• 대한수학회논문집
• /
• 제11권1호
• /
• pp.245-252
• /
• 1996

The relative Nielsen number N(f;X,A) was introduced in 1986. It gives us a better, and ideally sharp, lower bound for the minimum number MF[f;X,A] of fixed points in the homotopy class of the map $f;(X,A) \to (X,A)$. Similarly, we also can think about the Nielsen map $f:(X,A) \to (X,A)$. Similarly, we also can be think about the Nielsen root theory. In this paper, we introduce a relative root Nielsen number N(f;X,A,c) of $f:(X,A) \to (Y,B)$ and show some basic properties.

• Journal of Ginseng Research
• /
• 제22권4호
• /
• pp.299-303
• /
• 1998

To know possibility of raw ginseng production for white- and red-ginseng by direct-sowing culture, seeds were directly sowed or seedlings were transplanted at soil condition of sandy loam in ginseng field. After cultivation, the characters of 5-year-old ginseng were investigated. Number of survived plants was increased with increase the seeding quantity in direct-sowing culture, the survived plants in direct-sowing culture was higher than that of transplanting one. Rate of the numbers of survived plants to numbers of seeds sowed in plots of 134 or 90 seeds sowed per tan, 180 x 90cm area, inspire of high number of survived plant was high compared to that of transplanting culture. Occurrence rate of rusty root of ginseng in direct-sowing culture was low significantly compared to that of transplanting culture. Root yield showed in the order of 134, 268, 90 seeds sowed, the values of yield in direct-sowing culture were high obviously compared to that of transplanting one. Individual root weight was increased with decrease the seeding quantity, however, the root weight in plot of 90 seeds sowed showed almost equal the weight in transplanting culture. The number of usable raw ginseng for white- and red-ginseng was increased with decrease of the seeding quantity; the numbers were higher than that of transplanting culture remarkably. We concluded that optimum seedling rate in direct-sowing culture of ginseng was 90 to 134 seeds per tan considering the yield per area and production rate of large root.

• Journal of applied mathematics & informatics
• /
• 제35권5_6호
• /
• pp.587-597
• /
• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• 한국자원식물학회지
• /
• 제14권3호
• /
• pp.183-187
• /
• 2001

남부지방에 적합한 품종의 효율적인 선발을 위한 기초자료를 얻고자 9품종을 공시하여 생육 및 수량조사, 유전분산, 환경 분산, 유전력, 상관을 조사한 결과를 요약하면 다음과 같다. 1. 다수성이며 꽃대발생수가 적어서 품질이 우수한 Sunwol 택사 품종이 남부지방에 가장 적합한 품종으로 나타났었다. 2. Sunwol 품종의 모든 형질에 대한 유전력은 대부분의 형질에서 높았다. 3.형질 상호간의 상관에서 건근 수량은 초장, 엽수와는 정의상관으로 유의성이 높았고 꽃대 발생수, 묘상의 초장, 묘상의 엽수와는 부의상관으로 나타났다. 4. 건근 수량과 상관이 높았던 형질들은 유전력 추정에서도 높게 나타났다.

• 한국약용작물학회지
• /
• 제4권1호
• /
• pp.38-46
• /
• 1996

길경의 화색에 따른 생육특성과 수량 및 품질에 차이가 나타나는지 그리고 재배년차에 따른 길경의 뿌리생육과 수량 및 사포닌과 정유함량 등에 차이가 있는지를 알아보고자 실험한 결과를 요약하면 다음과 같다. 1. 백화길경이 자화길경에 비해 줄기수, 꼬투리수, 초장, 종자수량과 같은 지상부 생육과 생근중, 건근중, 근장 및 근직경 등과 같은 뿌리 형질에서 다소 높은 경향을 보였으나 유의차는 없었다. 또한 사포닌 함량이나 정유 함량에도 차이가 없었다. 2. 2년생과 3년생에서 초장은 차이가 없었으나 개체당 줄기수와 꼬투리수는 3년생에서 많았다. 생근중, 근장 및 근직경은 3년생에서 높았다. 사포닌 함량과 정유함량은 2년생과 3년생간에 큰 차이를 보이지 않았다. 사포닌 함량은 2년생, 3년생 모두에서 5월에 채취한 것이 가장 높았고 9월에 채취한 것이 가장 낮았다. 정유함량은 8월에 채취한 것이 가장 높은 함량을 보였고 4월에 채취한 것이 가장 낮았다.

