• Nuclear Engineering and Technology
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• v.32 no.6
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• pp.605-617
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• 2000

Nodal transport methods are studied for the solution of two dimensional discrete-ordinates, simplified even-parity transport equation(SEP) which is known to be an approximation to the true transport equation. The polynomial expansion nodal method(PEN) and the analytic function expansion nodal method(AFEN）which have been developed for the diffusion theory are used for the solution of the discrete-ordinates form of SEP equation. Our study shows that while the PEN method in diffusion theory can directly be converted without complication, the AFEN method requires a theoretical modification due to the nonhomogeneous property of the transport equation. The numerical results show that the proposed two methods work well with the SEP transport equation with higher accuracies compared with the conventional finite difference method.

• Journal of Energy Engineering
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• v.17 no.4
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• pp.233-240
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• 2008

Conventionally, the second-order self-adjoint neutron transport equations have been studied using the even parity and the odd parity equations. Recently, however, the SAAF(self-adjoint angular flux) form of neutron transport equation has been introduced as a new option for the second-order self-adjoint equations. In this paper we validated the SAAF equation mathematically and clarified how it relates with the existing even and odd parity equations. We also developed a second-order SAAF differencing formula including DSA(diffusion synthetic acceleration) from the first-order difference equations. Numerical result is attached to show that the proposed methods increases accuracy with effective computational effort.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.16 no.2
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• pp.211-221
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• 2018

Nodal transport methods are proposed for solving the simplified even-parity neutron transport (SEP) equation. These new methods are attributed to the success of existing nodal diffusion methods such as the Polynomial Expansion Nodal and the Analytic Function Expansion Nodal Methods, which are known to be very effective for solving the neutron diffusion equation. Numerical results show that the simplified even-parity transport equation is a valid approximation to the transport equation and that the two nodal methods developed in this study also work for the SEP transport equation, without conflict. Since accuracy of methods is easily increased by adding node unknowns, the proposed methods will be effective for coarse mesh calculation and this will also lead to computation efficiency.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1017-1024
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• 2023

A celebrated result in the study of integer partitions is the identity due to Lehmer whereby the number of partitions of n with an even number of even parts minus the number of partitions of n with an odd number of even parts equals the number of partitions of n into distinct odd parts. Inspired by Lehmer's identity, we prove explicit formulas for evaluating generating functions for sequences that enumerate integer partitions of fixed width with an even/odd number of even parts. We introduce a technique for decomposing the even entries of a partition in such a way so as to evaluate, using a finite sum over q-binomial coefficients, the generating function for the sequence of partitions with an even number of even parts of fixed, odd width, and similarly for the other families of fixed-width partitions that we introduce.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.173-178
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• 1996

특정한 방향성분에 대한 방향중성자속을 정의하는 방향차분 수송 방정식(discrete ordinates or S$_{N}$ transport equation)과 달리 방향변수를 구분된 방향영역에 대하여 적분하고, 해당 방향영역 내에서의 방향중성자속이 일정하다고 가정하는 영역상수법(piecewise constant method)을 이용하여 유사방향차분방정식(discrete ordinates-like equation)을 유도하여, 이를 Boltzmann 수송식과 2계 우성수송식(even-parity transport equation)에 적용하여 기존의 방향차분법의 단점인 광첨두현상(ray effects)을 감소시키고, 우성수송식의 교차미분항을 제거한 단순우성방정식(simplified even-parity equation)을 사용하여 광첨두현상을 제거하였다. 이는 단순우성방정식의 또 다른 장점을 제시한다.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.1
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• pp.128-136
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• 2008

In this paper, we propose a new cache structure for effective error correction of soft error. We added check bit and SEEB(soft error evaluation block) to evaluate the status of cache line. The SEEB stores result of parity check into the two-bit shit register and set the check bit to '1' when parity check fails twice in the same cache line. In this case the line where parity check fails twice is treated as a vulnerable to soft error. When the data is filled into the cache, the new replacement algorithm is suggested that it can only use the valid block determined by SEEB. This structure prohibits the vulnerable line from being used and contributes to efficient use of cache by the reuse of line where parity check fails only once can be reused. We tried to minimize the side effect of the proposed cache and the experimental results, using SPEC2000 benchmark, showed 3% degradation in hit rate, 15% timing overhead because of parity logic and 2.7% area overhead. But it can be considered as trivial for SEEB because almost tolerant design inevitably adopt this parity method even if there are some overhead. And if only parity logic is used then it can have $5%{\sim}10%$ advantage than ECC logic. By using this proposed cache, the system will be protected from the threat of soft error in cache and the hit rate can be maintained to the level without soft error in the cache.

• Journal of Animal Reproduction and Biotechnology
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• v.34 no.1
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• pp.30-34
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• 2019

Milk fever is a metabolic disease with manifestation of clinical signs due to hypocalcemia, which usually occurs within 48-72 h after delivery. However, even after a successful treatment of milk fever, recurrence of milk fever may occur, and studies on recurrent milk fever are still lacking. Accordingly, the present study was conducted for the purpose of identifying the characteristics of recurrent milk fever according to farm, season, parity, and dystocia that can cause physiological changes in the mother during peri- and postpartum periods. The analysis results showed that the incidence rate of initial and recurrent milk fever according to breeding farm was 5.7%-14.1% and 3.1%-7.2%, respectively, demonstrating a positive correlation between the initial and recurrent milk fever (r = 0.613, p < 0.01). With respect to season, the incidence rate of initial and recurrent milk fever during summer was 12.3% and 7.5%, respectively, which were significantly higher than that of other seasons (p < 0.05). In addition, the recurrence rate, the ratio of recurrence relative to initial milk fever, was highest during summer with 62.7%. Regarding parity, the incidence rate of initial and recurrent milk fever in 3rd parity was 11.1% and 5.8%, respectively, which was significantly higher than in 1st and 2nd parity (p < 0.05). Furthermore, the recurrence rate in 4th parity was 64.1%, showing a pattern of increase in incidence rate with increase in parity. Finally, there were no differences in the incidence rate of initial and recurrent milk fever according to eutocia and dystocia. The findings indicated that the incidence rate of initial milk fever should be reduced to effectively prevent the recurrent milk fever, while animals with 3rd parity or higher should be expected to occur high rate of recurrent milk fever, especially during summer, and the necessary preparations should be made for intensive treatment of such individuals.

• Proceedings of the Korean Nuclear Society Conference
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• 2002.10a
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• pp.51.1-51
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• 2002

• 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.