• 대한환경공학회지
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• 제30권6호
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• pp.642-652
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• 2008

본 연구는 축산폐수 중 COD$_{Cr}$을 응집공정 후 Photo-Fenton 공정에 의해 산화분해 최적조건 및 제거 예측식에 수립에 관한 연구이다. 본 연구는 축산폐수 중 COD$_{Cr}$에 대한 Photo-Fenton 산화반응을 이용하여 이들 분해특성을 2차원 반응모델로 추정하기 위해 중심합설계법 대안으로 많이 사용되고 있는 박스-벤켄법(Box-Behnken method)을 이용하였다. 최적조건 수립을 위한 입력변수, 즉 3가지 변수(Fe(II)(x$_1$), $H_2O_2(x_2)$, pH(x$_3$)) 등을 램덤화, 반복화 및 블록화 원리에 따라 실험설계하여 반응값에 대한 예측식을 수학적으로 산출하였다. 수학적 및 통계적으로 산출된 예측식은 Y = 79.3 + 15.61x$_1$ - 7.31x$_2$ - 4.26x$_3$ - 18x$_1{^2}$ - 10x$_2{^2}$ - 11.9x$_3{^2}$ + 2.49x$_1x_2$ - 4.4x$_2x_3$ - 1.65x$_1x_3$와 같이 얻을 수 있었고 COD$^{Cr}$ 제거율(%)의 실측치에 대한 예측치의 적합도(goodness of fit) 검증시 결정계수(coefficient of determination: R$^2$) 0.96으로 에측식을 충분히 설명할 수 있었다. 예측 모형에 대한 최소제곱추정법으로 적합된 반응표면에서 1차 선형항(linear term)은 Fe(II)(x$_1$), $H_2O_2(x_2)$, 그리고 pH(x$_3$)은 상승작용(synergistic effect)으로 반응모델에 유의한 차이를 보였으며(p < 0.001) 그러나 교호항(cross-product term)은 $H_2O_2$ $\times$ pH(x$_2x_3$)와 순수이차항(quadratic terms)의 Fe(II) $\times$ Fe(II)(x$_1{^2}$), $H_2O_2$ $\times$ H$_2O_2$(x$_2{^2}$) 그리고 pH $times$ pH(x$_3{^2}$) 등은 대립적인(감쇠)(antagonistic effect) 작용으로 반응모델에 유의한 차이를 보였다(p < 0.01). 반응 모델에 대한 예측식 수립 후 COD$_{Cr}$ 제거율(%)의 최적조건을 도출하기 위해 정준분석(canonical analysis)와 능선분석(ridge analysis)에 이용한 결과 반응값(결과값: Y)은 84 $\pm$ 0.95%, COD$_{Cr}$ 최적처리를 위한 변수들의 조건은 Fe(II)(X$_1$) = 0.0146 mM, $H_2O_2$(X$_2$) = 0.0867 mM 그리고 pH(X$_3$) = 4.704 등의 결과를 얻을 수 있었다. 또한 이들 최적조건을 이용하여 재현성을 통한 모델검증 결과 높은 신뢰성을 보였다.

• Bulletin of the Korean Chemical Society
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• 제23권6호
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• pp.845-851
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• 2002

The synthesis of the intramolecular donor - stabilized silyl and germyl complexes of the type ($Cab^c.p) MMe_2X$ (2a:M=Si, X=Cl;2b;M= Ge, X=Cl;2e;M=Si,X=H) was achieved by the reaction of $LiCab^c,p$ (1) with $Me_2SiClX$ and $Me_2GeCl_2$ respectively. The intramolecular M←P interacion in 2a-2c is provided by $^1H$, $13^C.$, $31^P$ and $29^Si$ NMR spectroscopy. The salt elimination reactions of dichlorotetramethyldisilane and -digermane with 1 afforded the $bis(\sigma-carboranylphosphino)disilane$ and disgermane [$(Cab^C.P)MMe_2]_2(4a;M$ = Si;4b: M=Ge). The oxidative addition reaction of 4a-4b with $pd_2(dba)_3CHCl_3afforded$ the bis(silyl)-and bis(germyl)-palladium complexes. The chloro-bridged dipalladium complexes were obtained by the reaction of 2a-2b with $pd_2(dba)_3CHCl_3$ The crystal structures of 5a and 7b were determined by X-ray structural studies.

• 대한화학회지
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• 제55권1호
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• pp.38-45
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• 2011

