• Honam Mathematical Journal
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• v.31 no.3
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• pp.437-449
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• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• ETRI Journal
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• v.30 no.6
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• pp.818-825
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• 2008

This paper proposes an exponentiation method with Frobenius mappings. The main target is an exponentiation in an extension field. This idea can be applied for scalar multiplication of a rational point of an elliptic curve defined over an extension field. The proposed method is closely related to so-called interleaving exponentiation. Unlike interleaving exponentiation methods, it can carry out several exponentiations of the same base at once. This happens in some pairing-based applications. The efficiency of using Frobenius mappings for exponentiation in an extension field was well demonstrated by Avanzi and Mihailescu. Their exponentiation method efficiently decreases the number of multiplications by inversely using many Frobenius mappings. Compared to their method, although the number of multiplications needed for the proposed method increases about 20%, the number of Frobenius mappings becomes small. The proposed method is efficient for cases in which Frobenius mapping cannot be carried out quickly.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.177-182
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• 2019

This study is about the number expressed and the number not expressed in terms of the sum of consecutive natural numbers with a difference of 2k. Since it is difficult to generalize in cases of onsecutive positive integers with a difference of 2k, the table of cases of 4, 6, 8, 10, and 12 was examined to find the normality and to prove the hypothesis through the results. Generalized guesswork through tables was made to establish and prove the hypothesis of the number of possible and impossible numbers that are to all consecutive natural numbers with a difference of 2k. Finally, it was possible to verify the possibility and impossibility of the sum of consecutive cases of 124 and 2010. It is expected to be investigated the sum of consecutive natural numbers with a difference of 2k + 1, as a future research task.

• Journal of the Korean Institute of Landscape Architecture
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• v.45 no.6
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• pp.115-125
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• 2017

This study was to investigate the user's thermal environments under the pergola($L\;7,200{\times}W\;4,200{\times}H\;2,700mn$) covered with Wisteria floribunda(Willd.) DC. according to the variation of leaf area index(LAI). We carried out detailed measurements with two human-biometeorological stations on a popular square Jinju, Korea($N35^{\circ}10^{\prime}59.8^{{\prime}{\prime}}$, $E\;128^{\circ}05^{\prime}32.0^{{\prime}{\prime}}$, elevation: 38m). One of the stations stood under a pergola, while the other in the sun. The measurement spots were instrumented with microclimate monitoring stations to continuously measure air temperature and relative humidity, wind speed, shortwave and longwave radiation from the six cardinal directions at the height of 0.6m so as to calculate the Universal Thermal Climate Index(UTCI) from $9^{th}$ April to $27^{th}$ September 2017. The LAI was measured using the LAI-2200C Plant Canopy Analyzer. The analysis results of 18 day's 1 minute term human-biometeorological data absorbed by a man in sitting position from 10am to 4pm showed the following. During the whole observation period, daily average air temperatures under the pergola were respectively $0.7{\sim}2.3^{\circ}C$ lower compared with those in the sun, daily average wind speed and relative humidity under the pergola were respectively 0.17~0.38m/s and 0.4~3.1% higher compared with those in the sun. There was significant relationship in LAI, Julian day number and were expressed in the equation $y=-0.0004x^2+0.1719x-11.765(R^2=0.9897)$. The average $T_{mrt}$ under the pergola were $11.9{\sim}25.4^{\circ}C$ lower and maximum ${\Delta}T_{mrt}$ under the pergola were $24.1{\sim}30.2^{\circ}C$ when compared with those in the sun. There was significant relationship in LAI, reduction ratio(%) of daily average $T_{mrt}$ compared with those in the sun and was expressed in the equation $y=0.0678{\ln}(x)+0.3036(R^2=0.9454)$. The average UTCI under the pergola were $4.1{\sim}8.3^{\circ}C$ lower and maximum ${\Delta}UTCI$ under the pergola were $7.8{\sim}10.2^{\circ}C$ when compared with those in the sun. There was significant relationship in LAI, reduction ratio(%) of daily average UTCI compared with those in the sun and were expressed in the equation $y=0.0322{\ln}(x)+0.1538(R^2=0.8946)$. The shading by the pergola covered with vines was very effective for reducing daytime UTCI absorbed by a man in sitting position at summer largely through a reduction in mean radiant temperature from sun protection, lowering thermal stress from very strong(UTCI >$38^{\circ}C$) and strong(UTCI >$32^{\circ}C$) down to strong(UTCI >$32^{\circ}C$) and moderate(UTCI >$26^{\circ}C$). Therefore the pergola covered with vines used for shading outdoor spaces is essential to mitigate heat stress and can create better human thermal comfort especially in cities during summer. But the thermal environments under the pergola covered with vines during the heat wave supposed to user "very strong heat stress(UTCI>$38^{\circ}C$)". Therefore users must restrain themselves from outdoor activities during the heat waves.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.509-520
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• 2003

Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.353-359
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• 1998

Factorial designs with two-level factors represent the smallest factorial experiments. The system of notation and confounding and fractional factorial schemes developed for the $2^N$system are found in standard textbooks of experimental designs. Just as in the $2^N$ system, the general confounding and fractional factorial schemes are possible in $3^N,5^N$, .... , and $\rho^N$ where $\rho$ is a prime number. Hence, we have the $\rho^N$ system. In this article, the author proposes a new algorithm for constructing fractional factorial plans in the $\rho^N$ system.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.201-209
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• 2017

There exists already mass formula which is the number of self orthogonal codes in $GF(q)^n$, but not proof of it. In this paper we described some theories about finite geometry and by using them proved the mass formula when $q=p^m$, p is odd prime.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.27-32
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• 2000

The quadratic fields generated by $x^2$=ax+1($\alpha\geq$1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=$\alpha^2$+4 is a prime in $\mathbb{Z}$, such that $\mathbb{Q}(\sprt{p})$ has class numbers 1, 3 and 5.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.171-175
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• 2009

Let $A_1,\;A_2,\;{\cdots},\;A_n$ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A_{i}{^{\prime}}s$ which occur. We establish an improved lower bounds of Univariate Bonferroni-Type inequality by using the linearity of binomial moments $S_1,\;S_2,\;S_3,\;S_4$ and$S_5$.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.571-583
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• 2020

The Galois ring R of characteristic pⁿ having p^mn elements is a finite extension of the ring of integers modulo pⁿ, where p is a prime number and n, m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.