• 대한수학회보
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• 제22권1호
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• pp.7-10
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• 1985

For each a.mem.S and f.mem.m(S), denote by $l_{a}$ f(s)=f(as) for all s.mem.S. If A is a norm closed left translation invariant subalgebra of m(S) (i.e. $l_{a}$ f.mem.A whenever f.mem.A and a.mem.S) containing 1, the constant ont function on S and .phi..mem. $A^{*}$, the dual of A, then .phi. is a mean on A if .phi.(f).geq.0 for f.geq.0 and .phi.(1) = 1, .phi. is multiplicative if .phi. (fg)=.phi.(f).phi.(g) for all f, g.mem.A; .phi. is left invariant if .phi.(1sf)=.phi.(f) for all s.mem.S and f.mem.A. It is well known that the set of multiplicative means on m(S) is precisely .betha.S, the Stone-Cech compactification of S[7]. A subalgebra of m(S) is (extremely) left amenable, denoted by (ELA)LA if it is nom closed, left translation invariant containing contants and has a multiplicative left invariant mean (LIM). A semigroup S is (ELA) LA, if m(S) is (ELA)LA. A subset E.contnd.S is left thick (T. Mitchell, [4]) if for any finite subser F.contnd.S, there exists s.mem.S such that $F_{s}$ .contnd.E or equivalently, the family { $s^{-1}$ E : s.mem.S} has finite intersection property.y.

• 대한수학회보
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• 제22권1호
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• pp.1-5
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• 1985

The differential polynomial ring A[X, D] has been studied by many authors J. Cozzens, C. Faith, R.E. Johnson and D. Mathis and others. The main purpose of the present paper is to study some properties of .phi.-differential polynomial ring A[X, D, .phi.] and modules over the .phi.-differential polynomial ring X[X, D, .phi.].

• Nuclear Engineering and Technology
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• 제13권2호
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• pp.73-84
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• 1981

B$\Phi$rrensen은 3차원적 노심분석에 긴 시간이 요구되는 유한차분법의 대안으로서 경수형 원자로의 전체출력분포를 계산하는데 한가지의 coarse mesh 방법을 제안하였다. 이 방법은 계산시간이 매우 짧은 것으로 알려져 있지만. 그 계산의 정확도에 대한 것은 아직까지 알려져 있지 않다. 본 논문에서는 B$\Phi$rrensen의 방법을 IAEA benchmark 문제와 RIS$\Phi$ benchmark 문제에 적용시켜서 계산시간과 정확도에 대해서 고찰하였다. 두 문제에서 노심-반사체와의 경계조건과 B$\Phi$rrensen의 모델상수들의 개선으로 출력분포 계산의 정확도를 상당히 높힐 수 있었다.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• 충청수학회지
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• 제18권2호
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• pp.175-193
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• 2005

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. In this paper, we introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalizd (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalized (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras.

• Kyungpook Mathematical Journal
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• 제53권2호
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• pp.285-294
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• 2013

The present paper deals with a study of ${\phi}$-pseudo symmetric and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifolds. It is shown that every ${\phi}$-pseudo symmetric $(LCS)_n$-manifold and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifold are ${\eta}$-Einstein manifold.

• 설비공학논문집
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• 제3권2호
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• pp.123-130
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• 1991

The mixed convection heat transfer from vertical inline plates has been studied numerically by the finite difference method and experimentally with Mach-Zehnder interferometer. The dimensionless spacing, $s/L_1$, the relative length, $L_2/L_1$ and the dimensionless temperature ratio, ${\Phi}_2/{\Phi}_1$ are varied parametically. The lower plate mean Nusselt numbers show same values as $s/L_1$, ${\Phi}_2/{\Phi}_1$ and $L_2/L_1$ increase. The upper plate mean Nusselt numbers increase as $s/L_1$ and ${\Phi}_2/{\Phi}_1$ increase, but $L_2/L_1$ decreases. The upper plate mean Nusselt number is higher than the lower plate mean Nusselt for $s/L_1$ 1.8 at Re=100, $Gr=10^4$, Pr=0.71, $L_2/L_1=0.5$ and ${\Phi}_2/{\Phi}_1=1.0$. A comparison between the experimental and numerical results show good agreement.

• 대한수학회지
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• 제54권3호
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• pp.867-876
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• 2017

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^*$-algebras such that $\mathcal{A}$ is prime. In this paper, we investigate the additivity of maps ${\Phi}$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective and satisfy $${\Phi}(A^*B+{\eta}BA^*)={\Phi}(A)^*{\Phi}(B)+{\eta}{\Phi}(B){\Phi}(A)^*$$ for all $A,B{\in}\mathcal{A}$ where ${\eta}$ is a non-zero scalar such that ${\eta}{\neq}{\pm}1$. Moreover, if ${\Phi}(I)$ is a projection, then ${\Phi}$ is a ${\ast}$-isomorphism.

• 대한수학회논문집
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• 제28권1호
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• pp.63-69
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• 2013

On any semigroup S, there is an equivalence relation ${\phi}^S$, called the locally equivalence relation, given by a ${\phi}^Sb{\Leftrightarrow}aSa=bSb$ for all $a$, $b{\in}S$. In Theorem 4 [4], Tiefenbach has shown that if ${\phi}^S$ is a band congruence, then $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is a group. We show in this study that $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is also a group whenever a is any idempotent element of S. Another main result of this study is to investigate the relationships between $[a]_{{\phi}^S}$ and $aSa$ in terms of semigroup theory, where ${\phi}^S$ may not be a band congruence.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.61-74
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• 2018

Let $\mathcal{A}$ and $\mathcal{B}$ be two prime ${\ast}$-algebras. Let ${\Phi}:\mathcal{A}{\rightarrow}\mathcal{B}$ be a bijective and satisfies $${\Phi}(A{\bullet}B{\bullet}A)={\Phi}(A){\bullet}{\Phi}(B){\bullet}{\Phi}(A)$$, for all $A,B{\in}{\mathcal{A}}$ where $A{\bullet}B=A^{\ast}B+BA^{\ast}$. Then, ${\Phi}$ is additive. Moreover, if ${\Phi}(I)$ is idempotent then we show that ${\Phi}$ is ${\mathbb{R}}$-linear ${\ast}$-isomorphism.