• 대한수학회보
• /
• 제50권4호
• /
• pp.1289-1296
• /
• 2013

Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb{Z}_p$. From these relationships, we establish some interesting identities.

• 충청수학회지
• /
• 제28권4호
• /
• pp.575-582
• /
• 2015

The Newton-Raphson method is used to compute the q-th roots of a p-adic number for a prime number q. The sufficient conditions for the convergence of this method are obtained. The speed of its convergence and the number of iterations to obtain a number of corrected digits in the approximation are calculated.

• 충청수학회지
• /
• 제23권1호
• /
• pp.169-176
• /
• 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.

• 한국정보처리학회논문지
• /
• 제7권5호
• /
• pp.1370-1376
• /
• 2000

너비 우선 선정 트리기 이미 구성되어 있는 비동기식 네트워크상에서 네트워크 형상이 빈힐 경우 이로인해 구성되어 있던 너비 우선 선정 트리를 갱신해야 하는 경우가 발생한다. 본 논문에서는 이러한 경우 너비 우선 신장 트리를 효율적으로 갱신하는 메시지 복잡도와 이상시간 복잡도 모두 O($p\sqrt{q}$.q.a.n')인 분산 알고리즘을 제안한다. 여기서, a는 추가 링크의 수, n'는 네트워크의 토폴로지가 변한후의 네트워크상에 존재하는 노드수를 각각 나타낸다. 그리고 p는 삭제 또는 추가 링크를 가진 이중결합요소에 속하는 전체 노드 수를 나타내며, q는 삭제 또는 추가 링크를 가진 이중 결합요소에 속하는 전체 링크수를 나타낸다.

• 대한수학회논문집
• /
• 제20권3호
• /
• pp.467-485
• /
• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• Clinical and Experimental Reproductive Medicine
• /
• 제41권2호
• /
• pp.68-74
• /
• 2014

Objective: In search of an ideal method of assisted hatching (AH), we compared the effects of conventional micropipette-AH and laser-AH on the blastocyst formation rate (BFR) and blastocyst cell numbers. Methods: Four-to five-week-old ICR female mice were paired with male mice after superovulation using Pregnant mare's serum gonadotropin (PMSG) and hCG. The two-cell embryos were flushed from the oviducts of female mice. The retrieved two-cell embryos underwent one of five AH procedures: single mechanical assisted hatching (sMAH); cross mechanical assisted hatching (cMAH); single laser assisted hatching (sLAH); quarter laser assisted hatching (qLAH); and quarter laser zona thinning assisted hatching (qLZT-AH). After 72 hours incubation, double immunofluorescence staining was performed. Results: Following a 72 hours incubation, a higher hatching BFR was observed in the control, sMAH, cMAH, and sLAH groups, compared to those in the qLAH and qLZT-AH groups (p<0.05). The hatched BFR was significantly higher in the qLAH and qLZT-AH groups than in the others (p<0.05 for each group). The inner cell mass (ICM) was higher in the control and sMAH group (p<0.05). The trophectoderm cell number was higher in the cMAH and qLAH groups (p<0.05). Conclusion: Our results showed that the hatched BFR was higher in groups exposed the the qLAH and qLZT-AH methods compared to groups exposed to other AH methods. In the qLAH group, although the total cell number was significantly higher than in controls, the ICM ratio was significantly lower in than controls.

• 대한수학회보
• /
• 제55권2호
• /
• pp.599-610
• /
• 2018

We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving (p, q)-extended Bessel function $J_{{\nu},p,q}(z)$, which are expressed in terms of Hadamard product of the (p, q)-extended Gauss hypergeometric function and the Fox-Wright function $_p{\Psi}_q(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.

• 대한수학회논문집
• /
• 제38권3호
• /
• pp.715-723
• /
• 2023

In this paper, we construct explicitly an infinite family of primes P with h^±_P ≡ 0 (mod q^{deg P}), where h^±_P are the plus and minus parts of the divisor class number of the P-th cyclotomic function field over 𝔽_q(T). By using this result and Dirichlet's theorem, we give a condition of A, M ∈ 𝔽_q[T] such that there are infinitely many primes P satisfying with h^±_P ≡ 0 (mod p^e) and P ≡ A (mod M).

• 한국조경학회지
• /
• 제20권1호
• /
• pp.80-94
• /
• 1992

To inspect the changing of the forest soil and plants community structrure by air plooutand & acid rain during from September to November in 1990, the smapling sites were selected in the Piwon, Namsan and Kwangnung forest. In sites, plots were set up in Q. aliena forest at Piwon, Quercus mongolica and Pinus densiflora forest at Namsan and Q. mongolica and Pinus densiflora forest at Kwangnung. To obtain the individual number of trees, number of species, importance values and species diversity, using the Curtis & McIntosh methods. The results are following that; 1) In Pinus densiflora community, it was almost dominated by Q. spp. in the canopy layer and P. densiflora and Carpinus laxiflora through the subtree to shrub layer at Kwangnung. It wassaid that C. laxiflora is the climax species in moddle temperature zone. On the contrary, in Namsan forest, there is no appearance thesamplings of P. densiflora & C. laxiflora, but Styrax japonica and Stephanandra incisa that are acid-tolerance species are dominant ones. On the other hand, in Q. spp. community, Q. spp. and C. laxiflora are dominant ones. On the other hand, in Q. spp. community, Q. spp. and C. laxiflora are dominant species through all layer, and in addition C. cordata somewhat appear at Kwangnung. But at Namsan and Piwon forest, Q. mongolica & Q. aliena that were dominant species in canopy layer disappeared in the subtreeand shrub layer, and C. laxiflora and Corunus cordata absolutely disappeared. It were similarly dominated by Robinia pseudo-acacia, Styrax japonica, Sorbus alnifolia, Acer pseudo-sieboldianum, Rhododendrn mucronulatum and so on at Namsn and Piwon forest. In the light of these facts, it found out that disclimax was similar between Namsan and Piwon forest. 2) Species diversity and maximum species diversity were decreased in Kwangnumg, Namsan, Piwon in order. It was xpected that vegetational community was affected by environmental pollutant. 3) As the vegetational community structure analyses, using DCA technique among the ordination, ecological successional series are stopped to Q. spp. from P. densiflora at Namsan and Piwon, but that of Kwangnung is on the way that P. densiflora, Q. alena, C. laxiflora. It was obvi ously different from Namsan and Piwon. 4) In Q. spp. & P. densiflora community, the number of woody plants inNamsan & Piwon is much less than that of Kwangnung through all Layer. Especially, Piwon shown very severe difference. Through all community, the number of individuals of Piwon and Namsan are less than that of Kwangnung. Specially, that of the shrub layer is obvious. 5) In the growth rate of trees, it found out that all sites showed the growth decline phenomena. Especially, since in 1975, there have been the micro disclimax phenomena in Q. community of Kwangnung. 6) In the Q. community, soil acidity of Namsan & Piwon measured 4.57, 4.40 respectively. It was very strong acidity and far lower than that of Kwangnung. Also the content amount of Mg++ in Namsan & Piwon forest were still lower than Kwangnung.

• 대한수학회논문집
• /
• 제32권1호
• /
• pp.193-200
• /
• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.