• 한국세라믹학회지
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• 제28권10호
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• pp.824-830
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• 1991

$\alpha$-SiC(B; 0.4 wt, C; 3 wt%) was sintered in Ar atmosphere from 205$0^{\circ}C$ to 220$0^{\circ}C$ by means of pressureless sintering and gas pressure sintering in order to find optimum sintering condition of $\alpha$-SiC. Mechanical properties and microstructures of sintered bodies were investigated according to sintering method. The effect of sintering condition on sinterability of $\alpha$-SiC was also examined by using the dilatometer. 97.5% and 98.8% of theoretical density were obtained from pressureless sintering and gas pressure sintering of $\alpha$-SiC powder, respectively. And modulus of rupture was measured as 270~350 MPa and 420 MPa respectively.

• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

• 대한수학회지
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• 제47권3호
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• Journal of Radiation Protection and Research
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• 제9권2호
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• pp.61-66
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• 1984

Cellulose nitrate 의 ${\alpha}$입자비적특성(粒子飛跡特性), 특(特)히 화학부식조건(化學腐蝕條件)에 따른 ${\alpha}$입자(粒子)의 비적직경(飛跡直徑)을 중심(中心)으로 연구(硏究)하였다. Cellulose nitrate의 KOH 용액부식(溶液腐蝕)때에는 동일(同一)한 부식조건하에(腐蝕條件下)에서 NaOH 경우보다 ${\alpha}$비적직경(飛跡直徑)이 약(約) 3배(培) 크게 나타났다. 그밖에 부식시간(腐蝕時間) 및 ${\alpha}$입자(粒子)의 에너지에 따른 비적직경(飛跡直徑)의 데이타를 얻었고, ${\alpha}$입자(粒子)의 조사조건(照射條件)이 같을 때 흘루언스율(率)(fluence rate)이 부식시간(腐蝕時間)에 무관(無關)함을 알았다.

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• 대한수학회논문집
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• 제14권2호
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• pp.373-383
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• 1999

The ($\alpha$,$\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-from $\beta$;it has been sometimes treated in theoretical physics. The condition for a Finsler space with an ($\alpha$,$\beta$)-metric L($\alpha$,$\beta$) to be projectively flat was given by Matsumoto [11]. The present paper is devoted to studying the condition for a Finsler space with L=$\alpha$\ulcorner$\beta$\ulcorner or L=$\alpha$+$\beta$\ulcorner/$\alpha$ to be projectively flat on the basis of Matsumoto`s results.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.41-49
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• 2008

We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition $$u_{tt}-u_{xx}=au+b{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha-1}{\upsilon}_+^{\beta}+s{\phi}_{00}+f,\\{\upsilon}_{tt}-{\upsilon}_{xx}=cu+d{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha}{\upsilon}_+^{{\beta}-1}+t{\phi}_{00}+g,$$ where ${\alpha},{\beta}>1$ are real constants, $u_+={\max}\{u,0\},\;s,\;t{\in}R,\;{\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator and f, g are ${\pi}$-periodic, even in x and t and bounded functions.

• East Asian mathematical journal
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• 제5권1호
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• pp.35-47
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• 1989

Let $S_o*({\alpha},{\beta},{\mu})$ denote the class of functions $f(z)=a_1z-{\sum}{\limit}^{\infty}_{n=2}\;a_nz^n$ analytic in the unit disc $U=\{z:{\mid}z{\mid}<1\}$ and satisfying the condition $${\mid}\frac{\frac{zf'(z)}{f(z)}-1}{(1+\mu)\;\beta(\frac{zf'(z)}{f(z)}-\alpha)-(\frac{zf'(z)}{f(z)}-1)}\mid<1$$ for some $\alpha(0{\leq}{\alpha}<1),\;{\beta}(0<{\beta}{\leq}1),\;{\mu}(0{\leq}{\mu}{\leq}1)$ and for all $z{\in}U$. And it is the purpose of this paper to show a necessary and sufficient condition for the class $S_o*({\alpha},{\beta},{\mu})$, some results for the Hadamard products of two functions f(z) and g(z) in the class $S_o*({\alpha},{\beta},{\mu})$, the distortion theorem and the distortion theorems for the fractional calculus.

• KSBB Journal
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• 제11권1호
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• pp.86-91
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• 1996

전분이 충전된 폴리에틸렌 필름의 생분해도를 측정하기 위해, ${\alpha}$-amylase가 효과적으로 전분을 분해 시킬 수 있는 반응조건을 설정하고 설정된 반응조건 에서 반응시킨 후 산물인 당을 측정하여 분해정도를 결정하였다. 효과적 인 반응온도는 $80^{\circ}C$이고, pH는 6.3-7.3 사이가 적당하였다. 효소반응에 적당한 r amylase량은 1 mg 전분당 100unit이 었다. 이와 같 은 반응조건하에서, 전분의 무게함유량이 각각 5%. 10%, 15%. 20% 인 폴리에틸렌 필름을 ${\alpha}$-amylase 와 반응시킨 결과 전분이 함유된 비율과 생성된 환 원당간에 대융의 관계를 보였다. 따라서 필름 내에 함유된 생분해가 가능한 전분량을 정량화하는데 calibration 역할을 할 것으로 기대된다. 이 때 분해되 어진 전분의 양은 충전된 전체 전분량의 약 40%에 해당하는 값으로 나타났으며, 나머지는 필름 내부에 분산되 어 있어 ${\alpha}$-amylase의 공격을 받지 못하기 때 문으로 생각된다. 본 실험을 통해 최적화된 반응조 건하에셔 분해시킴으로써, 계면활성제를 첨가하여 분해도를 높인 기존의 데이타보다 더 높은 분해도를 얻을 수 있었다.

• 대한수학회논문집
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• 제25권3호
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• pp.349-364
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, $b\;{\in}\;R$. Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and $\alpha$ an endomorphism of R, we say that R is right (resp., left) $\alpha$-shifting if whenever $a{\alpha}(b)\;=\;0$ (resp., $\alpha{a)b\;=\;0$) for a, $b\;{\in}\;R$, $b{\alpha}{a)\;=\;0$ (resp., $\alpha(b)a\;=\;0$); and the ring R is called $\alpha$-shifting if it is both left and right $\alpha$-shifting. We investigate characterizations of $\alpha$-shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism $\alpha$ of a ring R, R is right (resp., left) $\alpha$-shifting if and only if Q(R) is right (resp., left) $\bar{\alpha}$-shifting, whenever there exists the classical right quotient ring Q(R) of R.