• Asian-Australasian Journal of Animal Sciences
• /
• 제29권4호
• /
• pp.487-499
• /
• 2016

The aim of the present study was to examine the effects of testosterone (T) and estradiol-$17{\beta}$ ($E_2$) on the production of progesterone ($P_4$) by granulosa cells, and of the $E_2$ on the production of $P_4$ and T by theca internal cells. In the first experiment, granulosa cells isolated from the largest ($F_1$) and third largest ($F_3$) preovulatory follicle were incubated for 4 h in short-term culture system, $P_4$ production by granulosa cells of both $F_1$ and $F_3$ was increased in a dose-dependent manner by ovine luteinizing hormone (oLH), but not T or $E_2$. In the second experiment, $F_1$ and $F_3$ granulosa cells cultured for 48 h in the developed monolayer culture system were recultured for an additional 48 h with increasing doses of various physiological active substances existing in the ovary, including T and $E_2$. Basal $P_4$ production for 48 h during 48 to 96 h of the cultured was about nine fold greater by $F_1$ granulosa cells than by $F_3$ granulosa cells. In substances examined oLH, chicken vasoactive intestinal polypeptide (cVIP) and T, but not $E_2$, stimulated in a dose-dependent manner $P_4$ production in both $F_1$ and $F_3$ granulosa cells. In addition, when the time course of $P_4$ production by $F_1$ granulosa cells in response to oLH, cVIP, T and $E_2$ was examined for 48 h during 48 to 96 h of culture, although $E_2$ had no effect on $P_4$ production by granulosa cells of $F_1$ during the period from 48 to 96 h of culture, $P_4$ production with oLH was found to be increased at 4 h of the culture, with a maximal 9.14 fold level at 6 h. By contrast, $P_4$ production with cVIP and T increased significantly (p<0.05) from 8 and 12 h of the culture, respectively, with maximal 6.50 fold response at 12 h and 6, 48 fold responses at 36 h. Furthermore, when $F_1$ granulosa cells were precultured with $E_2$ for various times before 4 h culture with oLH at 96 h of culture, the increase in $P_4$ production in response to oLH with a dose-related manner was only found at a pretreatment time of more than 12 h. In the third experiment, theca internal cells of $F_1$, $F_2$ and the largest third to fifth preovulatory follicles ($F_{3-5}$) were incubated for 4 h in short-term culture system with increasing doses of $E_2$. The production of $P_4$ and T by theca internal cells were increased with the addition of $E_2$ of $10^{-6}M$. These increases were greater in smaller follicles. These results indicate that, in granulosa cells of the hen, T may have a direct stimulatory action in the long term on $P_4$ production, and on $E_2$ in long-term action which may enhance the sensitivity to LH for $P_4$ production, and thus, in theca internal cells, $E_2$ in short term action may stimulate the production of $P_4$ and T.

• 한국정보통신학회논문지
• /
• 제9권1호
• /
• pp.188-198
• /
• 2005

부동소수점 제곱근 계산에 많이 사용하는 골드스미트 제곱근 알고리즘은 곱셈을 반복하여 제곱근을 계산한다. 본 논문에서는 골드스미트 제곱근 알고리즘의 반복 과정의 오차를 예측하여 오차가 정해진 값보다 작아지는 시점까지 반복 연산하는 알고리즘을 제안한다. 'F'의 제곱근 계산은 초기값 $X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t$에 대하여, $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$을 반복한다 곱셈 결과는 소수점 이하 p 비트 미만을 절삭하며, 절삭 오차는 $e_r=2^{-p}$보다 작다. p는 단정도실수에서 28, 배정도실수에서 58이다. $X_i=1{\pm}e_i$ 이면 $X_{i+1}$ = $1-e_{i+1}$ $e_{i+1} {\frac{3e^2_i}{4}{\mp}\frac{e^3_i}} $ +4$e_{r}$이다. $|X_i-1|$ < $2^{\frac{-p+2}{2}}$이면, $e_{i+1}$ < $8e_{r}$ 이 부동소수점으로 표현할 수 있는 최소값보다 작게 되며, $\sqrt{F}$ {\fallingdotseq}\frac{Y_{i+1}}{T}}$이다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 도출하고, 여러 크기의 근사 역수 제곱근 테이블 ($T=\frac{1}{\sqrt{F}}+e_i$)에서 단정도실수 및 배정도실수의 제곱근 계산에 필요한 평균 곱셈 횟수를 계산한다. 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복하므로 제곱근 계산기의 성능을 높일 수 있다. 또한 최적의 근사 역수 제곱근 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그래픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• 호남수학학술지
• /
• 제31권3호
• /
• pp.437-449
• /
• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• 대한수학회논문집
• /
• 제36권3호
• /
• pp.401-411
• /
• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.

