• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.403-412
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• 2015

Kato[6] and Torres[9] characterized the Weierstrass semigroup of ramification points on h-hyperelliptic curves. Also they showed the converse results that if the Weierstrass semigroup of a point P on a curve C satisfies certain numerical condition then C can be a double cover of some curve and P is a ramification point of that double covering map. In this paper we expand their results on the Weierstrass semigroup of a ramification point of a double covering map to the Weierstrass semigroup of a pair (P, Q). We characterized the Weierstrass semigroup of a pair (P, Q) which lie on the same fiber of a double covering map to a curve with relatively small genus. Also we proved the converse: if the Weierstrass semigroup of a pair (P, Q) satisfies certain numerical condition then C can be a double cover of some curve and P, Q map to the same point under that double covering map.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.641-645
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• 2013

In this article, we show that the modular equation ${\Phi}_p^{T_q}(X,Y)$ of Thompson series $T_q$ corresponding to ${\Gamma}_0(q)+q$ gives an affine model of a modular curve $X_0(pq)+q$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.6
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• pp.95-109
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• 2006

Elliptic Curve Cryptosystem (ECC) is suitable for resource-constrained devices such as smartcards, and sensor motes because of its short key size. This paper presents an efficient multi-scalar multiplication algorithm which is the main component of the verification procedure in Elliptic Curve Digital Signature Algorithm (ECDSA). The proposed algorithm can make use of a precomputed table of variable size and provides an optimal efficiency for that precomputed table. Furthermore, the given scalar is receded on-the-fly so that it can be merged with the main multiplication procedure. This can achieve more savings on memory than other receding algorithms. Through experiments, we have found that the optimal sizes of precomputed tables are 7 and 15 when uP+vQ is computed for u, v of 163 bits and 233 bits integers. This is shown by comparing the computation time taken by the proposed algorithm and other existing algorithms.

• Journal of Korean Society for Quality Management
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• v.50 no.3
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• pp.349-371
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• 2022

Purpose: Compared to the rapid growth rate of the domestic automotive LED industry so far, the predictive analysis method for demand forecasting or market outlook was insufficient. Accordingly, product characteristics are analyzed through the life trend of LEDs for automotive exterior lamps and the relative strengths of p and q using the Bass model. Also, future demands are predicted. Methods: We used sales data of a leading company in domestic market of automotive LEDs. Considering the autocorrelation error term of this data, parameters m, p, and q were estimated through the modified estimation method of OLS and the NLS(Nonlinear Least Squares) method, and the optimal method was selected by comparing prediction error performance such as RMSE. Future annual demands and cumulative demands were predicted through the growth curve obtained from Bass-NLS model. In addition, various nonlinear growth curve models were applied to the data to compare the Bass-NLS model with potential market demand, and an optimal model was derived. Results: From the analysis, the parameter estimation results by Bass-NLS obtained m=1338.13, p=0.0026, q=0.3003. If the current trend continues, domestic automotive LED market is predicted to reach its maximum peak in 2021 and the maximum demand is $102.23M. Potential market demand was $1338.13M. In the nonlinear growth curve model analysis, the Gompertz model was selected as the optimal model, and the potential market size was $2864.018M. Conclusion: It is expected that the Bass-NLS method will be applied to LED sales data for automotive to find out the characteristics of the relative strength of q/p of products and to be used to predict current demand and future cumulative demand.

• The Korean Journal of Ecology
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• v.18 no.2
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• pp.275-283
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• 1995

Seral changes in floristic composition during abandoned field succession after shifting cultivation was investigated in eastern Kangwon-Do, Korea. According to the DCA ordination based on the floristic composition, sere of the dominant species was shown as follows: Digitaria sanguinalis, Persicaria spp., Commelina communis etc. in the annual stage (0∼1 years); Erigeron spp., Artemisia spp., Rubus crataegus etc. in the Erigeron-Artemisia stage (2∼6 years); Pinus densiflora, Salix spp., Miscanthus sinensis, Arundinella hirta etc. in the shrub - earlier tree stage (10∼25 years); P. densiflora, Quercus mongolica, Spodiopogon sibiricus etc. in the mid-tree stage (25∼50 years); Q. mongolica, Tripterigium regelii, Lespedeza maximowiczii, Carex siderosticta etc. in the latter tree stage (50∼80 years). In mid-tree stage, size-frequency distribution of P. densiflora was plotted as a platycurtic curve and that of Q. mongolica as a reverse J-shaped curve, which meant P. densiflora was thinned through interspecific competition and Q. mongolica was regenerated by itself in the later tree stage.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.407-416
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• 2013

Let E be an elliptic curve over $\mathbb{Q}$ and $p$ be a prime of good supersingular reduction for E. Although the Iwasawa theory of E over the cyclotomic ${\mathbb{Z}}_p$-extension of $\mathbb{Q}$ is well known to be fundamentally different from the case of good ordinary reduction at p, we are able to combine the method of our earlier paper with the theory of Kobayashi [5] and Pollack [8], to give an explicit upper bound for the number of copies of ${\mathbb{Q}}_p/{\mathbb{Z}}_p$ occurring in the $p$-primary part of the Tate-Shafarevich group of E over $\mathbb{Q}$.

