have some differences in domestic textbooks & some foreign countries' books. This will be able to cause a chaos when students divide whether a sequence is a Geometrical Progression(Sequence) or not, and a question error when teachers compose questions about convergence conditions of Infinite Geometric progressions & series. We took a question investigation for students about definition of a Geometrical Progression(that is called G. P.), we discovered that high level students have an error about definition of a G. P.. So We modified expressions of terminology in domestic textbooks appropriately through a Geometrical Progression(Sequence), infinite series, & infinite geometrical series in some foreign countries' books.

• 대한수학회보
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• 제53권1호
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• pp.1-20
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• 2016

The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method [12] using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with $1{\leq}k{\leq}d-1$ and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficients can be precisely determined.

• ETRI Journal
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• 제43권4호
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• pp.650-659
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• 2021

Multi-carrier waveforms have several advantages over single-carrier waveforms for radar communication. Employing multi-carrier complementary phase-coded (MCPC) waveforms in radar applications has recently attracted significant attention. MCPC radar signals take advantage of orthogonal frequency division multiplexing properties, and several authors have explored the use of MCPC signals and the difficulties associated with their implementation. The sidelobe level and peak-to-mean-envelope-power ratio (PMEPR) are the key issues that must be addressed to improve the performance of radar signals. We propose a scheme that applies pattern-based scaling and geometric progression methods to enhance sidelobe and PMEPR levels in MCPC radar signals. Numerical results demonstrate the improvement of sidelobe and PMEPR levels in the proposed scheme. Additionally, autocorrelations are obtained and analyzed by applying the proposed scheme in extensive simulation experiments.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.218-220
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• 2004

Orthogonal frequency division multiplexing(OFDM) is one of the most promising technique for next generation wireless broadband communication systems. In this paper, we propose a new bit allocation algorithm in multiuser OFDM. The proposed algorithm is derived from the geometric progression of the additional transmit power of subcarriers and the arithmetic-geometric means inequality. The simulation shows that this algorithm has similar performance to the conventional adaptive bit allocation algorithm and lower computational complexity than the existing algorithms.

• 대한수학회보
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• 제38권2호
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• pp.231-236
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• 2001

In this note we construct a sequence of Picard iterates suitable for the approximation of solutions of K-positive definite operator equations in arbitrary real Banach spaces. Explicit error estimate is obtained and convergence is shown to be as fast as a geometric progression.

• ETRI Journal
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• 제29권4호
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• pp.445-451
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• 2007

An adaptive modulation scheme is presented for multiuser orthogonal frequency-division multiplexing systems. The aim of the scheme is to minimize the total transmit power with a constraint on the transmission rate for users, assuming knowledge of the instantaneous channel gains for all users using a combined bit-loading and subcarrier allocation algorithm. The subcarrier allocation algorithm identifies the appropriate assignment of subcarriers to the users, while the bit-loading algorithm determines the number of bits given to each subcarrier. The proposed bit-loading algorithm is derived from the geometric progression of the additional transmission power required by the subcarriers and the arithmetic-geometric means inequality. This algorithm has a simple procedure and low computational complexity. A heuristic approach is also used for the subcarrier allocation algorithm, providing a trade-off between complexity and performance. Numerical results demonstrate that the proposed algorithms provide comparable performance with existing algorithms with low computational cost.

• Asian Pacific Journal of Cancer Prevention
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• 제14권10호
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• pp.6151-6158
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• 2013

Radio frequency ablation (RFA) is an effective means of achieving local control of liver cancer. It is a particularly suitable mode of therapy for small and favorably located tumors. However, local progression rates are substantially higher for large tumors (>3.0 cm). In the current study, we report on a mathematical model based on geometric optimization to treat large liver tumors. A database of mathematical models relevant to the configuration of liver cancer was also established. The specific placement of electrodes and the frequency of ablation were also optimized. In addition, three types of liver cancer lesion were simulated by computer guidance incorporating mathematical models. This approach can be expected to provide a more effective and rationale mechanism for employing RFA in the therapy of hepatic carcinoma.

• 한국식품과학회지
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• 제37권3호
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• pp.492-497
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• 2005

잔류농약과 관련된 포장시험 및 기준설정에는 데이터의 변이성이 뒤따르기 때문에 여러가지 허수(default value)를 채택하고 있다. 잔류농약 분석상의 오차는 $RSD\;{\pm}30-40%$에 이르고 있어 잔류허용기준(MRL)은 이것을 감안하여 geometric progression에 따르고 있다. 과거 5년간(1998-2002)의 JMPR 보고서에 의하면 포장시험에서의 변이계수(중앙치에 대한 최고치 비율)은 LOQ 이상에서의 486개 농약-작물 조합에서 평균 3.8배에 이르고 있고 기준설정시의 절상효과는 최고치의 1.5배로 나타났다. 한편 국내에서 기준설정시의 규제마진(최고잔류치에 대한 최대잔류기준의 비율)은 822개 농약-작물 조합에서 평균 4.8배로 나타났다. 이와 같은 규제마진을 적용하는 경우 국내의 잔류기준은 Codex보다 높게 설정될 것으로 예상된다. 앞으로 농약잔류 허용기준의 설정에서 Codex기준과 국내기준의 조화를 이루기 위한 검증작업이 이루어져야 할 것이다.

• 한국통신학회논문지
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• 제36권10C호
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• pp.614-620
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• 2011

현재 가장 많이 쓰이는 공개키 암호시스템 중 하나인 RSA는 매우 큰 합성수 N의 인수분해가 어렵다는 것에 기반을 두고 있다. 120자리보다 큰 합성수를 인수분해하는데 가장 효율적인 알고리즘으로 알려진 Number Field Sieve (NFS)는 법 N에 대하여 공통근을 갖는 두 다항식 선택한 후에, sieving, linear algebra, square root 단계를 차례대로 거친다. 최근의 많은 연구 결과에 따르면 다항식을 얼마나 적합하게 선택하느냐에 따라 sieving step에서의 복잡도가 크게 달라질 수 있다는 것이 알려져 있다. Sieving 다항식은 차수가 같은 두 다항식을 선택하는 것이 이상적이며 두 개의 2차 다항식을 선택하는 방법은 이미 Montgomery가 제시하였다. 이 논문에서는 5항 등 비수열 방법을 이용하여 두 개의 3차 다항식 선택방법을 제시하고자 한다.

• 한국도로학회논문집
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• 제16권3호
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• pp.75-84
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• 2014

PURPOSES : Traffic congestions which occur in the intersections of arterials lead to mobility and environment problem, and then traffic agencies and engineers have been struggling for mitigating congestions with greenhouse gas emissions. As an alternative of solving theses problems, this study is to introduce a low-cost and high-effectiveness countermeasure as unconventional intersections which are successfully in operation in U.S.. The main feature of unconventional intersections is to reroute turning movement on an approach to other approach, which consequently more green time is available for the progression of through traffic. Due to improved progression, this unique geometric design contributes to reduce delays with greenhouse gas emission and provides a viable alternative to interchanges. This study is to evaluate the potential operation and environment benefits of unconventional intersections. METHODS : This study used the VISSIM model with Synchro and EnViVer. Synchro is to optimize signal phases and EnViVer model to estimate the amount of greenhouse gas emissions by each condition. RESULTS : The result shows that unconventional intersections lead to increase the capacity and to reduce greenhouse gas emissions, compared to existing intersections. CONCLUSIONS : Unconventional intersections have the ability to positively impact operations and environments as a low-cost and high-effectiveness countermeasure.