• 대한수학회논문집
• /
• 제30권3호
• /
• pp.313-325
• /
• 2015

An H-magic labeling in a H-decomposable graph G is a bijection $f:V(G){\cup}E(G){\rightarrow}\{1,2,{\cdots},p+q\}$ such that for every copy H in the decomposition, $\sum{_{{\upsilon}{\in}V(H)}}\;f(v)+\sum{_{e{\in}E(H)}}\;f(e)$ is constant. f is said to be H-V -super magic if f(V(G))={1,2,...,p}. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are H-V -super magic decomposable where $$H{\sim_=}K_{1,n}$$ with $n{\geq}1$.

• Journal of applied mathematics & informatics
• /
• 제34권1_2호
• /
• pp.167-178
• /
• 2016

In this paper, we study the stochastic integral of processes taking values of generalized operators based on a triple E ⊂ H ⊂ E^∗, where H is a Hilbert space, E is a countable Hilbert space and E^∗ is the strong dual space of E. For our purpose, we study E-valued Wiener processes and then introduce the stochastic integral of L(E, F^∗)-valued process with respect to an E-valued Wiener process, where F^∗ is the strong dual space of another countable Hilbert space F.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1489-1493
• /
• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

• 한국식품과학회지
• /
• 제44권2호
• /
• pp.207-215
• /
• 2012

본 연구에서는 쌀 막걸리의 발효제 종류 및 배합비율에 따른 담금유형을 설정하고 품질특성을 비교하였다. 알코올 함량은 담금 (C)형이 13.6%로 가장 높았으며, (D)형 13.5%, (A)형 13.1%, (B)형 12.9% 및 (E)형 12.7% 순이며, 담금 (F)형에서 12.1%로 가장 낮게 나타났다. 발효 후 당도는 담금 (A)-(E)형은 약 $8.6^{\circ}Bx$로 비슷하였으나 담금 (F)형에서는 $5.4^{\circ}Bx$로 낮게 나타났다. 적정산도는 발효 중 큰 변화는 없었으며, pH는 담금 (A)-(E)형에서는 pH 3.8-3.9, 담금 (F)형에서 pH 4.16으로 조금 높게 나타났다. 환원당 함량은 담금 (A)형에서 401.6 mg%로 가장 높았으며, 담금 (B)-(E)형에서는 337.3-380.9 mg%, 담금 (F)형에서는 119.2 mg%로 가장 낮게 나타났다. 알코올 성분 중 methanol, 1-propanol, 2-methyl-1-propanol 및 iso-amylalcohol이 검출되었으며, 발효 동안 증가하는 경향을 나타내었다. 올리고당 함량은 담금 (D)형에서 1251.27 mg%로 가장 높았으며, (E)형 1,219.2 mg%, (C)형 1,141.4 mg%, (A)형 1,049.9 mg%, (B)형 973.8 mg% 순이며, (F)형에서는 608.0 mg%로 가장 낮았다. 총 유리아미노산 함량은 담금 (B)형에서 781.4 mg%로 가장 높았으며, (C)형 703.2 mg%, (D)형 702.6 mg%, (E)형 678.7 mg%, (A)형 630.4 mg% 및 (F)형 328.7 mg% 순으로 나타났다. 휘발성 향기성분은 담금 (A)와 (B)형은 16종, (C)형 15종, (D)형과 (E), (F)형은 14종이 검출되었다. 전반적 기호도는 담금 (A)형과 (C)형에서 유의적인 차이를 나타내었으며, 쓴맛이 강한 (D)형과 (E)형, 단맛이 적은 (F)형에서는 전반적인 기호도 수치가 낮게 나타났다.

• 호남수학학술지
• /
• 제15권1호
• /
• pp.75-85
• /
• 1993

For A and B, $-1{\leq}B<A{\leq}1$, let P[A, B] be the class of functions p analytic in the unit disk E with P(0) = 1 and subordinate to $\frac{1+Az}{1+Bz}$. We introduce the class $T_{\alpha}[A,B]$ of functions $f:f(z)=z+\sum\limits_{n=2}^{{\infty}}a_nz^n$ which are analytic in E and for $z{\in}E$, ${\alpha}{\geq}0$, $[(1-{\alpha}){\frac{f(z)}{z}}+{\alpha}f^{\prime}(z)]{\in}P[A,B]$. It is shown that, for ${\alpha}{\geq}1$, $T_{\alpha}[A,B]$ consists entirely of univalent functions and the radius of univalence for $f{\in}T_{\alpha}[A,B]$, $0<{\alpha}<1$ is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.

• Journal of applied mathematics & informatics
• /
• 제6권1호
• /
• pp.273-277
• /
• 1999

In this paper we will consider interval-valued martin-gales. We obtain several results parallel to the case of real-valued martingales. For example an $L_1$-bounded interval-valued martingale converges a.e. An interval-valued martingale ${{F_n}^\infty}_{n=1}$ is uniformly in-tegrable if and only if there is an interval-valued random variable F with $\parallel F \parallel _1<\infty$ such that $F_n=E(F\mid A_n)$, for all $n\geq 1$