• Kyungpook Mathematical Journal
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• v.64 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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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.

• Honam Mathematical Journal
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• v.37 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.4
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• pp.452-462
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• 1985

The axisymmetric forward extrusion is analyzed by using the rigid-plastic finite element formulation. The distribution of stresses and strains as well as the deformation pattern in solid extrusion is very important for the improvement of product quality. The initial velocity field is determined by assuming the material as a Newtonian fluid through an arbitrarily shaped axisymmetric die. The workhardening effect and the friction of the die-material interface are considered in the formulation. Some reduction of area and die shapes(conical and biquadratic-curved) are chosen for computation. Experiments are carried out for steel alloy(SCM4) specimens using conical and curved dies. It is found that experimental observation is in good agreement with FEM results. The strain distribution is curved(biquadratic) dies is shown to be more uniform than in conical dies at the same reduction of area.

• Journal of Magnetics
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• v.2 no.3
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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.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.44 no.2
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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.