• The Mathematical Education
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• v.51 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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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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• v.43 no.4
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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.

• Proceedings of the KIEE Conference
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• 2004.11c
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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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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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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• v.29 no.4
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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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• v.14 no.10
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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.

• Korean Journal of Food Science and Technology
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• v.37 no.3
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• pp.492-497
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• 2005

In establishing legal limits of pesticide residues, various default values are employed to compensate for unavoidable variability in data. Because permissible errors in residue analysis reach ${\pm}30-40%$ RSD, maximum residue limits (MRLs) follow geometric progression. According to 5-yr period JMPR reports, variability factor (ratio of highest to median values) in field residue trials was 3.8-fold in 486 crop-pesticide combinations and round-up effort from highest residue to MRL was 1.5-fold, whereas regulatory margin (ratio of MRL to highest residue) used in Korea was 4.8-fold in 822 crop-pesticide combinations; Korean MRLs will be set at higher levels as compared with Codex limits if these margins are employed. Validation studies to compare and harmonize Korean and Codex MRLs of pesticide residues on food crops should be undertaken.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• International Journal of Highway Engineering
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• v.16 no.3
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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.