• 대한치과교정학회지
• /
• 제49권2호
• /
• pp.106-115
• /
• 2019

Objective: This study aimed to evaluate the effects of force loading on root damage caused by contact with temporary anchorage devices (TADs) during orthodontic treatment and to examine the repair process 4, 8, and 12 weeks after TAD contact by micro-computed tomography (CT). Methods: We enrolled 42 volunteers who required bilateral upper first premolar extractions. The experimental study design was as follows. For both first premolars, cantilever springs were placed, and then TADs were immediately inserted between the premolars of all volunteers. According to the removal order of the appliances, the participants were divided into the TAD group (Group T: n = 21, only TAD removal) and the spring group (Group S: n = 21, only spring removal). A splitmouth design was adopted in both groups as follows. For each volunteer, the left premolars were extracted 4, 8, or 12 weeks after TAD-root contact. The right premolars were extracted immediately after contact in both groups (Groups T-C and S-C) and used as positive controls. Resorption volumes and numbers of craters were determined by micro-CT. Results: The numbers of resorption craters were higher in Group T than in Group S at 8 and 12 weeks (p < 0.01). Crater volumes were higher in Group T than in Group S at 4 and 12 weeks (p < 0.01, both). Conclusions: Root injury was not completely repaired 12 weeks after root-TAD contact, even when the TADs were removed in cases of continuous force application.

• 충청수학회지
• /
• 제28권2호
• /
• pp.195-200
• /
• 2015

In this paper, we give the condition for the existence of the q-th roots of p-adic numbers in $\mathbb{Q}_p$ with an integer $q{\geq}2$ and (p, q) = 1. We have the conditions for the existence of the fifth root and the seventh root of p-adic numbers in $\mathbb{Q}_p$, respectively.

• Journal of the Korean Wood Science and Technology
• /
• 제39권5호
• /
• pp.406-419
• /
• 2011

This study was carried out to offer basic information on the wood anatomy of domestic yellow-poplar (Liriodendron tulipifera L.), a new plantation species selected by Korea Forest Service as one of the promising hardwood and bioenergy sources of the future, through comparison of stem wood with root wood in the qualitative and quantitative features. In the qualitative anatomical features, growth rings were distinct in stem wood but relatively less distinct in root wood. And stem wood appeared to have pores in radial multiples of 2 to 5, sometimes clusters but root wood to have pores in radial multiples of 2 to 3, rarely clusters. And numbers of bars in scalariform perforation plates were somewhat numerous in vessel elements of root wood than in those of stem wood. Interestingly, on the other hand, more extraneous materials in the wood rays of tap root than in those of lateral root and stem were confirmed in the chemical composition analyses. In the quantitative anatomical features, pore densities were significantly greater but vessel elements were considerably narrower in stem wood than in root wood. Vessel elements and wood fibers of root wood were considerably longer than those of stem wood. Rays were somewhat more numerous in stem wood than in root wood, and only ray heights of stem wood were more or less greater in cell numbers but both ray heights and widths of stem wood were lower in dimension than those of root wood. The anatomical differences between stem wood and root wood were thought to be associated with different growth environments between the stem above ground and the root below ground.

• Journal of the Korean Wood Science and Technology
• /
• 제44권2호
• /
• pp.157-165
• /
• 2016

This study investigated several anatomical characteristics of Paulownia tomentosa roots. The root wood was separated into three parts from stem base (top, middle, and base) at different positions below ground. Qualitative anatomical data suggested that the growth rings in earlywood and latewood were structurally different. Furthermore, the root wood vessels were found having 2 to 3 radial multiples and they were appeared in the form of clusters. In addition, some sheath cells and septate axial parenchyma were observed. Regarding the quantitative anatomical characteristics, vessel and ray numbers per $mm^2$, as well as ray width and height differed significantly among the top, middle, and base rood wood parts. However, there were no significant differences in vessel diameters, cell wall thickness, and width and length of wood fibers among those parts. The crystallinity of the root top part was slightly higher than that of the middle and base parts. Furthermore, the vessel numbers, ray numbers, and ray width and height in the near pith (NP) area were higher compared to those in the near bark (NB) area. However, the fiber width and fiber length at NP were lower than those at NB. Overall, this study demonstrated some significant differences in the anatomical characteristics of the top, middle, and base parts of root wood from Paulownia tomentosa.

• 대한수학회지
• /
• 제56권2호
• /
• pp.485-505
• /
• 2019

In 1935, D. H. Lehmer introduced and investigated generalized Euler numbers $W_n$, defined by $${\frac{3}{e^t+e^{wt}e^{w^2t}}}={\sum\limits_{n=0}^{\infty}}W_n{\frac{t^n}{n!}}$$, where ${\omega}$ is a complex root of $x^2+x+1=0$. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli and Euler numbers. These concepts can be generalized to the hypergeometric Bernoulli and Euler numbers by several authors, including Ohno and the second author. In this paper, we study more general numbers in terms of determinants, which involve Bernoulli, Euler and Lehmer's generalized Euler numbers. The motivations and backgrounds of the definition are in an operator related to Graph theory. We also give several expressions and identities by Trudi's and inversion formulae.