• 대한수학회지
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• 제54권4호
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• 대한수학회보
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• 제45권2호
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• 한국컴퓨터정보학회논문지
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• 제16권10호
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• pp.101-109
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• 2011

리만의 제타함수 $\zeta(s)$는 주어진 수 x보다 작은 소수의 개수 $\pi$(x)를 구하는 해답으로 알려져 있으며, 소수정리에서 지금까지 리만의 제타 함수 이외에 $\frac{x}{lnx}$,Li(x)와 R(x)의 근사치 함수가 제안되었다. 여기서 $\pi$(x)와의 오차는 R(x) < Li(x) < $\frac{x}{lnx}$이다. 로그적분함수 Li(x) = $\int_{2}^{x}\frac{1}{lnt}dt$, ~ $\frac{x}{lnx}\sum\limits_{k=0}^{\infty}\frac{k!}{(lnx)^k}=\frac{x}{lnx}(1+\frac{1!}{(lnx)^1}+\frac{2!}{(lnx)^2}+\cdots)$ 이다. 본 논문은 $\pi$(x)는 유한급수��Li(x)로 표현됨을 보이며, 일반화된 $\sqrt{ax}{\pm}{\beta}$의 소수계량함수를 제안한다. 첫 번째로, $\pi$(x)는 $0{\leq}t{\leq}2k$의 유한급수인 $Li_3(x)=\frac{x}{lnx}(\sum\limits_{t=0}^{{\alpha}}\frac{k!}{(lnx)^k}{\pm}{\beta})$와 $Li_4(x)=\lfloor\frac{x}{lnx}(1+{\alpha}\frac{k!}{(lnx)^k}{\pm}{\beta})\rfloor$, $k\geq2$ 함수로 표현됨을 보였다. $Li_3$(x)는 $\pi(x){\simeq}Li_3(x)$가 되도록 ${\alpha}$ 값을 구하고 오차를 보정하는 ${\beta}$ 값을 갖도록 조정하였다. 이 결과 $x=10^k$에 대해 $Li_3(x)=Li_4(x)=\pi(x)$를 얻었다. 일반화된 함수로 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$를 제안하였다. 제안된 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$ 함수는 리만의 제타함수에 비해 소수를 월등히 계량할 수 있었다.

• 대기
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• 제15권3호
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• pp.167-178
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• 2005

Using the FSSP-100(FSSP) and Microwave Radiometer (MWR), the fog and clear day characteristics (the size and number concentration of fog particles and the liquid water content) have been measured and analyzed at Daegwallyoung observation site ($37^{\circ}41^{\prime}N$, $128^{\circ}45^{\prime}E$) during 27 - 30 November 2003 (fog day) and 19 January 2004 (clear day). During the fog days, the measured fog-particle size by using FSSP is 0.8~8.4 ${\mu}m$, which is similar to the WMO typical value, the fog number concentration varies from 121 to 200 count ($No./cm^2$) and the fog liquid water content from $0.018g/m^3-0.1g/m^3$ in the site. The precipitable water vapor obtained by the MWR, showing the correlation coefficient $R^2$=0.83 between the total precipitable water vapor obtained from the radio sonde and MWR, shows the larger amount (0.75-8.3 cm) during the fog days than the clear-sky data (0.2 cm).

• 한국병원경영학회지
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• 제6권3호
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• pp.109-129
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• 2001

The purpose of this study was the acquisition of the optimum scale of the apportionment of standard & high-class bed for the maximum profit representative of the desire of customers in a General Hospital with 1,100 beds located in Seoul. This investigation was proceeded by the analysis of the result of the simulation with the survey of both the patients' needs for bed and the degree of the medical service by the grade of the ward. And finally the consequence was obtained as follows: 1. The result of the investigation of the inpatients' preference for the grade of ward classes shows that a private ward reflected 4.3 percent, a semi-private ward 1.7 percent, a three-bed ward 0.1 percent, and a ward with six beds 93.9 percent each other. 2. A questionnaire poll was paralleled of service terms of a medical doctor and a nurse by ward class, the data were used for the standard of the allotment of labor cost by the ward class. The poll shows that the service tenn of a medical doctor and a nurse based on a ward with six beds by ward class showed 1.7 times in internal medicine and 1.9 times in surgery at a private ward; 1.4 times in internal medicine and 1.7 times in surgery at a semi-private room; and 1.2 times both in internal medicine and in surgery at a three-bed ward 3. The resultant findings revealed the most profit per bed and per patient in a private ward. However, an analysis of profit with a standard of unit area by ward class represented a higher profit in both the internal medicine and the surgery semi-private ward than other ward classes. 4. The result of the analysis through simulation based on the data of the prime cost per the ward class proved the optimum scale of the distribution of beds by class as follows: sixteen beds of the internal medicine and twenty three beds of the surgery in the private ward; two hundreds and two of the internal medicine and one hundred and ninety eight of the surgery in the semi-private room; three of both the internal medicine and the surgery each other in the three-bed ward; one hundred and ninety eight of the internal medicine and two hundred and fifty two of the surgery in the ward with six beds. The result of this research exhibits that the income and expenditure of the hospital could be improved by changing parts of wards into private ones(containing the maximum profit per a unit of width) in case the scale of the number of beds is reset with the consideration of the profit per the unit width. In the near future it's strongly expected that the research for the more scientific standard of the allotment of labour cost by ward class and for definition of the optimum scale of the number of beds that actualize the maximum profit with the change of the three elements of the prime cost: cost of materials; labor costs; management expenses.

• 서비스연구
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• 제5권2호
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• pp.71-81
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• 2015

RSA 공개키 암호화 알고리즘에서는 소수, 키 생성, 소인수분해, 오일러 함수, 키 셋업, 합동식과 법, 지수 처리가 응용된다. 이와같은 알고리즘의 토대는 수학원리이다. 수학원리 중에서 첫 번째 개념은 소수를 구하여 응용하는 방법에서 출발한다. 두 개의 매우 큰 소수의 곱을 구하는 것은 용이 하지만 그 곱에서 원래의 두 개의 소수를 역 추적하는 것은 매우 어렵다는 원리를 이용한다. p와 q를 매우 큰 소수라 하면 이 두 개의 곱 $n=p{\times}q$를 구하는 것은 쉽지만 역으로, 합성수인 n에서 p와 q를 추적하는 방법은 거의 불가능하다. RSA 암호화 알고리즘에서는 수학적으로 역함수 계산이 어려운 일방향 함수를 구현하기 위해 자리수가 많은 양의 정수의 소인수 분해 문제를 사용하고 있다. 역 방향으로의 계산을 어렵게 하기 위해 mod의 개념을 소인수 분해 문제에 더해서 사용한다. 암호화에 대한 관심분야는 대개 알고리즘 구현과 사용에 집중되고 있지만 막상 암호 알고리즘을 처음 도입하는 경우에는 어떤 프로세스를 거쳐야 현장 업무에 적용되는지를 알 수 없다. 본 연구는 공개키 알고리즘 속성 진단을 기반으로 한 현장 업무 암호화 적용 프로세스 방안을 제시한다.

• Wind and Structures
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• 제7권5호
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• pp.317-332
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• 2004

Wind tunnel experiments were conducted under highly turbulent and disturbed flow conditions over a solid/perforated plate with a long splitter plate in its plane of symmetry. The effect of varied level of perforation of the normal plate on fluctuating velocities and fluctuating pressures measured across and along the separation bubble was studied. The different perforation levels of the normal plate; that is 0%, 10%, 20%, 30%, 40% and 50% are studied. The Reynolds number based on step height was varied from $4{\times}10^3$ to $1.2{\times}10^4$. The shape and size of the bubble vary with different perforation level of the normal plate that is to say the bubble is reduced both in height and length up to 30% perforation level. For higher perforation of the normal plate, bubble is completely swept out. The peak turbulence value occurs around 0.7 to 0.8 times the reattachment length. The turbulence intensity values are highest for the case of solid normal plate (bleed air is absent) and are lowest for the case of 50% perforation of the normal plate (bleed air is maximum in the present study). From the analysis of data it is observed that $\sqrt{\overline{u^{{\prime}2}}}/(\sqrt{\overline{u^{{\prime}2}}})_{max}$, (the ratio of RMS velocity fluctuation to maximum RMS velocity fluctuation), is uniquely related with dimensionless distance y/Y', (the ratio of distance normal to splitter plate to the distance where RMS velocity fluctuation is half its maximum value) for all the perforated normal plates. It is interesting to note that for 50% perforation of the normal plate, the RMS pressure fluctuation in the flow field gets reduced to around 60% as compared to that for solid normal plate. Analysis of the results show that the ratio [$C^{\prime}_p$ max/$-C_{pb}(1-{\eta})$], where $C^{\prime}_p$ max is the maximum coefficient of fluctuating pressure, $C_{pb}$ is the coefficient of base pressure and ${\eta}$ is the perforation level (ratio of open to total area), for surface RMS pressure fluctuation levels seems to be constant and has value of about 0.22. Similar analysis show that the ratio $[C^{\prime}_p$ max/$-C_{pb}(1-{\eta})]$ for flow field RMS pressure fluctuation levels seems to be constant and has a value of about 0.32.

• 한국정보과학회논문지:시스템및이론
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• 제35권2호
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• pp.75-83
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• 2008

Joye와 연구자들은 기존의 조합 소수 판단 검사에서 trial division 과정을 제거한 새로운 소수 생성 알고리즘 (이하 JPV 알고리즘)을 제시하였으며, 이 알고리즘이 기존의 조합 소수 생성 알고리즘에 비해 $30{\sim}40%$ 정도 빠르다고 주장하였다. 하지만 이 비교는 전체 수행시간이 아닌 Fermat 검사의 호출 횟수만을 비교한 것으로 정확한 비교와는 거리가 있다. 기존의 조합 소수 생성 알고리즘에 대해 이론적인 수행시간 예측 방법이 있음에도 불구하고 두 알고리즘의 전체 수행시간을 비교할 수 없었던 이유는 JPV 알고리즘에 대한 이론적인 수행 시간 예측 모델이 없었기 때문이다. 본 논문에서는 먼저 JPV 알고리즘을 확률적으로 분석하여 수행시간 예측 모델을 제시하고, 이 모델을 이용하여 JPV 알고리즘과 기존의 조차 소수 생성 알고리즘의 전체 수행시간을 비교한다. 이 모델을 이용하여 펜티엄4 시스템에서 512비트 소수의 생성 시간을 예측해 본 결과 Fermat 검사의 호출 횟수를 이용한 비교와는 달리 JPV 알고리즘이 기존의 조합 소수 생성 알고리즘보다 느리다는 결론을 얻었다. 이러한 이론적인 분석을 통한 비교는 실제 동일한 환경에서 실험을 통해서 검증되었다. 또한, 본 논문에서는 JPV 알고리즘의 성능 개선 방법을 제시한다. 이 방법을 사용하여 JPV 알고리즘을 개선하면 동일한 공간을 사용할 경우에 JPV 알고리즘이 기존의 조합 소수 생성 알고리즘과 비슷한 성능을 보인다.

• Structural Engineering and Mechanics
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• 제20권6호
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• pp.631-653
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• 2005

In this work, the mechanism of damping and its theoretical evaluation for layered aluminium cantilever structures jointed with a number of equispaced connecting bolts under an equal tightening torque have been considered. Extensive experiments have been conducted on a number of specimens for comparison with numerical results. Intensity of interface pressure, its distribution pattern, dynamic slip ratio and kinematic coefficient of friction at the interfaces, relative spacing of the connecting bolts, frequency and amplitude of excitation are found to play a major role on the damping capacity of such structures. It is established that the damping capacity of structures jointed with connecting bolts can be improved largely with an increase in number of layers maintaining uniform intensity of pressure distribution at the interfaces. Thus the above principle can be utilized in practice for construction of aircraft and aerospace structures effectively in order to improve their damping capacity which is one of the prime considerations for their design.

• 호남수학학술지
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• 제34권1호
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• pp.93-101
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• 2012

Let $E_A^B$ denote the elliptic curve $E_A^B:y^2=x^3+Ax+B$. In this paper, we calculate the number of points on elliptic curves $E_A^0:y^2=x^3+Ax$ over $\mathbb{F}_p$ mod 24. For example, if $p{\equiv}1$ (mod 24) is a prime, $3t^2{\equiv}1$ (mod p) and A(-1 + 2t) is a quartic residue modulo p, then the number of points in $E_A^0:y^2=x^3+Ax$ is congruent to 0 modulo 24.