• 대한수학회지
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• 제58권3호
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• pp.643-702
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• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• 한국정보과학회논문지:소프트웨어및응용
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• 제27권1호
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• pp.50-61
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• 2000

최근 원추곡선에 기반한 스테레오 비젼에 대한 연구가 주목을 받고 있는데, 이는 원추곡선이 행렬표현, 대응관계설정의 용이성, 그리고 실세계에서 쉽게 찾을 수 있다는 좋은 성질을 갖는다는 점에서 당연한 현상이라 여겨진다. 하지만, 일반적인 고차의 대수곡선에 대한 확장은 아직 성공적으로 이루어지지 못하고 있는 실정이다. 기약인 대수곡선 (irreducible algebraic curve)은 실세계에서 많지 않지만, 직선과 원추곡선은 무수히 많고, 따라서 이들의 곱으로 주어지는 높은 차수의 대수곡선도 무수히 많다. 본고에서는 2이상의 임의의 차수를 가지는 대수곡선을 calibration된 두 대의 카메라를 가지고 스테레오 문제를 푼다. 대응관계설정과 복원, 두 가지 문제 모두에 대한 closed form solution을 제시한다. $f_1,\;f_2,\;{\pi}$를 각각 두 이미지 곡선, 공간상의 평면이라 하고, $VC_P(g)$를 평면곡선 g와 점 P로 만들어지는 원추곡선이라 하면, $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ 의 관계를 이용하여 미지수인 평면 ${\pi}$의 계수들, $d_1,\;d_2,\;d_3$에 대한 다항 방정식들을 얻을 수 있다. 약간의 변형을 통하여 $d_1$에 대한 다항 방정식을 얻을 수 있고, 이 방정식의 유일한 양수해는 나머지 과정에서 매우 중요한 역할을 한다. 그 이후에는 $O(n^2)$개의 일변수 다항식에 대한 계산만으로 모든 스테레오 문제를 해결한다. 이는 과거의 여러 개의 다변수 다항식의 공통근을 구해야 했던 방법에 비교된다. synthetic 데이터와 실제 이미지에 대한 실험은 우리의 알고리듬이 옳음을 보여준다.

• 한국식품저장유통학회지
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• 제13권2호
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• pp.119-124
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• 2006

율무의 볶음 온도와 시간이 율무 추출액의 품질특성에 미치는 영향을 분석하기 위하여 볶음공정을 반응표면분석법으로 최적화하였다. 볶음 온도와 시간이 증가함에 따라 추출액의 갈색도와 폴리페놀함량 및 DPPH 소거능이 증가하는 경향을 나타내었으며 색도는 붉은 색을 나타내었다. 측정된 변수에 대하여 수립된 회귀식은 높은 결정계수값을 가졌으며, 볶음시간 보다는 온도가 더 중요한 변수로 작용하였고, 수립된 이차 회귀식에 대한 적합성 결여분석 결과 수립된 반응표면 모형이 통계적으로 유의하였다. 폴리페놀의 함량의 최대 예측값은 $2.78{\mu}g/mL$으로 이때의 조건은 $224^{\circ}C$와 35분이었으며, DPPH 소거능을 최대로 하는 조건은 $221^{\circ}C$와 37분의 조건에서 41.3%의 효과를 갖는 것으로 예측되었다. 율무 추출액의 갈변도가 0.2 에서 0.3사이, 폴리페놀함량은 2.0에서 $2.5{\mu}g/mL$사이, DPPH 소거능은 30에서 40%로, hue angle은 0에서 100사이인 조건을 만족하는 볶음처리 조건은 유음온도 $215^{\circ}C$, 볶음시간은 32분으로 나타났다.

• The Korean Journal of Ecology
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• 제10권3호
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• pp.119-127
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• 1987

On the east slope of the front ranges of the Colorado Rockies, USA, three species of Populus are distributed at different elevations from the Great Plains to the timberline. At elevations 1, 720m (P. sargentii), 2, 335m (P.angustifolia) and 3, 190m (P.tremuloides) chlorophyll cotents of leaves of thses dioecious trees were determined. Total chlorophyll content was in the range of 0.86-1.56mg/g leaf, increasing with elevation as a second-degree polynomial, and the peak content was estimated to be reached at about 2, 800m. Total chlorophyll content was greater in female than in male trees in the two higher elevation species, but not in P. sargentii, the low elevation species. Chlorophyll b content was greater than chlorophyll a content in the same two higher elevation species. The increase of chlorophyll b than to increase of chlorophyll a content. These phenomena appear to be the result of adaptation of these species to different environmental conditional at different elevation. Sequential distribution of plant populations on environmental gradients in such a way that variation in given plant characters paralell the environmental gradient must occur not only in ecotypes of a species, but also in different but closely related species.

