• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.223-238
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• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• Journal of the Korean Chemical Society
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• v.30 no.1
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• pp.9-18
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• 1986

MNDO and STO-3G calculations were performed to determine relative stabilities of rotamers for ${\alpha}$-substituted acetones, $CH_2XCOCH_3$, X = F, Cl, OH, SH, and $NH_2$. It was found that rotamers corresponding to gauche forms are preferred for all the ${\alpha}$-substituents except for X = F and NH$_2$, for which the cis forms were the preferred ones. The stability of gauche form was dictated by the stabilizing two-orbital-two-electron interaction ${\sigma}_{cx}$-${\pi}_{co}^*$, operating uniquely in the gauche form due to the substantial vicinal overlap and energy gap narrowing between ${\sigma}_{cx}$ and ${\pi}_{co}^*$ orbitals. The energy gap narrowing was caused by the lowering of ${\pi}_{co}^*$ level due to the hyperconjugative ${\sigma}_{cx}^*$-${\pi}_{co}^*$ interactions; the red shift in the n-${\pi}^*$ transition was another effect of the relatively large ${\sigma}_{cx}^*$-${\pi}_{co}^*$ splitting. Various ${\sigma}-{\pi}$ interactions in the gauche form were found to be stronger in the third-row hetero atom system, X = Cl and SH. Interactions between nonbonding orbital on N, $n_N$ and vicinal C-C ${\sigma}$ bond were shown to be stronger in the trans than in the cis orientation.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.441-452
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• 2006

We introduce the counting function ${\pi}^*_{2.8}(x)$ of the primes with difference 8 between consecutive primes ($p_n,\;p_{n+l}=p_n+8$) can be approximated by logarithm integral $Li^*_{2.8}$. We calculate the values of ${\pi}^*_{2.8}(x)$ and the sum $C_{2,8}(x)$ of reciprocals of primes with difference 8 between consecutive primes $p_n,\;p_{n+l}=p_n+8$ where x is counted up to $7{\times}10^{10}$. From the results of these calculations. we obtain ${\pi}^*_{2.8}(7{\times}10^{10}$)= 133295081 and $C_{2.8}(7{\times}10^{10}) = 0.3374{\pm}2.6{\times}10^{-4}$.

• Asian-Australasian Journal of Animal Sciences
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• v.25 no.4
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• pp.552-558
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• 2012

A $2{\times}2$ factorial experiment was conducted to study the effect of dietary calcium and non-phytate phosphorus (nPP) imbalance on calbindin and NaPi-IIb mRNA levels in the small intestine and tibia parameters of broiler chicks. One hundred and forty four 1-d-old Arbor Acres male broiler chicks were divided into four treatments consisted of six replicates with six chicks each. The two dietary calcium levels were 1.10% and 0.60%, and two dietary nPP levels were 0.50% and 0.27%. Results showed that a high Ca/nPP ratio diet (4.07:1) significantly depressed feed intake and weight gain of broilers (p<0.05), but a lower Ca:nPP ratio (1.2:1) had no influence (p>0.05). Low-Ca with low-P diet resulted in low tibia minerals and tibia breaking strength of broilers, and all the tibia parameters were further decreased when the dietary ratio of Ca to P was relative higher. Low dietary Ca or P up-regulated the calbindin and NaPi-IIb mRNA expression levels. Low Ca with normal P diet up-regulated duodenal calbindin mRNA expression level to the greatest extent. Low P with a normal Ca diet significantly enhanced NaPi-IIb mRNA expression level to the highest extent. These results suggest that the calbindin and NaPi-IIb mRNA expression were enhanced by the imbalance between dietary Ca and nPP, and their expression were not only influenced by Ca or nPP level, but also the ratio of Ca:nPP.

• Analytical Science and Technology
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• v.6 no.1
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• pp.39-45
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• 1993

We have examined Raman spectra of cis-peptide model complex, diketopiperazine in water and $D_2O$ with 320 nm through 218 nm excitation. Our study examines assignment of the resonance enhanced amide vibrations and characterizes their enhancement mechanism. Three resonance enhaned cis-peptide marker bands were observed in aqueous solution at 1676, 1533 and $806cm^{-1}$, which were assigned to the cis-amide I, II and S band, respectively. The $1533cm^{-1}$ amide II band, which is almost pure C-N stretching, was most dominant in water and shifted to $1520cm^{-1}$ upon N-deuteration. This band will be probably a potential probe band for cis-peptide moieties in proteins. The excitation profile data and an Albrecht A-term fit indicated that the cis-peptide vibrations derive their intensities from the 188 nm cis-peptide ${\pi}-{\pi}^*$ electronic transition. We Propose that the geometry of cis-peptide ${\pi}^*$ excited state is C-N bond displacement relative to that of electronic ground state.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2007.06a
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• pp.50-50
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• 2007

We report the effect of the film thickness on electrical properties of Ti(N) film resistors. The applications of titanium nitride thin film resistor in $\Pi$-type attenuators are also characterized. As film thickness decreases from 100 to 30 nm, temperature coefficient of resistance significantly decreases from -60 to -148 ppm/K, while sheet resistance increases from 37 to $270\;{\Omega}/{\square}$. The characterizations of 20dB-attenuators using thin film resistors are improved in comparison with those using thick film resistors. The $\Pi$-type attenuators using Ti(N) thin film resistors exhibit a attenuation of -19.94 dB and voltage standing wave ratio of 1.16 at a frequency of 2.7 GHz.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.475-490
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• 2006

We give a way to obtain formulas for ${\pi}*{\psi}^{\kappa}_{n+1}$ in terms ${\psi}$ and ${\lambda}-classes$ where ${\pi}=\bar M_{g,n+1}{\rightarrow}\bar M_{g,n}(g=0,\;1,\;2)$ by the localization theorem. By using the formulas, we obtain Kontsevich-Manin type reconstruction theorems for $\bar M_{0,\;n}(\mathbb{R^m}),\;\bar M_{1,\;n},\;and\;\bar M_{2,\;n}$. We also (re)produce a lot of well-known relations in tautological rings, such as WDVV equation, the Mumford relations, the string and dilaton equations (g = 0, 1, 2) etc. and new formulas for ${\pi}*({\lambda}_g{\psi}^{\kappa}_{n+1}+...+{\psi}^{g+{\kappa}_{n+1}$.

• Bulletin of the Korean Chemical Society
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• v.23 no.9
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• pp.1321-1324
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• 2002

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1077-1085
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• 1996

This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.527-534
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• 2007

This paper deals with the BK-AK property of the integrated rate space ${\int}{\ell}_{\pi}$. Importance of ${\delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${\int}{\ell}_{\pi}$. The set of all infinite matrices transforming ${\int}{\ell}_{\pi}$, into BK-AK space Y is denoted $({\int}{\ell}_{\pi}:\;Y)$. We characterize the classes $({\int}{\ell}_{\pi}:\;Y)$. When $Y={\ell}_{\infty},\;c_0,\;c,\;{\ell}^p,\;bv,\;bv_0,\;bs,\;cs,\;{\ell}_p,\;{\ell}_{\pi}$. In summary we have the following table: