• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.303-309
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• 2024

An imaginary bicyclic biquadratic number field K is a field of the form ${\mathbb{Q}}({\sqrt{-m}},{\sqrt{-n}})$ where m and n are squarefree positive integers. The ideal class number h_K of K is the order of the abelian group I_K/P_K, where I_K and P_K are the groups of fractional and principal fractional ideals in the ring of integers 𝒪_K of K, respectively. This provides a measure on how far is 𝒪_K from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.

• 대한수학회보
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• 제35권1호
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• pp.83-89
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• 1998

Using the list of all imaginary quadratic fields with class number 1, 2, 3 and 6, we determine all imaginary bicyclic biquadratic number fields of class number 3. There are exactly 163 such fields and their conductors are less than or equal to 163 $\cdot$883.

• 충청수학회지
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• 제23권1호
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• pp.169-176
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• 2010

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. In this paper, we obtain the the criterion for the parity of the ideal class number h(${\mathcal{O}}_K$) of the real biquadratic function field $K=k(\sqrt{P_1},\;\sqrt{P_2})$, where $P_1$, $P_2{\in}{\mathbb{A}}$ be two distinct monic primes of even degree.

• 호남수학학술지
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• 제37권1호
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• pp.1-6
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• 2015

Let A be an abelian variety defined over a number field K. Let L be a biquadratic extension of K with Galois group G and let III (A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming III(A/L) is finite, we compute [III(A/K)]/[III(A/L)] where [X] is the order of a finite abelian group X.

• 충청수학회지
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• 제30권1호
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• pp.77-102
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• 2017

As an analogy of $Poincar{\acute{e}}$ series in the space of modular forms, T. Ono associated a module $M_c/P_c$ for ${\gamma}=[c]{\in}H^1(G,R^{\times})$ where finite group G is acting on a ring R. $M_c/P_c$ is regarded as the 0-dimensional twisted Tate cohomology ${\hat{H}}^0(G,R^+)_{\gamma}$. In the case that G is the Galois group of a Galois extension K of a number field k and R is the ring of integers of K, the vanishing properties of $M_c/P_c$ are related to the ramification of K/k. We generalize this to arbitrary n-dimensional twisted cohomology of the ring of integers and obtain the extended version of theorems. Moreover, some explicit examples on quadratic and biquadratic number fields are given.

• 대한기계학회논문집
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• 제9권4호
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• pp.452-462
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• 1985

본 논문에서는 금형의 형상과 단면 감소율등이 이에 미치는 영향을 조사하였 다. 이론과의 비교를 위해서 풀림처리된 특수강 소재인 SCM4로 실험을 행하였다. 압출하중은 로드셀(loadcell)로 측정하였으며 수치계산에서 구해진 속도장과 실제속도 장의 차이를 살펴보기 위해서 시편단면에 포토에칭(photoetching)한 압출시킬 시편의 그리드변형을 강소성유한요소법으로 계산한 그리드패턴과 비교 검토하였다.

• Journal of Magnetics
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• 제2권3호
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• pp.93-95
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• 1997

We investigated the temperature dependence of magnetization of Fe/Al multilayers fabricated by dc magnetron sputtering system. As the temperature increased from 5 K in a low magnetic field (100G) the magnetization of the samples increased and made a broad peak at some critical temperature. Further increase of temperature decresed the magnetization as an ardinary ferromagnetic curve. Part of samples show rapid increase of magnetization at low temperature. A model developed in this study suggests that the biquadratic coupling yields such a rapidly increasing behavior of magnetization at low temperature.

• 한국작물학회지
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• 제44권2호
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• pp.149-153
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• 1999

Prediction of rice developmental stage is necessary for proper crop management and a prerequisite for growth simulation as well. The objectives of the present study were to find out the relationship between the plastochrone index(PI) and the developmental index(DVI) estimated by non-parametric phenology model which simulates the duration from seedling emergence(DVI=0) to heading(DVI=l) by employing daily mean air temperature and daylength as predictor variables, and to confirm the correspondency of developmental indice to panicle developmental stages based on this relationship. Four japonica rice cultivars, Kwanakbyeo, Sangpungbyeo, Dongjinbyeo, and Palgumbyeo which range from very early to very late in maturity, were grown by sowing directly in dry paddy field five times at an interval of two weeks. Data for seedling emergence, leaf appearance, differentiation stage of primary rachis branch and heading were collected. The non-parametric phenology model predicted well the duration from seedling emergence to heading with errors of less than three days in all sowings and cultivars. PI was calculated for every leaf appearance and related to the developmental index estimated for corresponding PI. The stepwise polynomial analysis produced highly significant square-rooted cubic or biquadratic equations depending on cultivars, and highly significant square-rooted biquadratic equation for pooled data across cultivars without any considerable reduction in accuracy compared to that for each cultivar. To confirm the applicability of this equation in predicting the panicle developmental stage, DVI at differentiation stage of primary rachis branch primordium was calculated by substituting PI with 82 corresponding to this stage, and the duration reaching this DVI from seedling emergence was estimated. The estimated duration revealed a good agreement with that observed in all sowings and cultivars. The deviations between the estimated and the observed were not greater than three days, and significant difference in accuracy was not found for predicting this developmental stage between those equations derived for each cultivar and for pooled data across all cultivars tested.