• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.361-372
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• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.107-120
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• 2016

Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2-absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly 2-absorbing) primary ideal if whenever $a,b,c{\in}R$ such that $abc{\in}I$ (resp., $0{\neq}abc{\in}I$), then either $ab{\in}I$ or $bc{\in}\sqrt{I}$ or $ac{\in}\sqrt{I}$. Moreover, when I is a Q-ideal and P is a k-ideal of R/I with $I{\subseteq}P$, it is shown that if P is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R, then P/I is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R/I and it is also proved that if I and P/I are weakly 2-absorbing primary ideals, then P is a weakly 2-absorbing primary ideal of R.

• YAKHAK HOEJI
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• v.14 no.1_2
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• pp.1-14
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• 1970

Seventeen N,N/sup I/-disubstituted thiourea derivatives were synthesized by the Hugershof reaction and reported. Antitumor activities of the synthesized compounds against ascitic Ehrlich Carcinoma and ascitic sarcoma 180 were reported. It was found that 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis (2-carboxyphenyl)-2,2/sup I/-dithiourea was considerably active against ascitic Ehrlich Carcinoma and Sarcoma 180 respectively. 1-(2-Carboxyphenyl)-3-(p-ethoxyphenyl)-2 thiourea was active against ascitic Sarcoma 180. 1-Salicyloyl-3-(p-ethoxyphenyl)-2-thiourea and 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis(2-hydroxyethyl)-2,2/sup I/-dithiourea were active against ascitic Ehrlich Carcinoma. Antitubercular activities of the synthesized compounds against Mycobacterium tuberculosis H/sub 37/ R/sub v/ were also reported. It was found that 1-Isonicotinyl-4-cyclohexyl-3-thiosemicarbazide was considerably active at 100 .mu.g/ml. 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis(2-hydroxyethyl)-2,2/sup I/-dithiourea and 1-Salicyloyl-3-(p-ethoxyphenyl)-2-thiourea were active at 1000 .mu.g/ml respectively. Antibacterial activities of nine compounds of the synthesized compounds against S. aureus and E. Coli were reported. It was found that 1,1-(p-Phenylene)-4,4/sup I/-bis(isonicotinyl)-2,2/sup I/-dithiosemicarbazide and 1-Isonicotinyl-4-cyclohexyl-3-thiosemicarbazide were considerably active against S. aureus and E. Coli respectively. 1-(6-Methyl-2-benzothiazolyl)-3-(1-naphthyl)-2-thiourea was active against S. aureus. 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis (2-hydroxyethyl)-2,2/sup I/-dithiourea was active against E. Coli.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.549-560
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• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.457-469
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• 2008

In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary value problem with p-Laplacian: $\{{{{(\phi_p(u'))'\;+\;f(t,u(t))=0, \;0<t<1,} \atop u'(0)={\sum}{^{m-2}_{i=1}}\;a_iu'(\xi_i),} \atop u(1)={\sum}{^k_{i=1}}\;b_iu(\xi_i)\;-\;{\sum}{^s_{i=k+1}}\;b_iu(\xi_i)\;-\;{\sum}{^{m-2}_{i=s+1}}\;b_iu'(xi_i),}$ where ${\phi}_p(s)$ is p-Laplacian operator, i.e., ${\phi}_p(s)=\mid s\mid^{p-2}s$, p>1, ${\phi}_q\;=\;({\phi}_p)^{-1}$, $\frac{1}{p}+\frac{1}{q}=1$, $1\;{\leq}\;k\;{\leq}\;s\;{\leq}m\;-\;2$, $b_i\;{\in}\;(0,+{\infty})$ with $0\;<\;{\sum}{^k_{k=1}}\;b_i\;-\;{\sum}{^s_{i=k+1}}\;b_i\;<\;1$, $0\;<\;{\sum}{^{m-2}_{i=1}}\la_i\;<\;1$, $0\;<\;{\xi}_1\;<\;{\xi}_2\;<\;{\cdots}\;<\;{\xi}_{m-2}\;<\;1$, $f\;{\in}\;C([0,\;1]\;{\times}\;[0,\;+{\infty}),\;[0,\;+{\infty}))$. We show that there exists one or two positive solutions by using fixed-point theorem for operator on a cone. The conclusions in this paper essentially extend and improve the known results.

• Environmental Mutagens and Carcinogens
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• v.16 no.2
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• pp.97-102
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• 1996

In this study, we have quantified genotype frequency of the cytochrome P450 (P450) 2E1 which codes for the P450 enzyme primarily responsible for the metabolic activation of carcinogenic nitrosamines and low molecular organic solvents, in Korean population by using PCR and RFLP at two sites previously associated with some cancers; a PstI and RsaI RFLP in the transcriptional regulatory region of the human P450 2E1 gene. The genotype frequencies of homozygous wild type (PstI site-absent) and heterozygous mutant type (PstI site-present) in PstI RFLP were 0.70 and 030, respectively. The homozygous mutant type in Pstl RFLP was not observed in Korean population. The genotype frequencies of homozygous wild type (RsaI site-present), heterozygous mutant type (RsaI site-absent), and homozygous mutant type in RsaI RFLP were 0.71, 0.26, and 0.03, respectively.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.573-580
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• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.