• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제1권1호
• /
• pp.25-27
• /
• 1994

Suppose that X is a Banach space with continuous dual $X^{**}$, ($\Omega$, $\Sigma$, ${\mu}$) is a finite measure space. f : $\Omega\;{\longrightarrow}$ $X^{*}$ is a weakly measurable function such that $\chi$$^{**}$ f $\in$ $L_1$(${\mu}$) for each $\chi$$^{**}$ $\in$ $X^{**}$ and $T_{f}$ : $X^{**}$ \longrightarrow $L_1$(${\mu}$) is the operator defined by $T_{f}$($\chi$$^{**}$) = $\chi$$^{**}$f. In this paper we study the properties of bounded $X^{*}$ - valued weakly measurable functions and bounded $X^{*}$ - valued weak＊ measurable functions.(omitted)

• ALGAE
• /
• 제27권2호
• /
• pp.83-94
• /
• 2012

The taxonomic distinctiveness and cosmopolitan distributions of the red algae $Gelidium$ $crinale$ and $G.$ $pusillum$ remain unclear. Both species were first described in Devon in southwestern England; namely in Ilfracome for $G.$ $crinale$ and Sidmouth for $G.$ $pusillum$. We analyzed mitochondrial $cox$1 and plastid $rbc$L sequences from specimens collected in East Asia, Australia, Europe and North America. In all phylogenetic analyses of $cox$1 and $rbc$L sequences, $G.$ $crinale$ was distinct from congeners of the genus. The analyses also revealed a sister relationship with the $G.$ $coulteri$ and $G.$ $capense$ clade. Nineteen $cox$1 haplotypes were identified for $G.$ $crinale$, and they were likely geographically structured. Despite the distinctiveness in both $cox$1 and $rbc$L datasets, the sister relationship of $G.$ $pusillum$ in the genus was not resolved. Our $cox$1 and $rbc$L datasets indicate that $G.$ $crinale$ is a cosmopolitan species, found in East Asia, Australia, Europe and North America, while the distribution of $G.$ $pusillum$ is restricted to Europe and Atlantic North America. Our results suggest that infraspecific classification of $G.$ $pusillum$ may be abandoned.

• Kyungpook Mathematical Journal
• /
• 제49권3호
• /
• pp.473-481
• /
• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Kyungpook Mathematical Journal
• /
• 제47권3호
• /
• pp.403-410
• /
• 2007

Using the belongs to relation (${\in}$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha}$, ${\beta}$)-fuzzy subalgebras where ${\alpha}$ and ${\beta}$ areany two of {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} with ${\alpha}{\neq}{\in}{\wedge}q$ was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra to be an (${\in}$, ${\in}$)-fuzzy subalgebra. We provide characterizations of an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra. We show that a proper (${\in}$, ${\in}$)-fuzzy subalgebra $\mathfrak{A}$ of X with additional conditions can be expressed as the union of two proper non-equivalent (${\in}$, ${\in}$)-fuzzy subalgebras of X. We also prove that if $\mathfrak{A}$ is a proper (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra of a CK/BCI-algebra X such that #($\mathfrak{A}(x){\mid}\mathfrak{A}(x)$ < 0.5} ${\geq}2$, then there exist two prope non-equivalent (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebras of X such that $\mathfrak{A}$ can be expressed as the union of them.

• 한국세라믹학회지
• /
• 제38권5호
• /
• pp.431-437
• /
• 2001

본 연구에서는 양이온 교환반응에 의해 Na-Mont와 R$_{11}$SO$_4$로부터 R$_{11}$SO$_4$-Mont 층간화합물을 합성한 후, 이 R$_{11}$SO$_4$-Mont 층간화합물을 다시 제 4차 유기 양이온인 (Et)$_4$N$^{+}$ 이온 및 (Bu)$_4$N$^{+}$ 이온과 반응시켜 그 거동을 살펴보았다. R$_{11}$SO$_4$-Mont를 (Et)$_4$N$^{+}$이온과 반응시켰을 대보다 (Bu)$_4$N$^{+}$ 이온과 반응시킨 경우에 좀 더 큰 층간거리가 얻어졌다. R$_{11}$SO$_4$-Mont를 (Et)$_4$N$^{+}$이온 및 (Bu)$_4$N$^{+}$과 반응시켜 얻은 층간화합물을 다시 아세토니트릴, 에탄올 및 디옥산과 팽윤반응을 수행한 결과 층간거리가 확장되었으나, 이는 Na-Mont를 R$_{11}$SO$_4$와 48시간 교환 반응시킨 후에 교환용액 하에서 얻은 R$_{11}$SO$_4$-Mont의 층간거리에 불과했다. 원소분석결과, R$_{11}$SO$_4$-Mont와 (Bu)$_4$N$^{+}$를 반응시킬 경우 반응이 반응식 b에 의거 진행되고, (Bu)$_4$N-Mont를 R$_{11}$SO$_4$와 반응시킬 경우에는 반응식 c에 의거 진행됨을 예측할 수 있었다.의거 진행됨을 예측할 수 있었다.

