• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1157-1163
• /
• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• 대한수학회논문집
• /
• 제20권4호
• /
• pp.645-648
• /
• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Kyungpook Mathematical Journal
• /
• 제58권4호
• /
• pp.747-759
• /
• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 한국정보통신학회논문지
• /
• 제9권2호
• /
• pp.380-389
• /
• 2005

부동소수점 나눗셈에서 많이 사용하는 골드스미트 나눗셈 알고리즘은 일정한 횟수의 곱셈을 반복한다. 본 논문에서는 오차가 정해진 값보다 작아질 때까지 곱셈을 반복하여 나눗셈을 수행하는 가변 시간 골드스미트 부동소수점 나눗셈 알고리즘을 제안한다. 부동소수점 나눗셈 ‘$\frac{N}{F}$'는 'T=$\frac{1}{F}+e_t$'를 분모와 분자에 곱하면 ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'가 된다. ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'를 반복한다. 중간 곱셈 결과는 소수점이하 p 비트 미만을 절삭하며, 절삭 오차는 ‘$e_r=2^{-p}$', 보다 작다. p는 단정도실수에서 29, 배정도실수에서 59이다. ’$F_i=1+e_i$'이라고 하면 ‘$F_{i+1}=1-e_{i+1},\;e_{i+1},\;e_{i+1}'이 된다. '$[F_i-1]<2^{\frac{-p+3}{2}}$'이면, ’$e_{i+1}<16e_r$'이 부동소수점으로 표현 가능한 최소값보다 작아지며, ‘$N_{i+1}\risingdotseq\frac{N}{F}$이다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 도출하고, 여러 크기의 근사 역수 테이블($T=\frac{1}{F}+e_t$)에서 단정도실수 및 배정도실수의 나눗셈 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 반복 연산을 수행하므로 나눗셈기의 성능을 높일 수 있다. 또한 최적의 근사 역수 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스,, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• Mycobiology
• /
• 제39권4호
• /
• pp.243-248
• /
• 2011

The ubiquitin-proteasome system is one of the major protein turnover mechanisms that plays important roles in the regulation of a variety of cellular functions. It is composed of E1 (ubiquitin-activating enzyme), E2 (ubiquitin-conjugating enzyme), and E3 ubiquitin ligases that transfer ubiquitin to the substrates that are subjected to degradation in the 26S proteasome. The Skp1, Cullin, F-box protein (SCF) E3 ligases are the largest E3 gene family, in which the F-box protein is the key component to determine substrate specificity. Although the SCF E3 ligase and its F-box proteins have been extensively studied in the model yeast Saccharomyces cerevisiae, only limited studies have been reported on the role of F-box proteins in other fungi. Recently, a number of studies revealed that F-box proteins are required for fungal pathogenicity. In this communication, we review the current understanding of F-box proteins in pathogenic fungi.

• 대한수학회논문집
• /
• 제9권3호
• /
• pp.731-737
• /
• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• 충청수학회지
• /
• 제23권4호
• /
• pp.679-689
• /
• 2010

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.

• 대한수학회보
• /
• 제44권2호
• /
• pp.241-246
• /
• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• 대한가정학회지
• /
• 제28권4호
• /
• pp.1.1-13
• /
• 1990

Authors have performed the sensory evaluation tests according to each given items after selecting various lines in order to assess the visual effects by the lines in cloth designing. The evaluations were done by means of ranking tests followed by paired comparison tests. The results obtained were as follows : 1. In the item in than "Shoulder width looks wide", the design C3 showed the best visual effect, and then B1, F8, and A5 comes in order. In "Shoulder width looks narrow", they were A2, F5, F7, and B2 in order. 2. In "Bust looks big", the effect was best in F9, and then B1, F5, C3, and A5 and order. "Bust looks small" item showed A3, C1, and F1 in order. 3. In "Waist looks thick", they were B2, D1, and F7 while in "Waist looks thin", they were B3, F8, and D6 in order. 4. In the item in that "Hip looks big", the best effect was in F9, and then E3, C2, and B4 in order. In "Hip looks small", the best one was C1, and then comes. E1, F6, and F8. 5. In "Upper body looks thick", they were D2, D4, F8, C3 and A5 in order whild in "Upper body looks thin", they were A1, F5, and D7 in order. 6. In the item "Lower body lookds thick", they were F9, C2, E3, B3, and D3 in order. In "Lower body looks thin", the best one was C1, and then D1, E2, F6, and F8 comes in order. 7. In "whole body looks thick", they were F9, F3, D3, and A5, and in "Whole body looks thin", they were F5, A1, C1, and D6 in order. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. F9, B4, D2, and D1.

• 한국안전학회지
• /
• 제18권3호
• /
• pp.46-53
• /
• 2003

For the tensile tests of the F.E.M., microvoids are created by the boundary separation process at the martensite boundary or neighborhood and at inclusions within the fracture. to grow to the ductile dimple fracture. For the case of the M.E.F., microvoids created at the discontinuities of the martensite phase which exists at the grain boundary of the primary ferrite are grown to coalescence with the cleavage cracks induced at the interior of the ferrite, which as a result show the discontinuous brittle fracture behavior. In spite of their similar tensile strengths, the fatigue limit and the notch sensitivity of the M. E.F. is superior to those of the F.E.M., The M.E.F. is much more insensitive to notch than F.E.M. from the stress concentration factor($\alpha$).