전이금속 이온인 수은(II) 및 은(I)에 대한 $\alpha$-케토안정화된 일리드화 인 $Ph_3P$=CHC(O) $C_6H_4$-X (X=Br, Ph)의 착물 반응 행동을 연구하였다. 수은(II) 착물 {$HgX_2$ [Y]} 2 ($Y_1$=4-bromo benzoyl methylene triphenyl phosphorane; X=Cl(1), Br(2), I(3), $Y_2$=4-phenyl benzoyl methylene triphenyl phosphorane; X=Cl(4), Br(5), I(6))는 $Y_1$ 및 $Y_2$를 $HgX_2$ (X=Cl, Br, I)와 각각 반응시켜 제조하였다. $\alpha$-케토안정화된 일리드화 인($Y_2$)의 은(I) 착물 [Ag$(Y_2)_2$] X(X=$BF_4$(7), OTf(8))는 이러한 일리드와 AgX(X=$BF_4$, OTf)를 아세톤에서 반응시켜 얻었다. 착물 (1)과 (4)의 결정구조를 고찰하였다. 일리드의 C-배위 이핵착물과 트랜스-구조의 착물$[Y_1HgCl_2]_2$. $CHCl_3$ (1) 및 $[Y_2HgCl_2]_2$ (4)를 형성하는 이들 반응에 대해 단결정 X-선 분석을 통해 고찰하였다. 모든 착물(1-3)은 IR, $^1H$ 및 $^{31}P$ NMR 뿐만아니라 $^{13}$CNMR을 통하여 확인하였다.

• 대한수학회논문집
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• 제38권4호
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• pp.1045-1061
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• 2023

Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝ^N is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|^p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|^p(x)-2∇u, where g ∈ L^∞(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

• 대한수학회지
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• 제39권1호
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• pp.103-117
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• 2002

We consider the situation that ${\mathbb{Z}_p}\;=\;{\mathbb{Z}/p\mathbb{Z}}$ acts freely on a closed oriented 4-manifold X with ${b_2}^{+}\;{\geq}\;2$. In this situation, we study the relation between the Seiberg-Witten invariants of X and those of the quotient manifold $X/{\mathbb{Z}}_p$. We prove that the invariants of X are equal to those of $X/{\mathbb{Z}}_p$ modulo p.

• 대한화학회지
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• 제41권6호
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• pp.277-283
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• 1997

질소를 포함한 평면형리간드가 배위된 백금(II)착물([$Pt(L)_2X_2$]; L=isoxazole(isox), 3,5-dimethylisoxazole(3,5-diMeisox), 3-methyl,5-phenylisoxazole(3-Me,5-Phisox), and 4-amino-3,5-dimethylisoxazole(4-ADI); X=Cl, Br)의 항암활성을 분자역학(MM2)법으로 최소에너지를 갖는 구조를 구한 후 확장분자궤도함수(Extended Huckel Molecular Orbital)법으로 조사하였다. X 원자의 알짜전하 값은 cis-, trans-이성체 모두 평면리간드의 N 원자보다 음의 값으로 크게 나타나서, N 원자보다 X 원자의 이탈이 용이함을 알 수가 있었고, ${\sigma}MO$에너지 준위로 비교한 결과도 $Pt(d_{x2-y2})-X(P_x)$의 ${\sigma}MO$에너지 준위$(E{\sigma}_{(Pt-X)})$가 $Pt(d_{x2-y2})-N(P_x)$의 ${\sigma}MO$에너지 준위$(E{\sigma}_{(Pt-N)})$보다 예외없이 높아서 Pt-N보다 Pt-X의 결합이 약함을 알 수 있었다. 또한 X 원자의 cis-, trans-이성체에서의 이탈 용이성을 비교하기 위하여 중심금속과 리간드사이의 ${\sigma}MO$에너지준위로 비교한 결과, trans-이성체에서 $Pt(d_{x2-y2})-N(P_x)$의 ${\sigma}MO$에너지준위$(E{\sigma}_{(Pt-X)})$가 cis-이성체에서 보다 예외없이 높아서 결합이 약함을 알 수 있었다. 아울러 같은 착물에서 cis-보다 trans-착물에서 Pt-X의 결합이 약함을 알 수 있었다, 따라서 $X^-$이온으로 떨어져 나가는 용이성과 그 구조변화가 항암활성과 관계가 있을 것으로 생각하였다. 즉, $E{\sigma}_{(P-N)}-E{\sigma}_{(P1-X)}$가 클수록 저해활성 계수 logIA값이 크게 나타나서 실험적 사실과 일치함을 알 수 있었다.

• 한국산림과학회지
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• 제58권1호
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• pp.48-53
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• 1982

현행(現行)의 형태학적수목분류법(形態學的樹木分類法)에 계획적특성(計劃的特性)을 이용(利用)한 소위(所謂) 판별분석법(判別分析法)에 의(依)할 독일(獨逸)가문비(Picea abies(L.) Karsten)와 종비나무(樅榧)(Picea koraiensis Nak.)와의 분류시험(分類試驗)을 실시(實施)하고 그 결과(結果)를 다음과 같이 요약(要約)한다. 1) 본(本) 시험(試驗)에서 얻은 판별식(判別式)과 판별영역(判別領域)은, Z(x)=Z($x_1,\;x_2$)=$0.000379x_1+0.004354x_2-0.311061$ 또는 Z(x)=Z($x_1,\;x_2$)=$0.000379(x_1-60.4428)+0.004354(x_2-66.1851)$, $$R_1=\{x{\mid}0.000379x_1+0.004354x_2-0.311061{\geq_-}0\}$$, $R_2$={$x{\mid}0.000379x_1+0.004354x_2-0.311061$ <0)} 또는 $$R_1=\{x{\mid}0.000379(x_1-60.4428)+0.004354(x_2-66.1851){\geq_-}0%\}$$, $R_2$={$x{\mid}0.000379(x_1-60.4428)+0.004354(x_2-66.1851)$ <0}. 2) 위의 판별영역(判別領域)에 의(依)한 오판율(誤判率)(오분류확율(誤分類確率))은, P($2{\mid}1$)=($P1{\mid}2$)=0.444로서, P($2{\mid}1$)와 P($P1{\mid}2$)의 동시오판율(同時誤判率)은 P=44.4%. 3) 본(本) 시험(試驗)에서 얻은 판별식(判別式)에 의(依)한 오판율(誤判率)은 상당(相當)히 높게 나타났지만 그의 정도(精度)보다는 오히려 판별(判別)에 대(對)한 신뢰도(信賴度)를 알 수 있다는데 보다 큰 의의(意義)가 있는 것으로 사료(思料)된다.

