• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1049-1067
• /
• 2019

In this paper, we discuss the number of distinct fuzzy subgroups of the group ${\mathbb{Z}}_{p^n}{\times}{\mathbb{Z}}_{q^m}{\times}{\mathbb{Z}}_r$, m = 1, 2, 3 where p, q, r are distinct primes for any $n{\in}{\mathbb{Z}}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group G and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.985-1000
• /
• 2019

Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.285-301
• /
• 2019

Let $p_1$ and $p_2$ be two distinct odd primes with gcd($p_1-1$, $p_2-1$) = 6. In this paper, we compute the linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that their linear complexity is quite good. So, the sequence can be used in many domains such as cryptography and coding theory. This article enrich a method to construct several classes of cyclic codes over GF(q) with length $n=p_1p_2$ using the two-prime WGCS-I of order 6. We also obtain the lower bounds on the minimum distance of these cyclic codes.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.1035-1059
• /
• 2023

Let p be an odd prime. Let E be an elliptic curve defined over a quadratic imaginary field, where p splits completely. Suppose E has supersingular reduction at primes above p. Under appropriate hypotheses, we extend the results of [17] to ℤ²_p-extensions. We define and study the fine double-signed residual Selmer groups in these settings. We prove that for two residually isomorphic elliptic curves, the vanishing of the signed 𝜇-invariants of one elliptic curve implies the vanishing of the signed 𝜇-invariants of the other. Finally, we show that the Pontryagin dual of the Selmer group and the double-signed Selmer groups have no non-trivial pseudo-null submodules for these extensions.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.26 no.6
• /
• pp.1401-1411
• /
• 2016

The Multi-Prime RSA and the Prime Power RSA are the variants of the RSA cryptosystem, where the Multi-Prime RSA uses the modulus $N=p_1p_2{\cdots}p_r$ for distinct primes $p_1,p_2,{\cdots},p_r$ (r>2) and the Prime Power RSA uses the modulus $N=p^rq$ for two distinct primes p, q and a positive integer r(>1). This paper analyzes the security of these systems by using the technique given by Heninger and Shacham. More specifically, this paper shows that if the $2-2^{1/r}$ random portion of bits of $p_1,p_2,{\cdots},p_r$ is given, then $N=p_1p_2{\cdots}p_r$ can be factorized in the expected polynomial time and if the $2-{\sqrt{2}}$ random fraction of bits of p, q is given, then $N=p^rq$ can be factorized in the expected polynomial time. The analysis is then validated with experimental results for $N=p_1p_2p_3$, $N=p^2q$ and $N=p^3q$.

• Journal of the Daesoon Academy of Sciences
• /
• v.38
• /
• pp.47-82
• /
• 2021

At the age of 15, Song Gyu, the second patriarch of Won Buddhism, met Jeungsan-gyo members and was substantially influenced by them. Jeongsan cultivated himself for three months in Mount Gaya based on their recommendations. He instructed his family members to practice reciting the Tae-eul Mantra. Henceforth, Jeongsan was said to attain supernatural power when he was around 18 years old, and he pursued the traces left by Jeungsan in Jeolla Province. Once there, he asked Jeungsan's younger sister to move to his hometown, Seongju, Gyeongsang Province, and he served her with his utmost sincerity. He went back to the birthplace of Jeungsan and received a Daoist book from Jeungsan's daughter titled, Essentials for an Upright Mind (正心要訣). Jeongsan practiced holy works for 10 months at Daewon-sa Temple in Mount Moak where Jeungsan was said to have attained unification with the Dao. After he had met Jeungsan-gyo members at the temple, he was able to stay in her house where he ended up meeting So Taesan. Before their meeting, it is obvious that Jeongsan was a member of Jeungsan-gyo. Afterward, Jeongsan entered into Won Buddhism and used the passage, 'saving lives by curing the world (濟生醫世).' He recited the writing of Jeungsan, which had been given to his disciples, as if it had been a mantra. In addition, he mentioned Jeungsan's poems or the Chinese poems that he had quoted many times. Jeongsan also interpreted passages from The Hyunmu Scripture (玄武經) written by Jeungsan in a unique manner. Jeongsan answered his disciples in his own way when they asked questions on the teachings of Jeungsan. He recognized Jeungsan as one of the Three Primes, who presided over the Great Opening.

• The Bulletin of The Korean Astronomical Society
• /
• v.40 no.1
• /
• pp.46.4-47
• /
• 2015

Carnegie Hubble Program II (hereafter CHP II) is a large Hubble Space Telescope (HST) observing campaign in the cycle 22 composed of a total of 184 orbits (132 primes + 52 parallels), which aims to measure H0 directly with an unprecedented accuracy. Unlike our previous efforts in CHP I which used Cepheids as a yardstick, CHP II takes the Population II (Pop II) distance indicators such as RR Lyraes and tip of the red giant branch stars (TRGBs) to set up a new calibration to Type Ia supernovae (SN Ia) distance. The Pop II distance scales have two immediate advantages over the classical Cepheid method: 1) The period-luminosity relation of the RR Lyrae has a scatter that is a factor of 2 smaller; 2) The RR Lyrae/TRGB distance scale can be applied to both elliptical and spiral galaxies. This will provide a great systematic benefit by ultimately allowing us to double the number of SN Ia distances based on geometry. By taking advantage of this Pop II route, we expect to measure H0 value to 3 % of error which will be the highest accuracy H0 measurement to date using the "Distance Ladder" method. In this talk I will present a brief background/overview on the CHP II, observations/data acquisition status, and ongoing research progress/preliminary results.

• Journal of Applied Tourism Food and Beverage Management and Research
• /
• v.16 no.2
• /
• pp.17-31
• /
• 2005

Recently, hotel industry has realized the importance of food and beverage sales for the profit maximization, and the focuses on restaurant management has been growing. Accordingly, menu management in the F/B department is one of the most key factors determining the success or failure of business. Therefore, in this study, entree menu items of french restaurant in the deluxe hotel was analysed with presently theorized model of menu analysis, classified into four menu items. Also it was analyzed how those classified menu items influence on sales, number of sold, food cost percentage, contribution margin And, proper ways was presented to make restaurant managers and menu planner in order to increase food operation sales through proper modifications and methods on various menu analysis matrix. In Pavesic's menu analysis method, all of menu items have impact on the sales, number of sold, contribution margin and Primes, Sleepers do so on the food cost. The finding of this study was that Pavesic's menu analysis is superior to menu analysis in terms of the sales, number of sold, food cost percentage, contribution margin. Therefore, Pavesic's menu analysis is useful and efficient method in order to conduct menu engineering.

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

• JSTS:Journal of Semiconductor Technology and Science
• /
• v.16 no.5
• /
• pp.564-581
• /
• 2016

We present an efficient hardware prime generator that generates a prime p by combining trial division and Fermat test in parallel. Since the execution time of this parallel combination is greatly influenced by the number k of the smallest odd primes used in the trial division, it is important to determine the optimal k to create the fastest parallel combination. We present probabilistic analysis to determine the optimal k and to estimate the expected running time for the parallel combination. Our analysis is conducted in two stages. First, we roughly narrow the range of optimal k by using the expected values for the random variables used in the analysis. Second, we precisely determine the optimal k by using the exact probability distribution of the random variables. Our experiments show that the optimal k and the expected running time determined by our analysis are precise and accurate. Furthermore, we generalize our analysis and propose a guideline for a designer of a hardware prime generator to determine the optimal k by simply calculating the ratio of M to D, where M and D are the measured running times of a modular multiplication and an integer division, respectively.