• Journal of the Korean Institute of Landscape Architecture
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• v.22 no.1
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• pp.85-100
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• 1994

This study was to analyze the relationship between the community or species and environmental variables of the vegetation landscape in Naejangsan National Park. The analysis was performed by the ordination of DCA and CCA. The study was to compare and analyze the species composition status by the layer and the growth characterisics of the following vegetations ; Torreya nucifera community, Quercus variabilis - Acer palmatum community, Q. variabilis community, Q. variabilis - Sasa purpurascens community and Daphniphyllam macropodum community. The results are as follows; 1. The result of the study on the relationshkp between the stand scores of DCA ordination and environmental variables showed that the soil pH, the ammount of AV-P2O5 and the ammount of C.E.C. tend to increase while Pinus densiflora community changes to Q. variabilis - Q. serrata community and finally Carpinus laxiflora species community siginigicantly. The relation between the stand scores of CCA ordination and several enviromental variables suggested that the species of C. laxiflora and C. tschonoskii the species of Q. cariabilis and Q. serrata the species of C. pisifera, P. densiflora and Q. aliana in sequence grows in more fertile soil. 2. As the result of the analysis of the T. nucifera community showed, reproduction did not increase, and the characteristic of growth was not affected. The result is shown in the growth curve that was damaged by the climate and the human interference. 3. The A. palmatum was found to be as minor species in the middle layer and the crown areas did not have sufficient crown. 4. The result of the analysis of the relationship between Q. variabilis community and Q. variabilis - S. purpurascens community showed a decreasing tendency in the growth and number of species. 5. D. macropodum which constituted the dominance species in the middle layer had a nomal growth curve, and then the successional trend of D. macropodum species seems to be located in the climax species.

• The Korean Journal of Ecology
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• v.19 no.3
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• pp.223-230
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• 1996

Five measurements of species diversity (richness index, diversity index, evenness index, dominance index and species sequences-importance curve) and their relationships with sltitude, tree age and community type were studied in $T\v{o}gyusan$ National Park, Korea. Altitude and tree age were the major variables explaining the differences of species diversity in the whole forest. Species richness index, diversity index and evenness index of Quercus mongolica and Pinus densiflora communities were lower than those of Carpinus laxiflora, Q. serrata, Fraxinus mandshurica, Q. mongolica - P. densiflora communities than that in the other communities. The species sequence-importance curve of the forest communities in $T\v{o}gyusan$ coincided with the ideal curve calculated by the lognormal-distribution theory.

• Proceedings of the KIEE Conference
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• 2002.11b
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• pp.154-156
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• 2002

PSS/E의 내부 시퀀스인 IPLAN을 이용하여 반복 조류계산을 함으로서 P-V, Q-V 곡선의 P, Q, V 값을 계산하는 IPLAN을 작성하였다. 작성된 곡선들은 유효전력 및 무효전력 예비력을 판단하는 지표, 전압안정도를 판별하는 지표 등 여러 방면에서 사용될 수 있다.

• Journal of the Korean Geotechnical Society
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• v.24 no.6
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• pp.5-16
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• 2008

This study investigated the existing theoretical backgrounds in order to examine the stability control method of lateral flow caused by the Plasticity of soils when unsymmetrical surcharge works on polluted soils and then compared and analyzed the results measured through model tests. Ultimate bearing power of ML and $ML_{p1}$ and $ML_{p2}$ obtained at surcharge(q)-settlement$(S_v)$ curve showed similar trends to ultimate bearing power obtained from control chart of deflection $(S_v-Y_m)$ by Tominaga.Hashimoto, that of $S_v-(Y_m/S_v)$ by Matsuo.Kawamura and that of $(q/Y_m)-q$ by Shibata.Sekiguchi and so it is considered that it has no problem in actual applicability. ${S_v-(Y_m/S_v)}$ of control chart of $ML_{p1}$ by Matsuo.Kawamura showed smaller value than ultimate bearing capacity value from surcharge-settlement curve $(q-S_v)$. Expression of ML of fracture baseline at stability control charge by Matsuo Kawamura is ${S_v=3.21exp}\{-0.48(Y_m/S_v)\}$ and expression of $ML_{p1}$ is ${S_v=3.26exp}\{-0.96(Y_m/S_v)\}$ and expression of $ML_{p2}$ is ${S_v=6.33exp}\{-0.45(Y_m/S_v)\}$.