• 대한수학회논문집
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• 제34권1호
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.387-398
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• 2021

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.

• 지역사회간호학회지
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• 제8권2호
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• pp.347-367
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• 1997

The purpose of this study was to investigate drug abuse and to find related factors among high school students. The subjects for this study were 973 students from 10 high schools in Taegu city. The data were collected from September 30, 1996 to October 30, 1996. The questionnaire developed by Kim Soyoaja (1991) surveyed adolescent drug use and questions on smoking and drinking were readjusted and added by the researcher based on review. The data was analyzed using frequency, percentage, $X^2-test$, t -test, Pearson Correlation Coefficient with the SPSS /PC+. The results of this study were summarized as follows: 1. The proportion of students who drank alcohol 1-2 times or more per year was 52.4% and smoked Cigarette 1 -2 times or more per year was 20.8%. The 7 different drugs(Analgetics 5.7%. sleeping pills and sedatives 4.2%, antihistamines 1.1%. stimulants 7.7%, hallucinogens 0.8%, inhalants 3.3%, and narcotics 0.6%) were also evaluated. 2. There was a significant relationship between drinking and type of school($X^2$=62.97, p<.0l), grades($X^2$=33.86, P<.001), school life($X^2$= 19.04, p<.001), and delinquent friends($X^2$= 64.72, P<.001). 3. There was a significant relationship between smoking and type of school($X^2$=153.65, p<.001), grades ($X^2$=67.53, p<.001), their respect for teachers ($X^2$=33.80, p<.001) school life($X^2$ =50.87, p<.001), and delinquent friends($X^2$ =85.28, p<.001). 4. There was a significant relationship between the 7 different kinds of drug abuse and type of school ($X^2$=14.65, p<.01), grades($X^2$=12.89, p<.01), their respect for teachers ($X^2$=8.46, p<.05), and delinquent friends($X^2$=22.42, p<.001). 5. There was a significant relationship between a parent's habitual drug abuse and the 7 different kinds of drug abuse($X^2$=7.78, p<.01), as well as a parent's attitude toward drugs and the 7 different kinds of drug abuse($X^2$=6.33, p<.05). 6. There was a significant difference between drinking(t=-12.53, p<.001), smoking(t=-15.98, p<.001), the 7 different kinds of drug abuse(t=-5.77, p<.001), and the respondant's delinquent experience. 7. There was a correlation between drinking and smoking(r=.4166, p<.001), drinking and the 7 different kinds of drug abuse(r=.2200, p<.001), smoking and the 7 different kinds of drug abuse(r=.1428, p<.05). There was a correlation between drinking and smoking(r=.5977, p<.001), drinking and the 7 different kinds of drug abuse(r=.2849, p<. 001), smoking and the 7 different kinds of drug abuse(r=.1711, p<.05) among male students. There was a correlation between drinking and smoking(r=.4219, p<.001), drinking and the 7 different kinds of drug abuse(r=.2611, p<.001), smoking and the 7 different kinds of drug abuse(r=.1764, p<.001) among female students. 8. There was a correlation between drinking and family stability(r=.0709, p<.05) drinkry and parent -child relationships (r=.1321, p<.01), drinking and mother's rearing attitude(r=.0704, P<.05), smoking and parent -child relationships(r=.0813, P<.05). There was a correlation between drinking and family stability(r=.14S7, p<.01), drinkng and parent-child relationships(r=.2147, p<.001), smoking and family stability(r=.1544, p<.01), smoking and parent. -child relationships (r=. 2018, P<.01) among male students. There was a correlation between drinking and family stability(r=.1l21, p<.05), drinking and mother's rearing attitude (r=.0988, P<.05), smoking and parent -child relationships (r=. 0940, P<.05) among female students. 9. There was a significant difference between the 7 different kinds of drug abuse and family stability (t=2.23, p<.05), parent-child relationships (t=4. 34, p<.001), satisfaction with family (t=4.02, p<.001), father's rearing attitude(t=3.04, p<.01), mother's rearing attitude(t=2.87, p<.01). The distribution channel of drugs including alcohol beverages and cigarettes should be evaluated and restructured to discourage student's temptation and to limit accessibility. The step by step preventive teaching on alcohol drinking and cigarette smoking is needed from middle school to help prevent further drug abuse.