• 한국전기전자재료학회:학술대회논문집
• /
• 한국전기전자재료학회 1997년도 추계학술대회 논문집
• /
• pp.60-63
• /
• 1997

Dieletric ailed piezoelectric properties of Pb[$Zr_{0.45}$/ $Ti_{0.5-x}$/L $u_{x}$ (M $n_{1}$3//S $b_{2}$3)$_{0.05}$] $O_3$(0$\leq$x $\leq$0.03) were investigated. The partial substitution of $Ti^{4+}$ by a L $u^{3+}$ permitted improvement of the piezoelectric constant( $d_{33}$ ), electromechanical coupling factor ( $k_{p}$ ) and dielectric constant($\varepsilon$$_{33}$ /Sup T/). The dielectric loss(tan $\delta$ ) increased and mechanical quality factor(Qm) decreased with an increase of x were observed. A new piezoelectric material for actuator application was developed at x=0.02 with $d_{33}$ =370$\times$10$^{-2}$ /C/N, $k_{p}$ =58.5%, $\varepsilon$$_{33}$ $^{T}$ =1321, $Q_{m}$ =714 and tan $\delta$ =0.98%.%..%.%.

• 공업화학
• /
• 제9권1호
• /
• pp.38-43
• /
• 1998

저온 상압하에서 $Li^+$, $Na^+$, $K^+$및 $Cs^+$과 같은 알칼리 양이온을 사용하여 M-ZSM-5를 합성한 결과 핵 생성반응 속도는 $Na^+>K^+>Li^+>Cs^+$순으로 감소하는 것을 알 수 있었다. 특히, 저온 상압하에서는 기존의 고온 고압법과 달리 핵 생성 반응 속도가 큰 경우, 결정의 크기도 크다는 것을 알 수 있었다. 즉, 결정의 크기는 $K^+>Na^+>Cs^+>Li^+$의 순으로 감소하였다. 또한 알칼리 양이온의 종류와 관계없이 52 시간 이내에 BET 표면적이 $300m^2/g$, 특히 $Na^+$이온의 경우 32 시간이내에 $400m^2/g$ 이상인 ZSM-5의 합성이 가능하다는 것을 알수 있었다.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제26권1호
• /
• pp.41-45
• /
• 1987

In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

• 생물환경조절학회지
• /
• 제7권3호
• /
• pp.246-252
• /
• 1998

1995년 경남지역에서 양액재배 원수로 사용되고 있는 77개 농가의 지하수 중의 무기성분 농도를 분석한 결과는 다음과 같다. 지하수의 깊이는 10~500m, pH는 6.2~8.4, EC는 0.11~1.44dS/m이었다. 1 liter당 무기성분의 평균함량은 N $H_{4}$-N 0.3mg, N $O_{3}$-N 3.1mg, P $O_{4}$$^{3-}$ 0.5mg, $Ca^{2＋}$ 25.4mg, $Mg^{2＋}$ 11.5mg, $Na^{＋}$ 21.7mg, C $l^{-}$ 42.6mg, S $O_{4}$$^{2-}$ 72.5mg였다. 지하수의 pH와 $Mg^{2＋}$(0.34$^{**}$ ), $Ca^{2＋}$(0.33$^{**}$ ) 및 EC(0.29$^{**}$ ) 사이에 유의적인 정(＋)의 상관을 보였다. 또한 EC와 $Na^{＋}$(0.68$^{**}$ ), $Ca^{2＋}$(0.67$^{**}$ ), S $O_{4}$$^{2-}$(0.62$^{**}$ ), $Mg^{2＋}$(0.60$^{**}$ ), N $H_{4}$-N(0.36$^{**}$ ), C $l^{-}$(0.53$^{**}$ ) 및 $K^{＋}$(0.26$^{**}$ ) 간에도 유의적인 정(＋)의 상관을 보였다..

• 한국잠사곤충학회지
• /
• 제15권2호
• /
• pp.29-33
• /
• 1973

잠품종에 따라서 차이가 견사섬도와 견층용해도가 견사의 탄성적성질에 미치는 영향에 대하여 알아보았다. 즉 21개품종의 견사에 대하여 견사섬도 (X$_1$)와 견층용해도 (X$_2$)를 측정하고, X$_1$ 및 X$_2$의 변화와 절단강도(Y$_1$), 절단신도 (Y$_2$) 및 양구율 (Y$_3$)과의 관계를 알아 본결과 다음과 같은 식을 찾았다. A. 견사섬도의 영향 $Y_1$= -0.4$\chi$$_1$＋5.03 $Y_2$=1.2$\chi$$_1$＋2.7 $Y_3$= -25.2$\chi$$_1$＋140.95 B. 견층 용해도의 영향 $Y_1$= -2.4$\chi$$_2$＋3.43 $Y_2$=20$\chi$$_2$＋3.7 $Y_3$= -120$\chi$$_2$＋78.37.