• 한국식품영양과학회지
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• 제19권3호
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• pp.234-238
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• 1990

The effects of salt concentration immersion time in a salt solution prior to air dehydration and heating of air temperature during dehydration upon the browning reaction and pyruvic acid content of air dried garlics to a 6.5% moisture content(wet basis) were analyzed by a response surface methodology(RSM), Those values were also predicted by using a second degree polynomial regression model. Heating of air temperature was the most significant factor affecting the both browning reaction and pyruvic acid content. Salt concentration had more influence to browning reaction than immersion time whereas immersion time was more impor-tant factor than salt concentration on a retention of pyruvic acid sugested different processing conditions. While the processing conditions to minimize the browning reaction(O.D=0.009) were 0.3% of salt solution 9 min of immersion time and 5$0^{\circ}C$ of air temperature compared to control(O.D=0.022) of air dehydration at 5$0^{\circ}C$ Pyruvic acid contents were maximized(174 $\mu$mole/g garlic solid) at the 0.1% of salt solution 3 min of immersion time and 5$0^{\circ}C$ of air temperature compared to control(147 $\mu$mole/g garlic solid) of air dehydration at 5$0^{\circ}C$

• 한국초전도ㆍ저온공학회논문지
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• 제17권3호
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• pp.28-32
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• 2015

Nowadays the magnetic field mapping is widely used in the design and analysis of the NMR/MRI magnet system, and the accuracy of mapping result has become more and more important. There are several factors affecting the accuracy of the mapping such as the mapping method, the precision of the sensor, the position of the measurement points, the calculation accuracy, and so on. In this paper the error due to the misalignment of the measurement points was discussed. The magnetic field in the central volume was mapped using an indirect method in an MRI magnet system and the magnetic field was fitted to a polynomial. Considering the misalignment between the original measurement points and the practical measurement points, there must be some errors in the mapping calculation and we called it positioning error. Several comparisons of the positioning error have been presented through the theoretical estimates and the exact magnetic field values. Finally, the allowable positioning errors were suggested to guarantee the accuracy of the magnetic field mapping within a certain degree for an example case.

• 한국농공학회지
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• 제43권3호
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• pp.85-93
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• 2001

In this study, a computer program considering shape imperfections of arch under dynamic loading was developed. The shape imperfection of arch was assumed as higher degree polynomial expressed as $\omega$$_{i}$ = $\omega$$_{o}$ (1-(2$\chi$/L)$^{m}$ )$^n$and sinusoidal curve such as $\omega$$_{i}$ = $\omega$$_{o}$ sin(η$\pi$$\chi$/L). In finite element formulation, the material nonlinear behavior was assumed the elasto-viscoplastic model highly corresponding to the real behavior of the material and the geometrically nonlinear behavior was modeled using Lagrangian description of motion. Also, the behavior of steel was modeled by applying yield criteria of Von Mises. The developed program was applied to the analysis of the dynamic behavior for the clamped beam subjected to the concentrated load at midspan and the results were compared with those from other research to investigate accuracy of the presented finite element program. In numerical examples, the shape imperfections of L/500, L/1,000 and L/2,000 were considered and the modes of shape imperfections of the symmetric and antisymmetric were adopted. The effects of the shape imperfections on the dynamic behavior of arch were conspicuous and results of analysis indicate that the reasonable values of arch rise to arch span ratio ranged between 0.1 and 0.3.

• 한국농공학회논문집
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• 제62권1호
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• pp.61-70
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• 2020

To estimate the ventilation volume of mechanically ventilated swine farms, various regression models were applied, and errors were compared to select the regression model that can best simulate actual data. Linear regression, linear spline, polynomial regression (degrees 2 and 3), logistic curve, generalized additive model (GAM), and gompertz curve were compared. Overfitting models were excluded even when the error rate was small. The evaluation criteria were root mean square error (RMSE) and mean absolute percentage error (MAPE). The evaluation results indicated that degree 3 exhibited the lowest error rate; however, an overestimation contradiction was observed in a certain section. The logistic curve was the most stable and superior to all the models. In the estimation of ventilation volume by all of the models, the estimated ventilation volume of the logistic curve was the smallest except for the model with a large error rate and the overestimated model.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.435-449
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• 2020

This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

• 한국인터넷방송통신학회논문지
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• 제11권6호
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• pp.183-191
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• 2011

본 논문은 하나의 도시가 여러 구역으로 분할되고, 응급환자가 발생하였을 때, 모든 구역에 대해 최대 허용 도착시간 T를 충족시키도록 응급시설을 배치하는 문제에 대한 알고리즘을 제안하였다. 이 문제는 일반적으로 다항시간으로 해를 구하는 알고리즘이 존재하지 않아 두 구역 간 소요시간이 최대허용 도착시간이내이면 1로, 그렇지 않으면 0으로 하는 정수계획법으로 변환시키고, 선형계획법 도구를 활용하여 해를 구한다. 본 논문은 최소차수 노드의 이웃 노드들 중 최대 차수 노드를 응급시설의 위치로 결정하는 집합피복 알고리즘을 적용하였다. 제안된 알고리즘을 텍사스 오스틴 시의 33개 구역에 대한 사례에 대해 $3{\leq}T{\leq}20$ (분)을 적용하고, Swain의 55개 노드 망에 대해 T=15에 대해 응급시설의 위치를 결정할 수 있는지 여부를 검증하였다. 선형계획법을 활용한 전통적인 집합피복 알고리즘은 몇 개의 T에 대해 해를 구하지 못한 반면에, 제안된 알고리즘은 18개의 모든 T에 대해 해를 구하였다.